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9772:{\displaystyle {\begin{aligned}r(Y,{\hat {Y}})&={\frac {\sum _{i}(Y_{i}-{\bar {Y}})({\hat {Y}}_{i}-{\bar {Y}})}{\sqrt {\sum _{i}(Y_{i}-{\bar {Y}})^{2}\cdot \sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}}}\\&={\frac {\sum _{i}(Y_{i}-{\hat {Y}}_{i}+{\hat {Y}}_{i}-{\bar {Y}})({\hat {Y}}_{i}-{\bar {Y}})}{\sqrt {\sum _{i}(Y_{i}-{\bar {Y}})^{2}\cdot \sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}}}\\&={\frac {\sum _{i}}{\sqrt {\sum _{i}(Y_{i}-{\bar {Y}})^{2}\cdot \sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}}}\\&={\frac {\sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}{\sqrt {\sum _{i}(Y_{i}-{\bar {Y}})^{2}\cdot \sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}}}\\&={\sqrt {\frac {\sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}{\sum _{i}(Y_{i}-{\bar {Y}})^{2}}}}.\end{aligned}}}
939:
1614:{\displaystyle {\begin{aligned}\mu _{X}={}&\operatorname {\mathbb {E} } \\\mu _{Y}={}&\operatorname {\mathbb {E} } \\\sigma _{X}^{2}={}&\operatorname {\mathbb {E} } \left\right)^{2}\,\right]=\operatorname {\mathbb {E} } \left-\left(\operatorname {\mathbb {E} } \right)^{2}\\\sigma _{Y}^{2}={}&\operatorname {\mathbb {E} } \left\right)^{2}\,\right]=\operatorname {\mathbb {E} } \left-\left(\,\operatorname {\mathbb {E} } \right)^{2}\\&\operatorname {\mathbb {E} } =\operatorname {\mathbb {E} } \right)\left(Y-\operatorname {\mathbb {E} } \right)\,]=\operatorname {\mathbb {E} } -\operatorname {\mathbb {E} } \operatorname {\mathbb {E} } \,,\end{aligned}}}
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41:
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6218:{\displaystyle f(r)={\frac {(n-2)\,\mathrm {\Gamma } (n-1)\left(1-\rho ^{2}\right)^{\frac {n-1}{2}}\left(1-r^{2}\right)^{\frac {n-4}{2}}}{{\sqrt {2\pi }}\,\operatorname {\Gamma } {\mathord {\left(n-{\tfrac {1}{2}}\right)}}(1-\rho r)^{n-{\frac {3}{2}}}}}{}_{2}\mathrm {F} _{1}{\mathord {\left({\tfrac {1}{2}},{\tfrac {1}{2}};{\tfrac {1}{2}}(2n-1);{\tfrac {1}{2}}(\rho r+1)\right)}}}
6908:{\displaystyle \pi (\rho \mid r)={\frac {\nu (\nu -1)\Gamma (\nu -1)}{{\sqrt {2\pi }}\Gamma \left(\nu +{\frac {1}{2}}\right)}}\left(1-r^{2}\right)^{\frac {\nu -1}{2}}\cdot \left(1-\rho ^{2}\right)^{\frac {\nu -2}{2}}\cdot \left(1-r\rho \right)^{\frac {1-2\nu }{2}}\operatorname {F} \left({\tfrac {3}{2}},-{\tfrac {1}{2}};\nu +{\tfrac {1}{2}};{\tfrac {1+r\rho }{2}}\right)}
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1911:{\displaystyle \rho _{X,Y}={\frac {\operatorname {\mathbb {E} } -\operatorname {\mathbb {E} } \operatorname {\mathbb {E} } }{{\sqrt {\operatorname {\mathbb {E} } \left-\left(\operatorname {\mathbb {E} } \right)^{2}}}~{\sqrt {\operatorname {\mathbb {E} } \left-\left(\operatorname {\mathbb {E} } \right)^{2}}}}}.}
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Several authors have offered guidelines for the interpretation of a correlation coefficient. However, all such criteria are in some ways arbitrary. The interpretation of a correlation coefficient depends on the context and purposes. A correlation of 0.8 may be very low if one is verifying a physical
4765:
Both the uncentered (non-Pearson-compliant) and centered correlation coefficients can be determined for a dataset. As an example, suppose five countries are found to have gross national products of 1, 2, 3, 5, and 8 billion dollars, respectively. Suppose these same five countries (in the same order)
60:
for each set. The correlation reflects the strength and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom). N.B.: the figure in the center has a slope of 0 but in that case the correlation coefficient is
13226:
The
Pearson "distance" defined this way assigns distance greater than 1 to negative correlations. In reality, both strong positive correlation and negative correlations are meaningful, so care must be taken when Pearson "distance" is used for nearest neighbor algorithm as such algorithm will only
12034:
14342:
It is always possible to remove the correlations between all pairs of an arbitrary number of random variables by using a data transformation, even if the relationship between the variables is nonlinear. A presentation of this result for population distributions is given by Cox & Hinkley.
101:
of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of children from a primary school to have a
Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an
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The values of both the sample and population
Pearson correlation coefficients are on or between −1 and 1. Correlations equal to +1 or −1 correspond to data points lying exactly on a line (in the case of the sample correlation), or to a bivariate distribution entirely
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values generated in step (2) that are larger than the
Pearson correlation coefficient that was calculated from the original data. Here "larger" can mean either that the value is larger in magnitude, or larger in signed value, depending on whether a
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13132:, the range of values is reduced and the correlations on long time scale are filtered out, only the correlations on short time scales being revealed. Thus, the contributions of slow components are removed and those of fast components are retained.
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will typically reveal a situation where lack of robustness might be an issue, and in such cases it may be advisable to use a robust measure of association. Note however that while most robust estimators of association measure
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For centered data (i.e., data which have been shifted by the sample means of their respective variables so as to have an average of zero for each variable), the correlation coefficient can also be viewed as the
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coefficient measures the strength of dependence between a pair of variables that is not accounted for by the way in which they both change in response to variations in a selected subset of the other variables.
13632:{\displaystyle r_{\text{circular}}={\frac {\sum _{i=1}^{n}\sin(x_{i}-{\bar {x}})\sin(y_{i}-{\bar {y}})}{{\sqrt {\sum _{i=1}^{n}\sin(x_{i}-{\bar {x}})^{2}}}{\sqrt {\sum _{i=1}^{n}\sin(y_{i}-{\bar {y}})^{2}}}}}}
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10635:, this is an important consideration. However, the existence of the correlation coefficient is usually not a concern; for instance, if the range of the distribution is bounded, ρ is always defined.
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4395:, without changing the correlation coefficient. (This holds for both the population and sample Pearson correlation coefficients.) More general linear transformations do change the correlation: see
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is zero. Thus, the sample correlation coefficient between the observed and fitted response values in the regression can be written (calculation is under expectation, assumes
Gaussian statistics)
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Scaled correlation is a variant of
Pearson's correlation in which the range of the data is restricted intentionally and in a controlled manner to reveal correlations between fast components in
97:; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear
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5732:-distribution in the null case (zero correlation). This holds approximately in case of non-normal observed values if sample sizes are large enough. For determining the critical values for
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provide a direct approach to performing hypothesis tests and constructing confidence intervals. A permutation test for
Pearson's correlation coefficient involves the following two steps:
5092:{\displaystyle \cos \theta ={\frac {\mathbf {x} \cdot \mathbf {y} }{\left\|\mathbf {x} \right\|\left\|\mathbf {y} \right\|}}={\frac {0.308}{{\sqrt {30.8}}{\sqrt {0.00308}}}}=1=\rho _{xy},}
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will be the identity matrix. This has to be further divided by the standard deviation to get unit variance. The transformed variables will be uncorrelated, even though they may not be
4907:{\displaystyle \cos \theta ={\frac {\mathbf {x} \cdot \mathbf {y} }{\left\|\mathbf {x} \right\|\left\|\mathbf {y} \right\|}}={\frac {2.93}{{\sqrt {103}}{\sqrt {0.0983}}}}=0.920814711.}
462:
13295:, can be applied, which will take both positive and negative correlations into consideration. The information on positive and negative association can be extracted separately, later.
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10535:
13293:
5167:
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8574:{\displaystyle 1={\frac {\sum _{i}(Y_{i}-{\hat {Y}}_{i})^{2}}{\sum _{i}(Y_{i}-{\bar {Y}})^{2}}}+{\frac {\sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}{\sum _{i}(Y_{i}-{\bar {Y}})^{2}}}.}
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3145:{\displaystyle r_{xy}={\frac {n\sum x_{i}y_{i}-\sum x_{i}\sum y_{i}}{{\sqrt {n\sum x_{i}^{2}-\left(\sum x_{i}\right)^{2}}}~{\sqrt {n\sum y_{i}^{2}-\left(\sum y_{i}\right)^{2}}}}},}
2386:{\displaystyle r_{xy}={\frac {\sum _{i=1}^{n}(x_{i}-{\bar {x}})(y_{i}-{\bar {y}})}{{\sqrt {\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}}{\sqrt {\sum _{i=1}^{n}(y_{i}-{\bar {y}})^{2}}}}}}
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A stratified analysis is one way to either accommodate a lack of bivariate normality, or to isolate the correlation resulting from one factor while controlling for another. If
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607:
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10780:, then calculate a correlation coefficient within each stratum. The stratum-level estimates can then be combined to estimate the overall correlation while controlling for
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15157:"The British Association: Section II, Anthropology: Opening address by Francis Galton, F.R.S., etc., President of the Anthropological Institute, President of the Section"
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12505:{\displaystyle \operatorname {corr} _{r}(X,Y)=\operatorname {corr} _{r}(Y,X)=\operatorname {corr} _{r}(X,bY)\neq \operatorname {corr} _{r}(X,a+bY),\quad a\neq 0,b>0.}
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The reflective correlation is a variant of
Pearson's correlation in which the data are not centered around their mean values. The population reflective correlation is
862:
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2812:{\displaystyle r_{xy}={\frac {\sum _{i}x_{i}y_{i}-n{\bar {x}}{\bar {y}}}{{\sqrt {\sum _{i}x_{i}^{2}-n{\bar {x}}^{2}}}~{\sqrt {\sum _{i}y_{i}^{2}-n{\bar {y}}^{2}}}}},}
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1995:
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4263:{\displaystyle \Sigma ={\begin{bmatrix}\sigma _{X}^{2}&\rho _{X,Y}\sigma _{X}\sigma _{Y}\\\rho _{X,Y}\sigma _{X}\sigma _{Y}&\sigma _{Y}^{2}\\\end{bmatrix}}}
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approaches may give more meaningful results in some situations where bivariate normality does not hold. However the standard versions of these approaches rely on
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law using high-quality instruments, but may be regarded as very high in the social sciences, where there may be a greater contribution from complicating factors.
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Lai, Chun Sing; Tao, Yingshan; Xu, Fangyuan; Ng, Wing W.Y.; Jia, Youwei; Yuan, Haoliang; Huang, Chao; Lai, Loi Lei; Xu, Zhao; Locatelli, Giorgio (January 2019).
12324:{\displaystyle \operatorname {corr} _{r}(X,Y)={\frac {\operatorname {\mathbb {E} } }{\sqrt {\operatorname {\mathbb {E} } \cdot \operatorname {\mathbb {E} } }}}.}
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16490:– A free web interface and R package for the statistical comparison of two dependent or independent correlations with overlapping or non-overlapping variables.
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If the sample size is large and the population is not normal, then the sample correlation coefficient remains approximately unbiased, but may not be efficient.
6500:{\displaystyle f(r)={\frac {\left(1-r^{2}\right)^{\frac {n-4}{2}}}{\operatorname {\mathrm {B} } {\mathord {\left({\tfrac {1}{2}},{\tfrac {n-2}{2}}\right)}}}},}
138:
of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first
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3204:
This formula suggests a convenient single-pass algorithm for calculating sample correlations, though depending on the numbers involved, it can sometimes be
10793:
12029:{\displaystyle \operatorname {cov} (x,y;w)={\frac {\sum _{i}w_{i}\cdot (x_{i}-\operatorname {m} (x;w))(y_{i}-\operatorname {m} (y;w))}{\sum _{i}w_{i}}}.}
16540:– A game where players guess how correlated two variables in a scatter plot are, in order to gain a better understanding of the concept of correlation.
10765:
of the data, meaning that there is no ordering or grouping of the data pairs being analyzed that might affect the behavior of the correlation estimate.
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3911:
15767:
Davey, Catherine E.; Grayden, David B.; Egan, Gary F.; Johnston, Leigh A. (January 2013). "Filtering induces correlation in fMRI resting state data".
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15736:"On the distribution of the correlation coefficient in small samples. Appendix II to the papers of "Student" and R.A. Fisher. A co-operative study"
12170:{\displaystyle \operatorname {corr} (x,y;w)={\frac {\operatorname {cov} (x,y;w)}{\sqrt {\operatorname {cov} (x,x;w)\operatorname {cov} (y,y;w)}}}.}
10745:
Statistical inference for
Pearson's correlation coefficient is sensitive to the data distribution. Exact tests, and asymptotic tests based on the
10023:
4409:
The correlation coefficient ranges from −1 to 1. An absolute value of exactly 1 implies that a linear equation describes the relationship between
3411:{\displaystyle r_{xy}={\frac {1}{n-1}}\sum _{i=1}^{n}\left({\frac {x_{i}-{\bar {x}}}{s_{x}}}\right)\left({\frac {y_{i}-{\bar {y}}}{s_{y}}}\right)}
15413:
Garren, Steven T. (15 June 1998). "Maximum likelihood estimation of the correlation coefficient in a bivariate normal model, with missing data".
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This figure gives a sense of how the usefulness of a
Pearson correlation for predicting values varies with its magnitude. Given jointly normal
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of the population correlation coefficient as long as the sample means, variances, and covariance are consistent (which is guaranteed when the
10427:
5809:
In the case where the underlying variables are not normal, the sampling distribution of Pearson's correlation coefficient follows a Student's
5410:
is calculated based on the resampled data. This process is repeated a large number of times, and the empirical distribution of the resampled
478:
18455:
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Schmid, John Jr. (December 1947). "The relationship between the coefficient of correlation and the angle included between regression lines".
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7157:
19020:
13219:
Considering that the Pearson correlation coefficient falls between , the Pearson distance lies in . The Pearson distance has been used in
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18605:
13227:
include neighbors with positive correlation and exclude neighbors with negative correlation. Alternatively, an absolute valued distance,
2000:
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Moriya, N. (2008). "Noise-related multivariate optimal joint-analysis in longitudinal stochastic processes". In Yang, Fengshan (ed.).
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tend to be simultaneously greater than, or simultaneously less than, their respective means. The correlation coefficient is negative (
13918:{\displaystyle \mathbb {Cor} (X,Y)={\frac {\mathbb {E} -\mathbb {E} \cdot \mathbb {E} }{\sqrt {\mathbb {V} \cdot \mathbb {V} }}}\,,}
11351:{\displaystyle r=\operatorname {\mathbb {E} } \approx r_{\text{adj}}-{\frac {r_{\text{adj}}\left(1-r_{\text{adj}}^{2}\right)}{2n}}.}
18927:
18003:
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Critical values of Pearson's correlation coefficient that must be exceeded to be considered significantly nonzero at the 0.05 level
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14856:
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are random variables, with a simple linear relationship between them with an additive normal noise (i.e., y= a + bx + e), then a
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reports degraded correlation values due to the heavy noise contributions. A generalization of the approach is given elsewhere.
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can be applied if the data are approximately normally distributed, but may be misleading otherwise. In some situations, the
8279:{\displaystyle \sum _{i}(Y_{i}-{\bar {Y}})^{2}=\sum _{i}(Y_{i}-{\hat {Y}}_{i})^{2}+\sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2},}
7218:
16865:
16565:
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16221:
11097:{\displaystyle r_{\text{adj}}=r\,\mathbf {_{2}F_{1}} \left({\frac {1}{2}},{\frac {1}{2}};{\frac {n-1}{2}};1-r^{2}\right),}
10663:, which roughly means that it is impossible to construct a more accurate estimate than the sample correlation coefficient.
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can be used to construct confidence intervals for Pearson's correlation coefficient. In the "non-parametric" bootstrap,
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9945:{\displaystyle r(Y,{\hat {Y}})^{2}={\frac {\sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}{\sum _{i}(Y_{i}-{\bar {Y}})^{2}}}}
5742:
1997:
by substituting estimates of the covariances and variances based on a sample into the formula above. Given paired data
15871:
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Suppose observations to be correlated have differing degrees of importance that can be expressed with a weight vector
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tend to lie on opposite sides of their respective means. Moreover, the stronger either tendency is, the larger is the
19025:
18252:
18144:
16461:
16278:
16099:
15998:; Gnanadesikan, R.; Kettenring J.R. (1975). "Robust estimation and outlier detection with correlation coefficients".
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is the data transformed so all variables have zero mean and zero correlation with all other variables – the sample
13353:, it is possible to define a circular analog of Pearson's coefficient. This is done by transforming data points in
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11154:
10922:{\displaystyle \operatorname {\mathbb {E} } \left=\rho -{\frac {\rho \left(1-\rho ^{2}\right)}{2n}}+\cdots ,\quad }
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Statistical inference based on Pearson's correlation coefficient often focuses on one of the following two aims:
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follows such a distribution. In some practical applications, such as those involving data suspected to follow a
19286:
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17558:
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17405:
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429:
17479:
10688:. The adjusted correlation coefficient must be used instead: see elsewhere in this article for the definition.
10544:
10511:
5641: − 2. Specifically, if the underlying variables have a bivariate normal distribution, the variable
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on a line (in the case of the population correlation). The Pearson correlation coefficient is symmetric: corr(
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18782:
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16644:
15385:
14806:
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12793:{\displaystyle rr_{xy,w}={\frac {\sum w_{i}x_{i}y_{i}}{\sqrt {(\sum w_{i}x_{i}^{2})(\sum w_{i}y_{i}^{2})}}}.}
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Variations of the correlation coefficient can be calculated for different purposes. Here are some examples.
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in some way, they are generally not interpretable on the same scale as the Pearson correlation coefficient.
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Python library implements Pearson correlation coefficient calculation as the default option for the method
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20:
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13712:. This measure can be useful in fields like meteorology where the angular direction of data is important.
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7130:{\displaystyle F(r)\equiv {\tfrac {1}{2}}\,\ln \left({\frac {1+r}{1-r}}\right)=\operatorname {artanh} (r)}
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If the sample size is moderate or large and the population is normal, then, in the case of the bivariate
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is measured counterclockwise within the first quadrant formed around the lines' intersection point if
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Rodgers and Nicewander cataloged thirteen ways of interpreting correlation or simple functions of it:
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16382:"Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification"
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are present. Specifically, the PMCC is neither distributionally robust, nor outlier resistant (see
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7943:, or (0.5814, 1.1532). Converting back to the correlation scale yields (0.5237, 0.8188).
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4931:. The Pearson correlation coefficient must therefore be exactly one. Centering the data (shifting
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A corresponding result exists for reducing the sample correlations to zero. Suppose a vector of
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10321:{\displaystyle r(Y,{\hat {Y}})^{2}={\frac {{\text{SS}}_{\text{reg}}}{{\text{SS}}_{\text{tot}}}}}
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lie on the same side of their respective means. Thus the correlation coefficient is positive if
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16292:"Minimum Pearson distance detection for multilevel channels with gain and / or offset mismatch"
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15937:"A robust correlation analysis framework for imbalanced and dichotomous data with uncertainty"
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To perform the permutation test, repeat steps (1) and (2) a large number of times. The
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under separate changes in location and scale in the two variables. That is, we may transform
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12633:{\displaystyle rr_{xy}={\frac {\sum x_{i}y_{i}}{\sqrt {(\sum x_{i}^{2})(\sum y_{i}^{2})}}}.}
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17393:
17349:
17111:
16887:
16767:
16503:– an interactive Flash simulation on the correlation of two normally distributed variables.
15230:
15114:
14986:
14961:
14951:
13065:
10692:
10674:
10670:
10656:
10598:
10571:
7548:
6990:
4639:
For uncentered data, there is a relation between the correlation coefficient and the angle
4062:
4026:
1627:
916:
721:{\displaystyle \rho _{X,Y}={\frac {\operatorname {\mathbb {E} } }{\sigma _{X}\sigma _{Y}}}}
585:
173:
142:
about the origin) of the product of the mean-adjusted random variables; hence the modifier
139:
16507:
4441:
decreases. A value of 0 implies that there is no linear dependency between the variables.
8:
18922:
18909:
18819:
18744:
18667:
18348:
18112:
18105:
18067:
17975:
17955:
17927:
17660:
17526:
17521:
17511:
17503:
17321:
17282:
17172:
17162:
17071:
16850:
16806:
16724:
16649:
16551:
15820:
Hotelling, Harold (1953). "New Light on the Correlation Coefficient and its Transforms".
14976:
14830:
13727:
13721:
13304:
11495:
11126:
10773:
10645:
10620:
10616:
7148:
5419:
5234:
5174:
4337:
4301:
4297:
4278:
Under heavy noise conditions, extracting the correlation coefficient between two sets of
3205:
1926:
15491:
15234:
15118:
10772:
represents cluster membership or another factor that it is desirable to control, we can
19242:
19208:
19088:
18917:
18833:
18644:
18498:
18394:
18343:
18219:
18116:
18100:
18077:
17854:
17588:
17571:
17531:
17442:
17337:
17299:
17270:
17230:
17190:
17136:
17053:
16739:
16734:
16424:
16321:
16252:
16169:
16128:
16124:
16015:
15959:
15936:
15837:
15833:
15802:
15654:
15549:
15514:
15271:
15199:
15132:
14891:
14607:
14449:
14189:
14136:
14018:
13965:
13762:
13742:
13115:
13092:
12864:
12844:
12824:
12809:
7294:
7274:
7012:
5609:
5580:
5560:
5465:
5445:
4418:
4290:
3817:{\displaystyle r_{xy}={\frac {\sum x_{i}y_{i}-n{\bar {x}}{\bar {y}}}{(n-1)s_{x}s_{y}}}}
3611:
2401:
2094:
867:
819:
405:
357:
351:
286:{\displaystyle \rho _{X,Y}={\frac {\operatorname {cov} (X,Y)}{\sigma _{X}\sigma _{Y}}}}
94:
18869:
15426:
12818:. Scaled correlation is defined as average correlation across short segments of data.
11846:{\displaystyle \operatorname {m} (x;w)={\frac {\sum _{i}w_{i}x_{i}}{\sum _{i}w_{i}}}.}
19237:
19126:
19073:
18828:
18739:
18709:
18701:
18521:
18512:
18437:
18368:
18224:
18209:
18184:
18072:
18013:
17879:
17867:
17493:
17410:
17354:
17277:
17121:
17043:
16822:
16696:
16457:
16353:
16291:
16274:
16244:
16240:
16111:
Hotelling, H. (1953). "New Light on the Correlation Coefficient and its Transforms".
16095:
16087:
16063:
15806:
15794:
15780:
15714:
15646:
15587:
15393:
15069:
14941:
14885:
14819:
12516:
10794:
Correlation and dependence § Other measures of dependence among random variables
10712:
7683:
The inverse Fisher transformation brings the interval back to the correlation scale.
4918:
4751:
15963:
12334:
The reflective correlation is symmetric, but it is not invariant under translation:
8325:
are the fitted values from the regression analysis. This can be rearranged to give
19260:
19045:
19010:
18947:
18900:
18764:
18719:
18483:
18470:
18363:
18338:
18272:
18204:
18082:
17690:
17583:
17516:
17429:
17376:
17195:
17066:
16860:
16744:
16659:
16626:
16438:
16434:
16393:
16325:
16313:
16256:
16236:
16159:
16120:
16055:
16007:
15951:
15894:
15829:
15784:
15776:
15749:
15638:
15545:
15541:
15506:
15422:
15261:
15191:
15136:
15122:
13220:
10754:
5253:
4515:
4422:
4279:
123:
7540:
To obtain a confidence interval for ρ, we first compute a confidence interval for
4012:{\textstyle s_{x}={\sqrt {{\frac {1}{n-1}}\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}}}
118:
in the 1880s, and for which the mathematical formula was derived and published by
19193:
19136:
19015:
18681:
18425:
18287:
18214:
17889:
17763:
17736:
17713:
17682:
17309:
17304:
17258:
16988:
16639:
15995:
10416:{\displaystyle {\text{SS}}_{\text{reg}}=\sum _{i}({\hat {Y}}_{i}-{\bar {Y}})^{2}}
7451:
6994:
5361:
5219:
4336:
A key mathematical property of the Pearson correlation coefficient is that it is
119:
18171:
15899:
15890:
13223:
and data detection for communications and storage with unknown gain and offset.
18630:
18625:
17088:
17018:
16664:
15994:
15440:
15290:"Analyse mathematique sur les probabilités des erreurs de situation d'un point"
15141:
In the "Appendix" on page 532, Galton uses the term "reversion" and the symbol
14991:
14946:
14611:
13779:, in a bipartite quantum system Pearson correlation coefficient is defined as
7342:
7213:
6249:
5483:
5365:
4537:
3242:
469:
115:
32:
Examples of scatter diagrams with different values of correlation coefficient (
16164:
16147:
16049:
16011:
15955:
15753:
7673:{\displaystyle 100(1-\alpha )\%{\text{CI}}:\operatorname {artanh} (\rho )\in }
7271:
is the sample size. The approximation error is lowest for a large sample size
6536:, which is one way of writing the density of a Student's t-distribution for a
19275:
19078:
18787:
18754:
18617:
18578:
18389:
18358:
17822:
17776:
17381:
17083:
16910:
16674:
16669:
16317:
16059:
15650:
14337:
8600:
6533:
16397:
15266:
15249:
10124:{\displaystyle \sum _{i}(Y_{i}-{\hat {Y}}_{i})({\hat {Y}}_{i}-{\bar {Y}})=0}
18729:
18662:
18639:
18554:
17884:
17180:
17078:
17013:
16955:
16940:
16877:
16832:
16248:
15798:
15672:
13726:
If a population or data-set is characterized by more than two variables, a
12841:
be the number of segments that can fit into the total length of the signal
11693:{\displaystyle r_{\text{adj}}={\sqrt {1-{\frac {(1-r^{2})(n-1)}{(n-2)}}}}.}
111:
16222:"Scaled correlation analysis: a better way to compute a cross-correlogram"
15568:
13052:{\displaystyle {\bar {r}}_{s}={\frac {1}{K}}\sum \limits _{k=1}^{K}r_{k},}
10669:
If the sample size is large, then the sample correlation coefficient is a
10619:
are defined and are non-zero. Some probability distributions, such as the
5718:{\displaystyle t={\frac {r}{\sigma _{r}}}=r{\sqrt {\frac {n-2}{1-r^{2}}}}}
28:
18772:
18734:
18417:
18318:
18180:
17993:
17960:
17452:
17369:
17364:
17008:
16965:
16945:
16925:
16915:
16684:
15731:
14919:
14914:
12815:
10726:
6537:
5626:
5301:
4796:
98:
15673:"Derivation of the standard error for Pearson's correlation coefficient"
15553:
15045:
As early as 1877, Galton was using the term "reversion" and the symbol "
10497:{\displaystyle {\text{SS}}_{\text{tot}}=\sum _{i}(Y_{i}-{\bar {Y}})^{2}}
5226:
is equal to 0, based on the value of the sample correlation coefficient
572:{\displaystyle \operatorname {cov} (X,Y)=\operatorname {\mathbb {E} } ,}
40:
19172:
19083:
19068:
17618:
17098:
16798:
16729:
16679:
16654:
16574:
16173:
16132:
16019:
15841:
15789:
15740:
15711:
The Advanced Theory of Statistics, Volume 2: Inference and Relationship
15658:
15626:
15518:
15275:
15203:
14971:
14789:'s statistics base-package implements the correlation coefficient with
10609:
5427:
3662:
are also available. For example, one can use the following formula for
319:
135:
90:
70:
10597:
The population Pearson correlation coefficient is defined in terms of
10588:
Correlation and dependence § Sensitivity to the data distribution
7958:
The square of the sample correlation coefficient is typically denoted
4921:. The above data were deliberately chosen to be perfectly correlated:
18990:
17771:
17623:
17243:
17038:
16950:
16935:
16930:
16895:
16410:
15184:
Journal of the Anthropological Institute of Great Britain and Ireland
15127:
13734:
10705:
10680:
If the sample size is small, then the sample correlation coefficient
7202:{\displaystyle {\text{mean}}=F(\rho )=\operatorname {artanh} (\rho )}
5802:
Another early paper provides graphs and tables for general values of
5426:
can be defined as the interval spanning from the 2.5th to the 97.5th
4425:: a value of +1 implies that all data points lie on a line for which
15735:
15642:
15510:
15195:
14444:
is the data transformed so every random variable has zero mean, and
14324:, and its absolute value is invariant under affine transformations.
12927:{\displaystyle K=\operatorname {round} \left({\frac {T}{s}}\right).}
7440:{\displaystyle z={\frac {x-{\text{mean}}}{\text{SE}}}={\sqrt {n-3}}}
5245:
Methods of achieving one or both of these aims are discussed below.
17287:
16905:
16782:
16777:
16772:
16481:
16113:
Journal of the Royal Statistical Society. Series B (Methodological)
10575:
4592:
4099:
16429:
15571:. ch. 5 (as illustrated for a special case in the next paragraph).
7499:
can be obtained from a normal probability table. For example, if
5806:, for small sample sizes, and discusses computational approaches.
5237:
that, on repeated sampling, has a given probability of containing
2084:{\displaystyle \left\{(x_{1},y_{1}),\ldots ,(x_{n},y_{n})\right\}}
89:
correlation between two sets of data. It is the ratio between the
19098:
18985:
18792:
18493:
16535:
15466:"Introductory Business Statistics: The Correlation Coefficient r"
15084:"Correlation Coefficient: Simple Definition, Formula, Easy Steps"
10716:
7496:
5352:
3608:
is the standard score (and analogously for the standard score of
15219:"Notes on regression and inheritance in the case of two parents"
14967:
Normally distributed and uncorrelated does not imply independent
10232:{\displaystyle {\text{RSS}}=\sum _{i}(Y_{i}-{\hat {Y}}_{i})^{2}}
5799:
Alternatively, large sample, asymptotic approaches can be used.
4766:
are found to have 11%, 12%, 13%, 15%, and 18% poverty. Then let
4717:.) One can show that if the standard deviations are equal, then
4710:, or counterclockwise from the fourth to the second quadrant if
18714:
17695:
17669:
17649:
16900:
16691:
16271:
Bioinformatics: Applications in Life and Environmental Sciences
15859:. Vol. Part 2 (2nd ed.). Princeton, NJ: Van Nostrand.
14873:
function for calculating the pearson's correlation coefficient.
4740:
4571:
Rescaled variance of the difference between standardized scores
4565:
Function of the angle between two standardized regression lines
86:
16289:
16207:"Weighted Correlation Matrix – File Exchange – MATLAB Central"
10134:
can be proved by noticing that the partial derivatives of the
7953:
Coefficient of determination § In a multiple linear model
7864:=50, and we wish to obtain a 95% confidence interval for
5197:
will be about 13% smaller than the 95% prediction interval of
5105:
4917:
This uncentered correlation coefficient is identical with the
16543:
14864:
14852:
14803:
12643:
The weighted version of the sample reflective correlation is
7966:. In this case, it estimates the fraction of the variance in
5312:
is selected randomly, with equal probabilities placed on all
4744:
122:
in 1844. The naming of the coefficient is thus an example of
13365:
function such that the correlation coefficient is given as:
5402:) are resampled "with replacement" from the observed set of
5316:! possible permutations. This is equivalent to drawing the
19177:
19149:
19144:
19121:
16634:
13362:
3601:{\textstyle \left({\frac {x_{i}-{\bar {x}}}{s_{x}}}\right)}
465:
16411:
Maccone, L.; Dagmar, B.; Macchiavello, C. (1 April 2015).
15250:"Francis Galton's account of the invention of correlation"
7901:{\textstyle \operatorname {arctanh} \left(r\right)=0.8673}
6543:
6350:(zero population correlation), the exact density function
5547:{\displaystyle \sigma _{r}={\sqrt {\frac {1-r^{2}}{n-2}}}}
2531:{\textstyle {\bar {x}}={\frac {1}{n}}\sum _{i=1}^{n}x_{i}}
16148:"Unbiased Estimation of Certain Correlation Coefficients"
16084:
Multivariable Analysis – A Practical Guide for Clinicians
15854:
10537:
is called the regression sum of squares, also called the
7908:, so the confidence interval on the transformed scale is
5600:
5278:), randomly redefine the pairs to create a new data set (
16219:
15982:
Introduction to robust estimation and hypothesis testing
15766:
15734:; Young, A.W.; Cave, B.M.; Lee, A.; Pearson, K. (1917).
14763:{\displaystyle t=d(D^{\mathsf {T}}D)^{-{\frac {1}{2}}}.}
14618:
will be the identity matrix. If a new data observation
14582:{\displaystyle T=D(D^{\mathsf {T}}D)^{-{\frac {1}{2}}},}
10623:, have undefined variance and hence ρ is not defined if
8097:
around their average value can be decomposed as follows
6548:
Confidence intervals and tests can be calculated from a
4774:
be ordered 5-element vectors containing the above data:
4397:
933:
can be expressed in terms of uncentered moments. Since
18899:
16520:"Critical values for Pearson's correlation coefficient"
15872:"Correlation Coefficient—Bivariate Normal Distribution"
15627:"The Standard Deviation of the Correlation Coefficient"
14317:{\displaystyle \mathbb {Cor} (X,Y)=\mathbb {Cor} (Y,X)}
10581:
8584:
The two summands above are the fraction of variance in
7946:
5813:-distribution, but the degrees of freedom are reduced.
16451:
15612:
Statistical Power Analysis for the Behavioral Sciences
15492:"Thirteen ways to look at the correlation coefficient"
14327:
10753:
can be applied to construct confidence intervals, and
8603:
regression models, that the sample covariance between
7874:
7257:{\displaystyle ={\text{SE}}={\frac {1}{\sqrt {n-3}}},}
7057:
6878:
6863:
6842:
6824:
6465:
6450:
6179:
6146:
6131:
6116:
6028:
4433:
increases, whereas a value of -1 implies a line where
4139:
3914:
3548:
2471:
16345:
15180:"Regression towards mediocrity in hereditary stature"
14709:
14647:
14528:
14469:
14405:
14364:
14258:
14215:
14192:
14161:
14139:
14108:
14080:
14043:
14021:
13990:
13968:
13937:
13788:
13765:
13745:
13677:
13648:
13374:
13233:
13161:
13152:
can be defined from their correlation coefficient as
13118:
13095:
13068:
12982:
12943:
12890:
12867:
12847:
12827:
12652:
12528:
12343:
12194:
12180:
12044:
11861:
11757:
11603:
11594:
Another proposed adjusted correlation coefficient is
11498:
11391:
11248:
11157:
11129:
10979:
10939:
10835:
10757:
can be applied to carry out hypothesis tests. These
10547:
10514:
10430:
10340:
10252:
10165:
10026:
9961:
9791:
8697:
8645:
8609:
8334:
8295:
8106:
8030:
7984:
7914:
7846:{\displaystyle 100(1-\alpha )\%{\text{CI}}:\rho \in }
7692:
7575:
7551:
7509:
7460:
7354:
7317:
7297:
7277:
7221:
7160:
7040:
7015:
6943:
6923:
6564:
6516:
6367:
6330:
6258:
6234:
5846:
5745:
5650:
5583:
5563:
5495:
5468:
5448:
5132:
4978:
4812:
4580:
Function of test statistics from designed experiments
4577:
Related to the bivariate ellipses of isoconcentration
4127:
4107:
4065:
4054:
4029:
3836:
3701:
3668:
3638:
3614:
3506:
3430:
3254:
3217:
3161:
2940:
2907:
2828:
2610:
2577:
2544:
2426:
2404:
2149:
2117:
2097:
2003:
1973:
1935:
1925:
Pearson's correlation coefficient, when applied to a
1650:
1630:
942:
919:
891:
870:
843:
822:
795:
766:
739:
610:
588:
481:
432:
408:
381:
360:
329:
304:
214:
176:
154:
Pearson's correlation coefficient, when applied to a
18456:
Autoregressive conditional heteroskedasticity (ARCH)
16220:
Nikolić, D; Muresan, RC; Feng, W; Singer, W (2012).
15582:
Buda, Andrzej; Jarynowski, Andrzej (December 2010).
14881:
14626:
elements, then the same transform can be applied to
13089:
is Pearson's coefficient of correlation for segment
8088:
then as a starting point the total variation in the
8081:{\displaystyle {\hat {Y}}_{1},\dots ,{\hat {Y}}_{n}}
7936:{\displaystyle 0.8673\pm {\frac {1.96}{\sqrt {47}}}}
16145:
13298:
12515:The sample reflective correlation is equivalent to
11722:
10801:
5336:are equal and drawn with replacement from {1, ...,
5320:randomly without replacement from the set {1, ...,
3899:{\displaystyle n,x_{i},y_{i},{\bar {x}},{\bar {y}}}
3493:{\displaystyle n,x_{i},y_{i},{\bar {x}},{\bar {y}}}
2891:{\displaystyle n,x_{i},y_{i},{\bar {x}},{\bar {y}}}
17918:
14762:
14694:
14581:
14513:
14424:
14383:
14316:
14244:
14198:
14178:
14145:
14125:
14092:
14066:
14027:
14007:
13974:
13954:
13917:
13771:
13751:
13735:Pearson correlation coefficient in quantum systems
13692:
13663:
13631:
13287:
13208:
13124:
13101:
13081:
13051:
12965:
12926:
12873:
12853:
12833:
12792:
12632:
12504:
12323:
12169:
12028:
11845:
11692:
11510:
11459:
11350:
11208:
11141:
11096:
10948:
10921:
10652:of the population correlation coefficient, and is
10562:
10529:
10496:
10415:
10320:
10231:
10123:
9998:
9944:
9771:
8680:
8631:
8573:
8317:
8278:
8080:
8016:
7935:
7900:
7845:
7672:
7557:
7521:
7479:
7439:
7330:
7303:
7283:
7256:
7201:
7129:
7021:
6978:
6967:
6929:
6907:
6524:
6499:
6342:
6309:
6240:
6217:
5788:
5717:
5589:
5569:
5546:
5474:
5454:
5355:for the permutation test is the proportion of the
5161:
5091:
4906:
4568:Function of the angle between two variable vectors
4262:
4113:
4083:
4042:
4011:
3898:
3816:
3684:
3654:
3620:
3600:
3532:
3492:
3410:
3233:
3193:
3144:
2923:
2890:
2811:
2593:
2559:
2530:
2452:
2410:
2385:
2133:
2103:
2083:
1989:
1951:
1910:
1636:
1613:
925:
901:
876:
856:
828:
808:
779:
752:
720:
594:
571:
456:
414:
394:
366:
342:
310:
285:
202:(for example, Height and Weight), the formula for
194:
16290:Immink, K. Schouhamer; Weber, J. (October 2010).
15730:
15489:
12937:The scaled correlation across the entire signals
12803:
10156:are equal to 0 in the least squares model, where
7487:, given the assumption that the sample pairs are
5789:{\displaystyle r={\frac {t}{\sqrt {n-2+t^{2}}}}.}
19273:
15311:Wright, S. (1921). "Correlation and causation".
5181:may be reduced given the corresponding value of
18004:Multivariate adaptive regression splines (MARS)
15631:Journal of the American Statistical Association
15334:
15332:
15330:
15328:
15326:
11731:. To calculate the correlation between vectors
10959:The unique minimum variance unbiased estimator
10704:Like many commonly used statistics, the sample
6310:{\displaystyle {}_{2}\mathrm {F} _{1}(a,b;c;z)}
5816:
3211:An equivalent expression gives the formula for
15584:Life Time of Correlations and its Applications
15581:
15023:Pearson product-moment correlation coefficient
2460:are the individual sample points indexed with
158:, is commonly represented by the Greek letter
52:) points, with the correlation coefficient of
18885:
16559:
16352:. New Jersey: World Scientific. p. 176.
11460:{\displaystyle r_{\text{adj}}\approx r\left,}
11209:{\displaystyle \mathbf {_{2}F_{1}} (a,b;c;z)}
10691:Correlations can be different for imbalanced
7951:For more general, non-linear dependency, see
4791:By the usual procedure for finding the angle
902:{\displaystyle \operatorname {\mathbb {E} } }
16346:Jammalamadaka, S. Rao; SenGupta, A. (2001).
16146:Olkin, Ingram; Pratt, John W. (March 1958).
16086:. 2nd Edition. Cambridge University Press.
15323:
15113:(388, 389, 390): 492–495, 512–514, 532–533.
10695:data when there is variance error in sample.
10648:, the sample correlation coefficient is the
6937:is the Gaussian hypergeometric function and
4562:Mean cross-product of standardized variables
4421:. The correlation sign is determined by the
4289:In case of missing data, Garren derived the
2901:Rearranging again gives us this formula for
16213:
15441:"2.6 - (Pearson) Correlation Coefficient r"
14780:
14695:{\displaystyle d=x-{\frac {1}{m}}Z_{1,m}X,}
14074:is the expectation value of the observable
14015:is the expectation value of the observable
13962:is the expectation value of the observable
10243:In the end, the equation can be written as
5248:
5189:= 0.5, then the 95% prediction interval of
5106:Interpretation of the size of a correlation
4587:
4556:Geometric mean of the two regression slopes
4417:perfectly, with all data points lying on a
18892:
18878:
16604:
16566:
16552:
15934:
15605:
15603:
15223:Proceedings of the Royal Society of London
14514:{\displaystyle D=X-{\frac {1}{m}}Z_{m,m}X}
6540:sample correlation coefficient, as above.
5833:) for the sample correlation coefficient
5629:Pearson's correlation coefficient follows
4398:§ Decorrelation of n random variables
4307:
168:population Pearson correlation coefficient
93:of two variables and the product of their
17217:
16428:
16307:
16163:
16110:
15975:
15973:
15898:
15888:
15819:
15788:
15586:. Wydawnictwo Niezależne. pp. 5–21.
15381:Progress in Applied Mathematical Modeling
15300:: 255–332. 1844 – via Google Books.
15265:
15126:
14440:square matrix with every element 1. Then
14295:
14292:
14289:
14266:
14263:
14260:
14223:
14220:
14217:
14163:
14110:
14045:
13992:
13939:
13911:
13895:
13878:
13862:
13845:
13822:
13796:
13793:
13790:
12311:
12300:
12289:
12280:
12269:
12258:
12250:
12246:
12242:
12231:
11559:has minimum variance for large values of
11257:
10996:
10838:
10601:, and therefore exists for any bivariate
7068:
6005:
5880:
4559:Square root of the ratio of two variances
4553:Standardized slope of the regression line
1885:
1881:
1870:
1853:
1842:
1829:
1805:
1801:
1790:
1773:
1762:
1749:
1739:
1735:
1724:
1718:
1714:
1703:
1694:
1690:
1686:
1675:
1603:
1599:
1595:
1584:
1578:
1574:
1563:
1554:
1550:
1546:
1535:
1526:
1517:
1513:
1502:
1480:
1476:
1465:
1451:
1440:
1431:
1378:
1367:
1345:
1341:
1330:
1327:
1312:
1301:
1288:
1277:
1249:
1234:
1221:
1178:
1174:
1163:
1146:
1135:
1122:
1111:
1083:
1068:
1055:
1023:
1019:
1008:
981:
977:
966:
894:
635:
508:
457:{\displaystyle \operatorname {cov} (X,Y)}
134:Pearson's correlation coefficient is the
16048:Vaart, A. W. van der (13 October 1998).
15822:Journal of the Royal Statistical Society
15433:
14614:of a matrix. The correlation matrix of
10822:for the sample correlation coefficient
10563:{\displaystyle {\text{SS}}_{\text{tot}}}
10530:{\displaystyle {\text{SS}}_{\text{reg}}}
5608:
5109:
4967:= (−0.028, −0.018, −0.008, 0.012, 0.042)
4591:
39:
27:
16296:IEEE Transactions on Information Theory
15600:
15247:
15216:
14997:Spearman's rank correlation coefficient
13288:{\displaystyle d_{X,Y}=1-|\rho _{X,Y}|}
11540:can also be obtained by maximizing log(
10017:In the derivation above, the fact that
7860: = 0.7 with a sample size of
7489:independent and identically distributed
6544:Using the exact confidence distribution
5406:pairs, and the correlation coefficient
5162:{\displaystyle 1-{\sqrt {1-\rho ^{2}}}}
2538:(the sample mean); and analogously for
19274:
18530:Kaplan–Meier estimator (product limit)
15979:
15970:
15624:
15566:
15531:
15412:
15377:
15310:
15177:
15154:
15100:
14728:
14547:
13715:
13349:} that are defined on the unit circle
13209:{\displaystyle d_{X,Y}=1-\rho _{X,Y}.}
5222:that the true correlation coefficient
2571:Rearranging gives us this formula for
1965:sample Pearson correlation coefficient
102:unrealistically perfect correlation).
18873:
18603:
18170:
17917:
17216:
16986:
16603:
16547:
16152:The Annals of Mathematical Statistics
16047:
16032:
15869:
15609:
15351:
15070:"SPSS Tutorials: Pearson Correlation"
15049:" for what would become "regression".
14839:function, or (with the P value) with
13135:
11374:An approximate solution to equation (
11237:and solving this truncated equation:
7978:. So if we have the observed dataset
105:
18840:
18540:Accelerated failure time (AFT) model
16508:"Correlation coefficient calculator"
16379:
16189:"Re: Compute a weighted correlation"
15855:Kenney, J.F.; Keeping, E.S. (1951).
15575:
15415:Statistics & Probability Letters
13140:A distance metric for two variables
11382:
11239:
11224:An approximately unbiased estimator
10970:
10715:, so its value can be misleading if
10582:Sensitivity to the data distribution
8681:{\displaystyle Y_{i}-{\hat {Y}}_{i}}
7947:In least squares regression analysis
5371:
5343:Construct a correlation coefficient
311:{\displaystyle \operatorname {cov} }
162:(rho) and may be referred to as the
18852:
18135:Analysis of variance (ANOVA, anova)
16987:
16339:
15700:, Charles Griffin and Company, 1968
15534:The Journal of Educational Research
15296:. Sci. Math, et Phys. (in French).
14932:Concordance correlation coefficient
14927:Coefficient of multiple correlation
14245:{\displaystyle \mathbb {Cor} (X,Y)}
13016:
10806:The sample correlation coefficient
10722:Robust statistics § Definition
9999:{\displaystyle r(Y,{\hat {Y}})^{2}}
8592:(right) and that is unexplained by
7003:Variance-stabilizing transformation
7001:are usually carried out using the,
5414:values are used to approximate the
4282:is nontrivial, in particular where
4273:
3241:as the mean of the products of the
170:. Given a pair of random variables
149:
13:
18230:Cochran–Mantel–Haenszel statistics
16856:Pearson product-moment correlation
16456:. Chapman & Hall. Appendix 3.
16413:"Complementarity and Correlations"
16125:10.1111/j.2517-6161.1953.tb00135.x
15834:10.1111/j.2517-6161.1953.tb00135.x
15709:Kendall, M. G., Stuart, A. (1973)
15698:A Course in Theoretical Statistics
14793:, or (with the P value also) with
14186:is the variance of the observable
14133:is the variance of the observable
12181:Reflective correlation coefficient
11974:
11934:
11758:
10010:explained by a linear function of
8017:{\displaystyle Y_{1},\dots ,Y_{n}}
7711:
7594:
6930:{\displaystyle \operatorname {F} }
6924:
6812:
6637:
6607:
6552:. An exact confidence density for
6518:
6434:
6270:
6235:
6098:
6007:
5882:
5328:, a closely related approach, the
4643:between the two regression lines,
4304:) do not have a defined variance.
4128:
4108:
4055:For jointly gaussian distributions
164:population correlation coefficient
114:from a related idea introduced by
61:undefined because the variance of
14:
19303:
16474:
16452:Cox, D.R.; Hinkley, D.V. (1974).
15294:Mem. Acad. Roy. Sci. Inst. France
14773:This decorrelation is related to
10006:is the proportion of variance in
7533:, where Φ is the standard normal
5486:associated to the correlation is
5437:
5173:) is the factor by which a given
4404:
18851:
18839:
18827:
18814:
18813:
18604:
16241:10.1111/j.1460-9568.2011.07987.x
16229:European Journal of Neuroscience
15781:10.1016/j.neuroimage.2012.08.022
15313:Journal of Agricultural Research
15155:Galton, F. (24 September 1885).
14884:
13299:Circular correlation coefficient
11723:Weighted correlation coefficient
11218:Gaussian hypergeometric function
11173:
11169:
11163:
11012:
11008:
11002:
10802:Adjusted correlation coefficient
7856:For example, suppose we observe
7535:cumulative distribution function
6319:Gaussian hypergeometric function
5736:the inverse function is needed:
5260:Using the original paired data (
5027:
5014:
5003:
4995:
4861:
4848:
4837:
4829:
4786:= (0.11, 0.12, 0.13, 0.15, 0.18)
4762:observations of each variable).
4547:Function of raw scores and means
4540:of the correlation coefficient.
19248:Pearson correlation coefficient
18489:Least-squares spectral analysis
16445:
16404:
16373:
16283:
16263:
16199:
16181:
16139:
16104:
16076:
16041:
16026:
15988:
15928:
15882:
15863:
15848:
15813:
15760:
15724:
15703:
15690:
15665:
15618:
15560:
15525:
15483:
15458:
15406:
15371:
15345:
15304:
15282:
14957:Maximal information coefficient
14630:to get the transformed vectors
12480:
10918:
10810:is not an unbiased estimate of
10776:the data based on the value of
10684:is not an unbiased estimate of
7480:{\displaystyle \rho =\rho _{0}}
6979:Using the Fisher transformation
5617:For pairs from an uncorrelated
5169:(plotted here as a function of
4574:Estimated from the balloon rule
1920:
75:Pearson correlation coefficient
17470:Mean-unbiased minimum-variance
16573:
16439:10.1103/PhysRevLett.114.130401
16054:. Cambridge University Press.
15546:10.1080/00220671.1947.10881608
15342:", retrieved 22 February 2015.
15338:Real Statistics Using Excel, "
15241:
15217:Pearson, Karl (20 June 1895).
15210:
15171:
15148:
15101:Galton, F. (5–19 April 1877).
15094:
15076:
15062:
15039:
15008:
14738:
14719:
14557:
14538:
14311:
14299:
14282:
14270:
14239:
14227:
14173:
14167:
14120:
14114:
14061:
14049:
14002:
13996:
13949:
13943:
13905:
13899:
13888:
13882:
13872:
13866:
13855:
13849:
13838:
13826:
13812:
13800:
13684:
13655:
13615:
13608:
13586:
13546:
13539:
13517:
13483:
13477:
13455:
13446:
13440:
13418:
13281:
13260:
12990:
12966:{\displaystyle {\bar {r}}_{s}}
12951:
12804:Scaled correlation coefficient
12781:
12750:
12747:
12716:
12621:
12600:
12597:
12576:
12474:
12453:
12434:
12419:
12400:
12388:
12369:
12357:
12312:
12297:
12281:
12266:
12251:
12239:
12220:
12208:
12158:
12140:
12131:
12113:
12102:
12084:
12069:
12051:
11995:
11992:
11980:
11958:
11955:
11952:
11940:
11918:
11886:
11868:
11776:
11764:
11679:
11667:
11662:
11650:
11647:
11628:
11271:
11265:
11233:can be obtained by truncating
11203:
11179:
10638:
10485:
10478:
10456:
10404:
10397:
10376:
10366:
10278:
10271:
10256:
10220:
10207:
10184:
10112:
10106:
10085:
10075:
10072:
10060:
10037:
9987:
9980:
9965:
9930:
9923:
9901:
9880:
9873:
9852:
9842:
9817:
9810:
9795:
9749:
9742:
9720:
9699:
9692:
9671:
9661:
9625:
9618:
9597:
9587:
9565:
9558:
9536:
9515:
9508:
9487:
9477:
9442:
9435:
9414:
9404:
9382:
9375:
9353:
9338:
9329:
9322:
9301:
9291:
9285:
9279:
9258:
9248:
9245:
9233:
9210:
9207:
9172:
9165:
9144:
9134:
9112:
9105:
9083:
9068:
9062:
9041:
9031:
9028:
9022:
9001:
8979:
8956:
8921:
8914:
8893:
8883:
8861:
8854:
8832:
8817:
8811:
8790:
8780:
8777:
8771:
8749:
8726:
8720:
8705:
8666:
8632:{\displaystyle {\hat {Y}}_{i}}
8617:
8556:
8549:
8527:
8506:
8499:
8478:
8468:
8440:
8433:
8411:
8390:
8377:
8354:
8318:{\displaystyle {\hat {Y}}_{i}}
8303:
8264:
8257:
8236:
8226:
8204:
8191:
8168:
8146:
8139:
8117:
8066:
8038:
7840:
7837:
7808:
7802:
7793:
7781:
7752:
7746:
7737:
7728:
7708:
7696:
7667:
7638:
7632:
7623:
7617:
7611:
7591:
7579:
7421:
7418:
7405:
7396:
7390:
7384:
7196:
7190:
7178:
7172:
7124:
7118:
7050:
7044:
6622:
6610:
6604:
6592:
6580:
6568:
6377:
6371:
6304:
6280:
6205:
6190:
6172:
6157:
6062:
6046:
5898:
5886:
5877:
5865:
5856:
5850:
5031:
5023:
5018:
5010:
4960:= (−2.8, −1.8, −0.8, 1.2, 4.2)
4865:
4857:
4852:
4844:
4284:Canonical Correlation Analysis
4078:
4066:
3998:
3991:
3969:
3890:
3875:
3788:
3776:
3768:
3756:
3575:
3484:
3469:
3385:
3336:
2882:
2867:
2789:
2732:
2684:
2672:
2551:
2478:
2369:
2362:
2340:
2306:
2299:
2277:
2249:
2243:
2221:
2218:
2212:
2190:
2073:
2047:
2035:
2009:
1967:. We can obtain a formula for
1961:sample correlation coefficient
1959:and may be referred to as the
1886:
1878:
1806:
1798:
1740:
1732:
1719:
1711:
1695:
1683:
1600:
1592:
1579:
1571:
1555:
1543:
1527:
1518:
1510:
1481:
1473:
1448:
1432:
1375:
1346:
1338:
1263:
1257:
1179:
1171:
1097:
1091:
1024:
1016:
982:
974:
690:
687:
668:
665:
646:
643:
563:
560:
541:
538:
519:
516:
500:
488:
451:
439:
402:is the standard deviation of
255:
243:
189:
177:
1:
19187:Deep Learning Related Metrics
18783:Geographic information system
17999:Simultaneous equations models
16349:Topics in circular statistics
15824:. Series B (Methodological).
15427:10.1016/S0167-7152(98)00035-2
15386:Nova Science Publishers, Inc.
15340:Basic Concepts of Correlation
15055:
14775:principal components analysis
14350:random variables is observed
10816:bivariate normal distribution
10699:
8599:Next, we apply a property of
7962:and is a special case of the
7493:bivariate normal distribution
6968:{\displaystyle \nu =n-1>1}
5825:, the exact density function
5823:bivariate normal distribution
5619:bivariate normal distribution
5233:The other aim is to derive a
3194:{\displaystyle n,x_{i},y_{i}}
1929:, is commonly represented by
464:can be expressed in terms of
129:
16:Measure of linear correlation
17966:Coefficient of determination
17577:Uniformly most powerful test
15490:Rodgers; Nicewander (1988).
15248:Stigler, Stephen M. (1989).
15033:, or simply the unqualified
15002:
14179:{\displaystyle \mathbb {V} }
14126:{\displaystyle \mathbb {V} }
14067:{\displaystyle \mathbb {E} }
14008:{\displaystyle \mathbb {E} }
13955:{\displaystyle \mathbb {E} }
10592:
7964:coefficient of determination
6525:{\displaystyle \mathrm {B} }
5817:Using the exact distribution
5209:
4401:for an application of this.
21:Coefficient of determination
7:
19031:Sensitivity and specificity
18535:Proportional hazards models
18479:Spectral density estimation
18461:Vector autoregression (VAR)
17895:Maximum posterior estimator
17127:Randomized controlled trial
16380:Reid, M. D. (1 July 1989).
16269:Fulekar (Ed.), M.H. (2009)
15900:10.13140/RG.2.2.23673.49769
15891:"Confidence in Correlation"
15569:"Understanding Correlation"
14877:
14395:th variable of observation
11485:
11473:
11376:
11364:
11110:
10787:
10650:maximum likelihood estimate
7868:. The transformed value is
7341:Using the approximation, a
4803:correlation coefficient is
4478:is positive if and only if
3533:{\displaystyle s_{x},s_{y}}
2453:{\displaystyle x_{i},y_{i}}
780:{\displaystyle \sigma _{X}}
753:{\displaystyle \sigma _{Y}}
395:{\displaystyle \sigma _{Y}}
343:{\displaystyle \sigma _{X}}
10:
19308:
18295:Multivariate distributions
16715:Average absolute deviation
16082:Katz., Mitchell H. (2006)
15889:Taraldsen, Gunnar (2020).
15103:"Typical laws of heredity"
14937:Correlation and dependence
14910:Coefficient of colligation
14335:
14093:{\displaystyle X\otimes Y}
13719:
13693:{\displaystyle {\bar {y}}}
13664:{\displaystyle {\bar {x}}}
13302:
13112:By choosing the parameter
12807:
11529:is a suboptimal estimator,
10814:. For data that follows a
10791:
10585:
7950:
7147:) approximately follows a
6982:
4296:Some distributions (e.g.,
3500:are defined as above, and
2560:{\displaystyle {\bar {y}}}
18:
19256:
19230:
19207:
19186:
19163:
19135:
19107:
19044:
18976:
18908:
18809:
18763:
18700:
18653:
18616:
18612:
18599:
18571:
18553:
18520:
18511:
18469:
18416:
18377:
18326:
18317:
18283:Structural equation model
18238:
18195:
18191:
18166:
18125:
18091:
18045:
18012:
17974:
17941:
17937:
17913:
17853:
17762:
17681:
17645:
17636:
17619:Score/Lagrange multiplier
17604:
17557:
17502:
17428:
17419:
17229:
17225:
17212:
17171:
17145:
17097:
17052:
17034:Sample size determination
16999:
16995:
16982:
16886:
16841:
16815:
16797:
16753:
16705:
16625:
16616:
16612:
16599:
16581:
16486:comparingcorrelations.org
16033:Huber, Peter. J. (2004).
15956:10.1016/j.ins.2018.08.017
15857:Mathematics of Statistics
15499:The American Statistician
15354:"Statistical Correlation"
11715:for large values of
10933:is a biased estimator of
10826:of a normal bivariate is
10633:heavy-tailed distribution
7338:and increases otherwise.
7331:{\displaystyle \rho _{0}}
6324:In the special case when
5837:of a normal bivariate is
5418:of the statistic. A 95%
5347:from the randomized data.
4795:between two vectors (see
4750:between the two observed
4683:, obtained by regressing
4021:sample standard deviation
3906:are defined as above and:
3632:Alternative formulae for
18778:Environmental statistics
18300:Elliptical distributions
18093:Generalized linear model
18022:Simple linear regression
17792:Hodges–Lehmann estimator
17249:Probability distribution
17158:Stochastic approximation
16720:Coefficient of variation
16527:frank.mtsu.edu/~dkfuller
16318:10.1109/tit.2014.2342744
16060:10.1017/cbo9780511802256
15980:Wilcox, Rand R. (2005).
14905:Association (statistics)
14781:Software implementations
10603:probability distribution
10539:explained sum of squares
7976:simple linear regression
7210:
5637:with degrees of freedom
5601:Testing using Student's
5249:Using a permutation test
4758:-dimensional space (for
4731:, where sec and tan are
4588:Geometric interpretation
857:{\displaystyle \mu _{Y}}
809:{\displaystyle \mu _{X}}
19:Not to be confused with
19059:Calinski-Harabasz index
18438:Cross-correlation (XCF)
18046:Non-standard predictors
17480:Lehmann–Scheffé theorem
17153:Adaptive clinical trial
16536:"Guess the Correlation"
16417:Physical Review Letters
16398:10.1103/PhysRevA.40.913
16165:10.1214/aoms/1177706717
16012:10.1093/biomet/62.3.531
15754:10.1093/biomet/11.4.328
15035:correlation coefficient
14858:correlation_coefficient
14777:for multivariate data.
14425:{\displaystyle Z_{m,m}}
14384:{\displaystyle X_{i,j}}
11739:with the weight vector
10136:residual sum of squares
8024:and the fitted dataset
7531:2 Φ(−2.2) = 0.028
7522:{\displaystyle \rho =0}
7495:. Thus an approximate
6550:confidence distribution
6343:{\displaystyle \rho =0}
6241:{\displaystyle \Gamma }
5821:For data that follow a
5577:is the correlation and
5218:One aim is to test the
4733:trigonometric functions
4550:Standardized covariance
4308:Mathematical properties
4114:{\displaystyle \Sigma }
4023:); and analogously for
1644:can also be written as
602:can also be written as
83:correlation coefficient
19282:Correlation indicators
18834:Mathematics portal
18655:Engineering statistics
18563:Nelson–Aalen estimator
18140:Analysis of covariance
18027:Ordinary least squares
17951:Pearson product-moment
17355:Statistical functional
17266:Empirical distribution
17099:Controlled experiments
16828:Frequency distribution
16606:Descriptive statistics
16454:Theoretical Statistics
15916:Cite journal requires
15625:Bowley, A. L. (1928).
14982:Polychoric correlation
14870:correl(array1, array2)
14764:
14696:
14583:
14515:
14426:
14385:
14318:
14246:
14200:
14180:
14147:
14127:
14094:
14068:
14029:
14009:
13976:
13956:
13919:
13773:
13753:
13694:
13665:
13633:
13579:
13510:
13411:
13289:
13210:
13126:
13103:
13083:
13053:
13035:
12967:
12928:
12875:
12855:
12835:
12794:
12634:
12506:
12325:
12171:
12030:
11847:
11694:
11512:
11461:
11352:
11210:
11143:
11098:
10950:
10949:{\displaystyle \rho .}
10923:
10740:statistical dependence
10564:
10531:
10498:
10417:
10322:
10233:
10125:
10000:
9946:
9773:
8682:
8633:
8575:
8319:
8280:
8082:
8018:
7937:
7902:
7847:
7674:
7559:
7523:
7481:
7441:
7332:
7305:
7285:
7258:
7203:
7131:
7023:
6969:
6931:
6909:
6526:
6501:
6344:
6311:
6242:
6219:
5790:
5719:
5614:
5591:
5571:
5548:
5476:
5456:
5202:
5163:
5093:
4908:
4636:
4264:
4115:
4085:
4044:
4013:
3968:
3900:
3818:
3686:
3685:{\displaystyle r_{xy}}
3656:
3655:{\displaystyle r_{xy}}
3622:
3602:
3534:
3494:
3412:
3309:
3235:
3234:{\displaystyle r_{xy}}
3201:are defined as above.
3195:
3146:
2925:
2924:{\displaystyle r_{xy}}
2898:are defined as above.
2892:
2813:
2595:
2594:{\displaystyle r_{xy}}
2561:
2532:
2517:
2454:
2412:
2387:
2339:
2276:
2189:
2135:
2134:{\displaystyle r_{xy}}
2105:
2085:
1991:
1990:{\displaystyle r_{xy}}
1953:
1952:{\displaystyle r_{xy}}
1912:
1638:
1615:
927:
903:
878:
858:
830:
810:
781:
754:
722:
596:
573:
458:
416:
396:
368:
344:
312:
287:
196:
66:
37:
19287:Parametric statistics
19222:Intra-list Similarity
18750:Population statistics
18692:System identification
18426:Autocorrelation (ACF)
18354:Exponential smoothing
18268:Discriminant analysis
18263:Canonical correlation
18127:Partition of variance
17989:Regression validation
17833:(Jonckheere–Terpstra)
17732:Likelihood-ratio test
17421:Frequentist inference
17333:Location–scale family
17254:Sampling distribution
17219:Statistical inference
17186:Cross-sectional study
17173:Observational studies
17132:Randomized experiment
16961:Stem-and-leaf display
16763:Central limit theorem
16273:, Springer (pp. 110)
16051:Asymptotic Statistics
15696:Rahman, N. A. (1968)
15567:Rummel, R.J. (1976).
15267:10.1214/ss/1177012580
15031:bivariate correlation
14825:pandas.DataFrame.corr
14765:
14697:
14592:where an exponent of
14584:
14516:
14427:
14386:
14319:
14247:
14201:
14181:
14148:
14128:
14095:
14069:
14030:
14010:
13977:
13957:
13920:
13774:
13754:
13739:For two observables,
13695:
13666:
13634:
13559:
13490:
13391:
13303:Further information:
13290:
13211:
13127:
13104:
13084:
13082:{\displaystyle r_{k}}
13054:
13015:
12968:
12929:
12876:
12856:
12836:
12795:
12635:
12507:
12326:
12172:
12038:Weighted correlation
12031:
11848:
11695:
11518:are defined as above,
11513:
11462:
11353:
11211:
11149:are defined as above,
11144:
11099:
10951:
10924:
10747:Fisher transformation
10725:). Inspection of the
10586:Further information:
10574:(proportional to the
10565:
10532:
10499:
10418:
10323:
10234:
10126:
10001:
9947:
9774:
8683:
8634:
8588:that is explained by
8576:
8320:
8281:
8083:
8019:
7970:that is explained by
7938:
7903:
7848:
7675:
7560:
7558:{\displaystyle \rho }
7524:
7482:
7442:
7333:
7306:
7286:
7259:
7204:
7132:
7024:
7007:Fisher transformation
6985:Fisher transformation
6970:
6932:
6910:
6527:
6502:
6345:
6312:
6243:
6220:
5791:
5720:
5623:sampling distribution
5612:
5592:
5572:
5549:
5477:
5457:
5416:sampling distribution
5164:
5113:
5094:
4909:
4699:respectively. (Here,
4596:Regression lines for
4595:
4265:
4116:
4098:, with mean zero and
4086:
4084:{\displaystyle (X,Y)}
4045:
4043:{\displaystyle s_{y}}
4014:
3948:
3901:
3819:
3687:
3657:
3623:
3603:
3535:
3495:
3413:
3289:
3236:
3196:
3147:
2926:
2893:
2814:
2596:
2562:
2533:
2497:
2455:
2413:
2388:
2319:
2256:
2169:
2136:
2106:
2086:
1992:
1954:
1913:
1639:
1637:{\displaystyle \rho }
1616:
928:
926:{\displaystyle \rho }
904:
879:
859:
831:
811:
782:
755:
723:
597:
595:{\displaystyle \rho }
574:
459:
417:
397:
369:
345:
313:
288:
197:
195:{\displaystyle (X,Y)}
43:
31:
18673:Probabilistic design
18258:Principal components
18101:Exponential families
18053:Nonlinear regression
18032:General linear model
17994:Mixed effects models
17984:Errors and residuals
17961:Confounding variable
17863:Bayesian probability
17841:Van der Waerden test
17831:Ordered alternative
17596:Multiple comparisons
17475:Rao–Blackwellization
17438:Estimating equations
17394:Statistical distance
17112:Factorial experiment
16645:Arithmetic-Geometric
16514:. Linear regression.
16193:sci.tech-archive.net
15944:Information Sciences
14987:Quadrant count ratio
14962:Multiple correlation
14952:Distance correlation
14707:
14645:
14526:
14467:
14403:
14362:
14256:
14252:is symmetric, i.e.,
14213:
14190:
14159:
14137:
14106:
14078:
14041:
14019:
13988:
13966:
13935:
13786:
13763:
13743:
13675:
13646:
13372:
13231:
13159:
13116:
13093:
13066:
12980:
12973:is then computed as
12941:
12888:
12865:
12845:
12825:
12650:
12526:
12341:
12192:
12042:
11859:
11855:Weighted covariance
11755:
11743:(all of length
11601:
11574:has a bias of order
11496:
11389:
11246:
11155:
11127:
10977:
10937:
10833:
10675:law of large numbers
10671:consistent estimator
10617:population variances
10572:total sum of squares
10545:
10512:
10428:
10338:
10250:
10163:
10024:
9959:
9789:
8695:
8643:
8607:
8332:
8293:
8104:
8028:
7982:
7912:
7872:
7690:
7573:
7549:
7507:
7458:
7352:
7315:
7295:
7275:
7219:
7158:
7038:
7013:
6991:confidence intervals
6941:
6921:
6562:
6514:
6365:
6358:) can be written as
6328:
6256:
6232:
5844:
5743:
5648:
5581:
5561:
5493:
5466:
5446:
5308:}. The permutation
5130:
4976:
4810:
4298:stable distributions
4280:stochastic variables
4125:
4105:
4063:
4027:
3912:
3834:
3699:
3666:
3636:
3612:
3546:
3504:
3428:
3252:
3215:
3206:numerically unstable
3159:
2938:
2905:
2826:
2608:
2575:
2542:
2469:
2424:
2402:
2147:
2115:
2095:
2001:
1971:
1933:
1648:
1628:
940:
917:
889:
868:
841:
820:
793:
787:are defined as above
764:
737:
608:
586:
479:
430:
406:
379:
358:
327:
302:
212:
174:
110:It was developed by
18745:Official statistics
18668:Methods engineering
18349:Seasonal adjustment
18117:Poisson regressions
18037:Bayesian regression
17976:Regression analysis
17956:Partial correlation
17928:Regression analysis
17527:Prediction interval
17522:Likelihood interval
17512:Confidence interval
17504:Interval estimation
17465:Unbiased estimators
17283:Model specification
17163:Up-and-down designs
16851:Partial correlation
16807:Index of dispersion
16725:Interquartile range
15870:Weisstein, Eric W.
15352:Weisstein, Eric W.
15254:Statistical Science
15235:1895RSPS...58..240P
15178:Galton, F. (1886).
15119:1877Natur..15..492.
14977:Partial correlation
14831:Wolfram Mathematica
14622:is a row vector of
13728:partial correlation
13722:Partial correlation
13716:Partial correlation
13305:Circular statistics
12780:
12746:
12620:
12596:
11511:{\displaystyle r,n}
11328:
11142:{\displaystyle r,n}
10646:normal distribution
10621:Cauchy distribution
10612:is defined and the
7149:normal distribution
5420:confidence interval
5235:confidence interval
5175:prediction interval
4384:are constants with
4325:) = corr(
4302:normal distribution
4251:
4156:
3100:
3039:
2775:
2718:
1211:
1045:
909:is the expectation.
95:standard deviations
19292:Statistical ratios
19243:Euclidean distance
19209:Recommender system
19089:Similarity measure
18903:evaluation metrics
18765:Spatial statistics
18645:Medical statistics
18545:First hitting time
18499:Whittle likelihood
18150:Degrees of freedom
18145:Multivariate ANOVA
18078:Heteroscedasticity
17890:Bayesian estimator
17855:Bayesian inference
17704:Kolmogorov–Smirnov
17589:Randomization test
17559:Testing hypotheses
17532:Tolerance interval
17443:Maximum likelihood
17338:Exponential family
17271:Density estimation
17231:Statistical theory
17191:Natural experiment
17137:Scientific control
17054:Survey methodology
16740:Standard deviation
15610:Cohen, J. (1988).
14900:Anscombe's quartet
14892:Mathematics portal
14760:
14692:
14608:matrix square root
14579:
14511:
14450:correlation matrix
14422:
14381:
14358:be a matrix where
14314:
14242:
14196:
14176:
14143:
14123:
14090:
14064:
14025:
14005:
13972:
13952:
13915:
13769:
13749:
13690:
13661:
13629:
13285:
13206:
13150:Pearson's distance
13136:Pearson's distance
13122:
13099:
13079:
13049:
12963:
12924:
12871:
12861:for a given scale
12851:
12831:
12810:Scaled correlation
12790:
12766:
12732:
12630:
12606:
12582:
12502:
12321:
12167:
12026:
12009:
11904:
11843:
11826:
11794:
11690:
11508:
11457:
11348:
11314:
11206:
11139:
11094:
10946:
10919:
10818:, the expectation
10560:
10527:
10494:
10455:
10413:
10365:
10318:
10229:
10183:
10121:
10036:
9996:
9942:
9900:
9841:
9769:
9767:
9719:
9660:
9586:
9535:
9476:
9403:
9352:
9206:
9133:
9082:
8955:
8882:
8831:
8748:
8678:
8629:
8571:
8526:
8467:
8410:
8353:
8315:
8276:
8225:
8167:
8116:
8078:
8014:
7933:
7898:
7843:
7670:
7555:
7519:
7477:
7437:
7328:
7301:
7281:
7254:
7199:
7127:
7066:
7019:
6965:
6927:
6905:
6898:
6872:
6851:
6833:
6522:
6497:
6482:
6459:
6340:
6307:
6238:
6215:
6188:
6155:
6140:
6125:
6037:
5786:
5715:
5615:
5587:
5567:
5544:
5472:
5452:
5304:of the set {1,...,
5203:
5185:. For example, if
5159:
5089:
4904:
4637:
4583:Ratio of two means
4291:maximum likelihood
4260:
4254:
4237:
4142:
4111:
4081:
4040:
4009:
3896:
3814:
3682:
3652:
3618:
3598:
3530:
3490:
3408:
3231:
3191:
3142:
3086:
3025:
2921:
2888:
2809:
2761:
2760:
2704:
2703:
2639:
2591:
2557:
2528:
2450:
2408:
2383:
2131:
2101:
2081:
1987:
1949:
1908:
1634:
1611:
1609:
1197:
1031:
923:
899:
874:
854:
826:
806:
777:
750:
718:
592:
569:
454:
412:
392:
364:
352:standard deviation
340:
308:
283:
192:
106:Naming and history
67:
38:
19269:
19268:
19238:Cosine similarity
19074:Hopkins statistic
18867:
18866:
18805:
18804:
18801:
18800:
18740:National accounts
18710:Actuarial science
18702:Social statistics
18595:
18594:
18591:
18590:
18587:
18586:
18522:Survival function
18507:
18506:
18369:Granger causality
18210:Contingency table
18185:Survival analysis
18162:
18161:
18158:
18157:
18014:Linear regression
17909:
17908:
17905:
17904:
17880:Credible interval
17849:
17848:
17632:
17631:
17448:Method of moments
17317:Parametric family
17278:Statistical model
17208:
17207:
17204:
17203:
17122:Random assignment
17044:Statistical power
16978:
16977:
16974:
16973:
16823:Contingency table
16793:
16792:
16660:Generalized/power
16386:Physical Review A
16359:978-981-02-3778-3
16302:(10): 5966–5974.
16092:978-0-521-54985-1
16069:978-0-511-80225-6
16035:Robust Statistics
15984:. Academic Press.
15876:Wolfram MathWorld
15399:978-1-60021-976-4
15358:Wolfram MathWorld
15088:Statistics How To
14942:Correlation ratio
14753:
14668:
14572:
14490:
14328:Decorrelation of
14199:{\displaystyle Y}
14146:{\displaystyle X}
14028:{\displaystyle Y}
13975:{\displaystyle X}
13909:
13908:
13772:{\displaystyle Y}
13752:{\displaystyle X}
13687:
13658:
13627:
13624:
13611:
13555:
13542:
13480:
13443:
13382:
13125:{\displaystyle s}
13102:{\displaystyle k}
13013:
12993:
12954:
12915:
12874:{\displaystyle s}
12854:{\displaystyle T}
12834:{\displaystyle K}
12785:
12784:
12625:
12624:
12517:cosine similarity
12316:
12315:
12162:
12161:
12021:
12000:
11895:
11838:
11817:
11785:
11685:
11683:
11611:
11481:
11480:
11447:
11399:
11372:
11371:
11343:
11321:
11300:
11284:
11118:
11117:
11065:
11044:
11031:
10987:
10907:
10755:permutation tests
10557:
10552:
10524:
10519:
10481:
10446:
10440:
10435:
10400:
10379:
10356:
10350:
10345:
10316:
10313:
10308:
10301:
10296:
10274:
10210:
10174:
10169:
10109:
10088:
10063:
10027:
9983:
9940:
9926:
9891:
9876:
9855:
9832:
9813:
9760:
9759:
9745:
9710:
9695:
9674:
9651:
9635:
9634:
9621:
9600:
9577:
9561:
9526:
9511:
9490:
9467:
9452:
9451:
9438:
9417:
9394:
9378:
9343:
9325:
9304:
9282:
9261:
9236:
9197:
9182:
9181:
9168:
9147:
9124:
9108:
9073:
9065:
9044:
9025:
9004:
8982:
8946:
8931:
8930:
8917:
8896:
8873:
8857:
8822:
8814:
8793:
8774:
8739:
8723:
8669:
8620:
8566:
8552:
8517:
8502:
8481:
8458:
8450:
8436:
8401:
8380:
8344:
8306:
8260:
8239:
8216:
8194:
8158:
8142:
8107:
8069:
8041:
7931:
7930:
7835:
7779:
7717:
7665:
7600:
7529:, the p-value is
7435:
7379:
7378:
7373:
7304:{\displaystyle r}
7284:{\displaystyle n}
7249:
7248:
7228:
7164:
7103:
7065:
7022:{\displaystyle F}
6897:
6871:
6850:
6832:
6809:
6761:
6712:
6667:
6659:
6635:
6492:
6481:
6458:
6428:
6187:
6154:
6139:
6124:
6085:
6080:
6036:
6003:
5990:
5944:
5781:
5780:
5713:
5712:
5672:
5597:the sample size.
5590:{\displaystyle n}
5570:{\displaystyle r}
5542:
5541:
5475:{\displaystyle y}
5455:{\displaystyle x}
5430:of the resampled
5372:Using a bootstrap
5368:test is desired.
5254:Permutation tests
5157:
5122:with correlation
5062:
5059:
5052:
5036:
4919:cosine similarity
4896:
4893:
4886:
4870:
4779:= (1, 2, 3, 5, 8)
4007:
3994:
3946:
3893:
3878:
3812:
3771:
3759:
3621:{\displaystyle y}
3592:
3578:
3540:are defined below
3487:
3472:
3402:
3388:
3353:
3339:
3287:
3137:
3134:
3077:
3073:
2885:
2870:
2804:
2801:
2792:
2751:
2748:
2744:
2735:
2694:
2687:
2675:
2630:
2554:
2495:
2481:
2411:{\displaystyle n}
2381:
2378:
2365:
2315:
2302:
2246:
2215:
2104:{\displaystyle n}
1903:
1900:
1824:
1820:
877:{\displaystyle Y}
829:{\displaystyle X}
716:
415:{\displaystyle Y}
367:{\displaystyle X}
281:
44:Several sets of (
19299:
19261:Confusion matrix
19036:Logarithmic Loss
18901:Machine learning
18894:
18887:
18880:
18871:
18870:
18855:
18854:
18843:
18842:
18832:
18831:
18817:
18816:
18720:Crime statistics
18614:
18613:
18601:
18600:
18518:
18517:
18484:Fourier analysis
18471:Frequency domain
18451:
18398:
18364:Structural break
18324:
18323:
18273:Cluster analysis
18220:Log-linear model
18193:
18192:
18168:
18167:
18109:
18083:Homoscedasticity
17939:
17938:
17915:
17914:
17834:
17826:
17818:
17817:(Kruskal–Wallis)
17802:
17787:
17742:Cross validation
17727:
17709:Anderson–Darling
17656:
17643:
17642:
17614:Likelihood-ratio
17606:Parametric tests
17584:Permutation test
17567:1- & 2-tails
17458:Minimum distance
17430:Point estimation
17426:
17425:
17377:Optimal decision
17328:
17227:
17226:
17214:
17213:
17196:Quasi-experiment
17146:Adaptive designs
16997:
16996:
16984:
16983:
16861:Rank correlation
16623:
16622:
16614:
16613:
16601:
16600:
16568:
16561:
16554:
16545:
16544:
16539:
16530:
16524:
16515:
16502:
16489:
16468:
16467:
16449:
16443:
16442:
16432:
16408:
16402:
16401:
16377:
16371:
16370:
16368:
16366:
16343:
16337:
16336:
16334:
16332:
16311:
16287:
16281:
16267:
16261:
16260:
16226:
16217:
16211:
16210:
16203:
16197:
16196:
16185:
16179:
16177:
16167:
16143:
16137:
16136:
16108:
16102:
16080:
16074:
16073:
16045:
16039:
16038:
16030:
16024:
16023:
15996:Devlin, Susan J.
15992:
15986:
15985:
15977:
15968:
15967:
15941:
15932:
15926:
15925:
15919:
15914:
15912:
15904:
15902:
15886:
15880:
15879:
15867:
15861:
15860:
15852:
15846:
15845:
15817:
15811:
15810:
15792:
15764:
15758:
15757:
15728:
15722:
15707:
15701:
15694:
15688:
15687:
15685:
15683:
15669:
15663:
15662:
15622:
15616:
15615:
15607:
15598:
15597:
15579:
15573:
15572:
15564:
15558:
15557:
15529:
15523:
15522:
15496:
15487:
15481:
15480:
15478:
15476:
15462:
15456:
15455:
15453:
15451:
15437:
15431:
15430:
15410:
15404:
15403:
15375:
15369:
15368:
15366:
15364:
15349:
15343:
15336:
15321:
15320:
15308:
15302:
15301:
15286:
15280:
15279:
15269:
15245:
15239:
15238:
15214:
15208:
15207:
15175:
15169:
15168:
15152:
15146:
15140:
15130:
15128:10.1038/015492a0
15098:
15092:
15091:
15080:
15074:
15073:
15066:
15050:
15043:
15037:
15012:
14894:
14889:
14888:
14871:
14867:has an in-built
14859:
14855:library via the
14843:
14837:
14826:
14813:
14797:
14792:
14769:
14767:
14766:
14761:
14756:
14755:
14754:
14746:
14733:
14732:
14731:
14701:
14699:
14698:
14693:
14685:
14684:
14669:
14661:
14605:
14604:
14600:
14597:
14588:
14586:
14585:
14580:
14575:
14574:
14573:
14565:
14552:
14551:
14550:
14520:
14518:
14517:
14512:
14507:
14506:
14491:
14483:
14431:
14429:
14428:
14423:
14421:
14420:
14390:
14388:
14387:
14382:
14380:
14379:
14332:random variables
14323:
14321:
14320:
14315:
14298:
14269:
14251:
14249:
14248:
14243:
14226:
14205:
14203:
14202:
14197:
14185:
14183:
14182:
14177:
14166:
14152:
14150:
14149:
14144:
14132:
14130:
14129:
14124:
14113:
14099:
14097:
14096:
14091:
14073:
14071:
14070:
14065:
14048:
14034:
14032:
14031:
14026:
14014:
14012:
14011:
14006:
13995:
13981:
13979:
13978:
13973:
13961:
13959:
13958:
13953:
13942:
13924:
13922:
13921:
13916:
13910:
13898:
13881:
13876:
13875:
13865:
13848:
13825:
13819:
13799:
13778:
13776:
13775:
13770:
13758:
13756:
13755:
13750:
13699:
13697:
13696:
13691:
13689:
13688:
13680:
13670:
13668:
13667:
13662:
13660:
13659:
13651:
13638:
13636:
13635:
13630:
13628:
13626:
13625:
13623:
13622:
13613:
13612:
13604:
13598:
13597:
13578:
13573:
13558:
13556:
13554:
13553:
13544:
13543:
13535:
13529:
13528:
13509:
13504:
13489:
13486:
13482:
13481:
13473:
13467:
13466:
13445:
13444:
13436:
13430:
13429:
13410:
13405:
13389:
13384:
13383:
13380:
13352:
13294:
13292:
13291:
13286:
13284:
13279:
13278:
13263:
13249:
13248:
13221:cluster analysis
13215:
13213:
13212:
13207:
13202:
13201:
13177:
13176:
13131:
13129:
13128:
13123:
13108:
13106:
13105:
13100:
13088:
13086:
13085:
13080:
13078:
13077:
13058:
13056:
13055:
13050:
13045:
13044:
13034:
13029:
13014:
13006:
13001:
13000:
12995:
12994:
12986:
12972:
12970:
12969:
12964:
12962:
12961:
12956:
12955:
12947:
12933:
12931:
12930:
12925:
12920:
12916:
12908:
12880:
12878:
12877:
12872:
12860:
12858:
12857:
12852:
12840:
12838:
12837:
12832:
12799:
12797:
12796:
12791:
12786:
12779:
12774:
12765:
12764:
12745:
12740:
12731:
12730:
12715:
12714:
12713:
12712:
12703:
12702:
12693:
12692:
12679:
12674:
12673:
12639:
12637:
12636:
12631:
12626:
12619:
12614:
12595:
12590:
12575:
12574:
12573:
12572:
12563:
12562:
12549:
12544:
12543:
12511:
12509:
12508:
12503:
12449:
12448:
12415:
12414:
12384:
12383:
12353:
12352:
12330:
12328:
12327:
12322:
12317:
12310:
12309:
12293:
12292:
12279:
12278:
12262:
12261:
12255:
12254:
12235:
12234:
12227:
12204:
12203:
12176:
12174:
12173:
12168:
12163:
12106:
12105:
12076:
12035:
12033:
12032:
12027:
12022:
12020:
12019:
12018:
12008:
11998:
11970:
11969:
11930:
11929:
11914:
11913:
11903:
11893:
11852:
11850:
11849:
11844:
11839:
11837:
11836:
11835:
11825:
11815:
11814:
11813:
11804:
11803:
11793:
11783:
11718:
11714:
11699:
11697:
11696:
11691:
11686:
11684:
11682:
11665:
11646:
11645:
11626:
11618:
11613:
11612:
11609:
11589:
11588:
11587:
11579:
11573:
11562:
11558:
11539:
11528:
11517:
11515:
11514:
11509:
11475:
11466:
11464:
11463:
11458:
11453:
11449:
11448:
11446:
11438:
11437:
11436:
11420:
11401:
11400:
11397:
11383:
11366:
11357:
11355:
11354:
11349:
11344:
11342:
11334:
11333:
11329:
11327:
11322:
11319:
11302:
11301:
11298:
11291:
11286:
11285:
11282:
11261:
11260:
11240:
11236:
11232:
11215:
11213:
11212:
11207:
11178:
11177:
11176:
11167:
11166:
11148:
11146:
11145:
11140:
11112:
11103:
11101:
11100:
11095:
11090:
11086:
11085:
11084:
11066:
11061:
11050:
11045:
11037:
11032:
11024:
11017:
11016:
11015:
11006:
11005:
10989:
10988:
10985:
10971:
10967:
10955:
10953:
10952:
10947:
10932:
10928:
10926:
10925:
10920:
10908:
10906:
10898:
10897:
10893:
10892:
10891:
10867:
10856:
10842:
10841:
10825:
10821:
10813:
10809:
10677:can be applied).
10569:
10567:
10566:
10561:
10559:
10558:
10555:
10553:
10550:
10536:
10534:
10533:
10528:
10526:
10525:
10522:
10520:
10517:
10503:
10501:
10500:
10495:
10493:
10492:
10483:
10482:
10474:
10468:
10467:
10454:
10442:
10441:
10438:
10436:
10433:
10422:
10420:
10419:
10414:
10412:
10411:
10402:
10401:
10393:
10387:
10386:
10381:
10380:
10372:
10364:
10352:
10351:
10348:
10346:
10343:
10327:
10325:
10324:
10319:
10317:
10315:
10314:
10311:
10309:
10306:
10303:
10302:
10299:
10297:
10294:
10291:
10286:
10285:
10276:
10275:
10267:
10238:
10236:
10235:
10230:
10228:
10227:
10218:
10217:
10212:
10211:
10203:
10196:
10195:
10182:
10170:
10167:
10141:
10130:
10128:
10127:
10122:
10111:
10110:
10102:
10096:
10095:
10090:
10089:
10081:
10071:
10070:
10065:
10064:
10056:
10049:
10048:
10035:
10005:
10003:
10002:
9997:
9995:
9994:
9985:
9984:
9976:
9951:
9949:
9948:
9943:
9941:
9939:
9938:
9937:
9928:
9927:
9919:
9913:
9912:
9899:
9889:
9888:
9887:
9878:
9877:
9869:
9863:
9862:
9857:
9856:
9848:
9840:
9830:
9825:
9824:
9815:
9814:
9806:
9778:
9776:
9775:
9770:
9768:
9761:
9758:
9757:
9756:
9747:
9746:
9738:
9732:
9731:
9718:
9708:
9707:
9706:
9697:
9696:
9688:
9682:
9681:
9676:
9675:
9667:
9659:
9649:
9648:
9640:
9636:
9633:
9632:
9623:
9622:
9614:
9608:
9607:
9602:
9601:
9593:
9585:
9573:
9572:
9563:
9562:
9554:
9548:
9547:
9534:
9525:
9524:
9523:
9522:
9513:
9512:
9504:
9498:
9497:
9492:
9491:
9483:
9475:
9465:
9457:
9453:
9450:
9449:
9440:
9439:
9431:
9425:
9424:
9419:
9418:
9410:
9402:
9390:
9389:
9380:
9379:
9371:
9365:
9364:
9351:
9342:
9341:
9337:
9336:
9327:
9326:
9318:
9312:
9311:
9306:
9305:
9297:
9284:
9283:
9275:
9269:
9268:
9263:
9262:
9254:
9244:
9243:
9238:
9237:
9229:
9222:
9221:
9205:
9195:
9187:
9183:
9180:
9179:
9170:
9169:
9161:
9155:
9154:
9149:
9148:
9140:
9132:
9120:
9119:
9110:
9109:
9101:
9095:
9094:
9081:
9072:
9071:
9067:
9066:
9058:
9052:
9051:
9046:
9045:
9037:
9027:
9026:
9018:
9012:
9011:
9006:
9005:
8997:
8990:
8989:
8984:
8983:
8975:
8968:
8967:
8954:
8944:
8936:
8932:
8929:
8928:
8919:
8918:
8910:
8904:
8903:
8898:
8897:
8889:
8881:
8869:
8868:
8859:
8858:
8850:
8844:
8843:
8830:
8821:
8820:
8816:
8815:
8807:
8801:
8800:
8795:
8794:
8786:
8776:
8775:
8767:
8761:
8760:
8747:
8737:
8725:
8724:
8716:
8687:
8685:
8684:
8679:
8677:
8676:
8671:
8670:
8662:
8655:
8654:
8638:
8636:
8635:
8630:
8628:
8627:
8622:
8621:
8613:
8580:
8578:
8577:
8572:
8567:
8565:
8564:
8563:
8554:
8553:
8545:
8539:
8538:
8525:
8515:
8514:
8513:
8504:
8503:
8495:
8489:
8488:
8483:
8482:
8474:
8466:
8456:
8451:
8449:
8448:
8447:
8438:
8437:
8429:
8423:
8422:
8409:
8399:
8398:
8397:
8388:
8387:
8382:
8381:
8373:
8366:
8365:
8352:
8342:
8324:
8322:
8321:
8316:
8314:
8313:
8308:
8307:
8299:
8285:
8283:
8282:
8277:
8272:
8271:
8262:
8261:
8253:
8247:
8246:
8241:
8240:
8232:
8224:
8212:
8211:
8202:
8201:
8196:
8195:
8187:
8180:
8179:
8166:
8154:
8153:
8144:
8143:
8135:
8129:
8128:
8115:
8087:
8085:
8084:
8079:
8077:
8076:
8071:
8070:
8062:
8049:
8048:
8043:
8042:
8034:
8023:
8021:
8020:
8015:
8013:
8012:
7994:
7993:
7942:
7940:
7939:
7934:
7932:
7926:
7922:
7907:
7905:
7904:
7899:
7891:
7852:
7850:
7849:
7844:
7836:
7833:
7831:
7830:
7826:
7780:
7777:
7775:
7774:
7770:
7718:
7715:
7679:
7677:
7676:
7671:
7666:
7663:
7661:
7660:
7656:
7601:
7598:
7564:
7562:
7561:
7556:
7532:
7528:
7526:
7525:
7520:
7486:
7484:
7483:
7478:
7476:
7475:
7446:
7444:
7443:
7438:
7436:
7425:
7417:
7416:
7380:
7376:
7375:
7374:
7371:
7362:
7337:
7335:
7334:
7329:
7327:
7326:
7310:
7308:
7307:
7302:
7290:
7288:
7287:
7282:
7263:
7261:
7260:
7255:
7250:
7238:
7234:
7229:
7226:
7211:
7208:
7206:
7205:
7200:
7165:
7162:
7136:
7134:
7133:
7128:
7108:
7104:
7102:
7091:
7080:
7067:
7058:
7028:
7026:
7025:
7020:
6995:hypothesis tests
6974:
6972:
6971:
6966:
6936:
6934:
6933:
6928:
6914:
6912:
6911:
6906:
6904:
6900:
6899:
6893:
6879:
6873:
6864:
6852:
6843:
6834:
6825:
6811:
6810:
6805:
6791:
6789:
6785:
6763:
6762:
6757:
6746:
6744:
6740:
6739:
6738:
6714:
6713:
6708:
6697:
6695:
6691:
6690:
6689:
6668:
6666:
6665:
6661:
6660:
6652:
6636:
6628:
6625:
6587:
6531:
6529:
6528:
6523:
6521:
6506:
6504:
6503:
6498:
6493:
6491:
6490:
6489:
6488:
6484:
6483:
6477:
6466:
6460:
6451:
6438:
6437:
6430:
6429:
6424:
6413:
6411:
6407:
6406:
6405:
6384:
6349:
6347:
6346:
6341:
6316:
6314:
6313:
6308:
6279:
6278:
6273:
6267:
6266:
6261:
6247:
6245:
6244:
6239:
6224:
6222:
6221:
6216:
6214:
6213:
6212:
6208:
6189:
6180:
6156:
6147:
6141:
6132:
6126:
6117:
6107:
6106:
6101:
6095:
6094:
6089:
6086:
6084:
6083:
6082:
6081:
6073:
6045:
6044:
6043:
6039:
6038:
6029:
6010:
6004:
5996:
5993:
5992:
5991:
5986:
5975:
5973:
5969:
5968:
5967:
5946:
5945:
5940:
5929:
5927:
5923:
5922:
5921:
5885:
5863:
5795:
5793:
5792:
5787:
5782:
5779:
5778:
5757:
5753:
5728:has a student's
5724:
5722:
5721:
5716:
5714:
5711:
5710:
5709:
5693:
5682:
5681:
5673:
5671:
5670:
5658:
5596:
5594:
5593:
5588:
5576:
5574:
5573:
5568:
5553:
5551:
5550:
5545:
5543:
5540:
5529:
5528:
5527:
5511:
5510:
5505:
5504:
5481:
5479:
5478:
5473:
5461:
5459:
5458:
5453:
5168:
5166:
5165:
5160:
5158:
5156:
5155:
5140:
5098:
5096:
5095:
5090:
5085:
5084:
5063:
5061:
5060:
5055:
5053:
5048:
5042:
5037:
5035:
5034:
5030:
5021:
5017:
5007:
5006:
4998:
4992:
4968:
4961:
4954:
4942:
4930:
4913:
4911:
4910:
4905:
4897:
4895:
4894:
4889:
4887:
4882:
4876:
4871:
4869:
4868:
4864:
4855:
4851:
4841:
4840:
4832:
4826:
4787:
4780:
4730:
4716:
4709:
4682:
4662:
4635:
4615:
4516:anti-correlation
4477:
4475:
4460:
4444:More generally,
4437:increases while
4423:regression slope
4394:
4367:
4353:
4274:Practical issues
4269:
4267:
4266:
4261:
4259:
4258:
4250:
4245:
4234:
4233:
4224:
4223:
4214:
4213:
4194:
4193:
4184:
4183:
4174:
4173:
4155:
4150:
4120:
4118:
4117:
4112:
4090:
4088:
4087:
4082:
4049:
4047:
4046:
4041:
4039:
4038:
4018:
4016:
4015:
4010:
4008:
4006:
4005:
3996:
3995:
3987:
3981:
3980:
3967:
3962:
3947:
3945:
3931:
3929:
3924:
3923:
3905:
3903:
3902:
3897:
3895:
3894:
3886:
3880:
3879:
3871:
3865:
3864:
3852:
3851:
3823:
3821:
3820:
3815:
3813:
3811:
3810:
3809:
3800:
3799:
3774:
3773:
3772:
3764:
3761:
3760:
3752:
3743:
3742:
3733:
3732:
3719:
3714:
3713:
3691:
3689:
3688:
3683:
3681:
3680:
3661:
3659:
3658:
3653:
3651:
3650:
3627:
3625:
3624:
3619:
3607:
3605:
3604:
3599:
3597:
3593:
3591:
3590:
3581:
3580:
3579:
3571:
3565:
3564:
3554:
3539:
3537:
3536:
3531:
3529:
3528:
3516:
3515:
3499:
3497:
3496:
3491:
3489:
3488:
3480:
3474:
3473:
3465:
3459:
3458:
3446:
3445:
3417:
3415:
3414:
3409:
3407:
3403:
3401:
3400:
3391:
3390:
3389:
3381:
3375:
3374:
3364:
3358:
3354:
3352:
3351:
3342:
3341:
3340:
3332:
3326:
3325:
3315:
3308:
3303:
3288:
3286:
3272:
3267:
3266:
3240:
3238:
3237:
3232:
3230:
3229:
3200:
3198:
3197:
3192:
3190:
3189:
3177:
3176:
3151:
3149:
3148:
3143:
3138:
3136:
3135:
3133:
3132:
3127:
3123:
3122:
3121:
3099:
3094:
3079:
3075:
3074:
3072:
3071:
3066:
3062:
3061:
3060:
3038:
3033:
3018:
3015:
3014:
3013:
3001:
3000:
2985:
2984:
2975:
2974:
2958:
2953:
2952:
2930:
2928:
2927:
2922:
2920:
2919:
2897:
2895:
2894:
2889:
2887:
2886:
2878:
2872:
2871:
2863:
2857:
2856:
2844:
2843:
2818:
2816:
2815:
2810:
2805:
2803:
2802:
2800:
2799:
2794:
2793:
2785:
2774:
2769:
2759:
2750:
2746:
2745:
2743:
2742:
2737:
2736:
2728:
2717:
2712:
2702:
2693:
2690:
2689:
2688:
2680:
2677:
2676:
2668:
2659:
2658:
2649:
2648:
2638:
2628:
2623:
2622:
2600:
2598:
2597:
2592:
2590:
2589:
2566:
2564:
2563:
2558:
2556:
2555:
2547:
2537:
2535:
2534:
2529:
2527:
2526:
2516:
2511:
2496:
2488:
2483:
2482:
2474:
2459:
2457:
2456:
2451:
2449:
2448:
2436:
2435:
2417:
2415:
2414:
2409:
2392:
2390:
2389:
2384:
2382:
2380:
2379:
2377:
2376:
2367:
2366:
2358:
2352:
2351:
2338:
2333:
2318:
2316:
2314:
2313:
2304:
2303:
2295:
2289:
2288:
2275:
2270:
2255:
2252:
2248:
2247:
2239:
2233:
2232:
2217:
2216:
2208:
2202:
2201:
2188:
2183:
2167:
2162:
2161:
2140:
2138:
2137:
2132:
2130:
2129:
2110:
2108:
2107:
2102:
2090:
2088:
2087:
2082:
2080:
2076:
2072:
2071:
2059:
2058:
2034:
2033:
2021:
2020:
1996:
1994:
1993:
1988:
1986:
1985:
1958:
1956:
1955:
1950:
1948:
1947:
1917:
1915:
1914:
1909:
1904:
1902:
1901:
1899:
1898:
1893:
1889:
1874:
1873:
1858:
1854:
1852:
1851:
1833:
1832:
1826:
1822:
1821:
1819:
1818:
1813:
1809:
1794:
1793:
1778:
1774:
1772:
1771:
1753:
1752:
1746:
1743:
1728:
1727:
1707:
1706:
1679:
1678:
1671:
1666:
1665:
1643:
1641:
1640:
1635:
1624:the formula for
1620:
1618:
1617:
1612:
1610:
1588:
1587:
1567:
1566:
1539:
1538:
1525:
1521:
1506:
1505:
1488:
1484:
1469:
1468:
1444:
1443:
1430:
1426:
1425:
1424:
1404:
1400:
1399:
1398:
1371:
1370:
1363:
1359:
1358:
1353:
1349:
1334:
1333:
1317:
1313:
1311:
1310:
1292:
1291:
1282:
1278:
1276:
1275:
1270:
1266:
1253:
1252:
1225:
1224:
1216:
1210:
1205:
1192:
1191:
1186:
1182:
1167:
1166:
1151:
1147:
1145:
1144:
1126:
1125:
1116:
1112:
1110:
1109:
1104:
1100:
1087:
1086:
1059:
1058:
1050:
1044:
1039:
1012:
1011:
1003:
998:
997:
970:
969:
961:
956:
955:
932:
930:
929:
924:
913:The formula for
908:
906:
905:
900:
898:
897:
883:
881:
880:
875:
863:
861:
860:
855:
853:
852:
835:
833:
832:
827:
815:
813:
812:
807:
805:
804:
786:
784:
783:
778:
776:
775:
759:
757:
756:
751:
749:
748:
727:
725:
724:
719:
717:
715:
714:
713:
704:
703:
693:
686:
685:
664:
663:
639:
638:
631:
626:
625:
601:
599:
598:
593:
582:the formula for
578:
576:
575:
570:
559:
558:
537:
536:
512:
511:
463:
461:
460:
455:
426:The formula for
421:
419:
418:
413:
401:
399:
398:
393:
391:
390:
373:
371:
370:
365:
349:
347:
346:
341:
339:
338:
317:
315:
314:
309:
292:
290:
289:
284:
282:
280:
279:
278:
269:
268:
258:
235:
230:
229:
201:
199:
198:
193:
150:For a population
19307:
19306:
19302:
19301:
19300:
19298:
19297:
19296:
19272:
19271:
19270:
19265:
19252:
19226:
19203:
19194:Inception score
19182:
19159:
19137:Computer Vision
19131:
19103:
19040:
18972:
18904:
18898:
18868:
18863:
18826:
18797:
18759:
18696:
18682:quality control
18649:
18631:Clinical trials
18608:
18583:
18567:
18555:Hazard function
18549:
18503:
18465:
18449:
18412:
18408:Breusch–Godfrey
18396:
18373:
18313:
18288:Factor analysis
18234:
18215:Graphical model
18187:
18154:
18121:
18107:
18087:
18041:
18008:
17970:
17933:
17932:
17901:
17845:
17832:
17824:
17816:
17800:
17785:
17764:Rank statistics
17758:
17737:Model selection
17725:
17683:Goodness of fit
17677:
17654:
17628:
17600:
17553:
17498:
17487:Median unbiased
17415:
17326:
17259:Order statistic
17221:
17200:
17167:
17141:
17093:
17048:
16991:
16989:Data collection
16970:
16882:
16837:
16811:
16789:
16749:
16701:
16618:Continuous data
16608:
16595:
16577:
16572:
16534:
16522:
16518:
16506:
16493:
16480:
16477:
16472:
16471:
16464:
16450:
16446:
16409:
16405:
16378:
16374:
16364:
16362:
16360:
16344:
16340:
16330:
16328:
16309:10.1.1.642.9971
16288:
16284:
16268:
16264:
16224:
16218:
16214:
16205:
16204:
16200:
16187:
16186:
16182:
16144:
16140:
16109:
16105:
16081:
16077:
16070:
16046:
16042:
16031:
16027:
15993:
15989:
15978:
15971:
15939:
15933:
15929:
15917:
15915:
15906:
15905:
15887:
15883:
15868:
15864:
15853:
15849:
15818:
15814:
15765:
15761:
15729:
15725:
15721:(Section 31.19)
15708:
15704:
15695:
15691:
15681:
15679:
15677:Cross Validated
15671:
15670:
15666:
15643:10.2307/2277400
15623:
15619:
15614:(2nd ed.).
15608:
15601:
15594:
15580:
15576:
15565:
15561:
15530:
15526:
15511:10.2307/2685263
15494:
15488:
15484:
15474:
15472:
15464:
15463:
15459:
15449:
15447:
15439:
15438:
15434:
15411:
15407:
15400:
15376:
15372:
15362:
15360:
15350:
15346:
15337:
15324:
15309:
15305:
15288:
15287:
15283:
15246:
15242:
15215:
15211:
15196:10.2307/2841583
15176:
15172:
15167:(830): 507–510.
15153:
15149:
15099:
15095:
15082:
15081:
15077:
15068:
15067:
15063:
15058:
15053:
15044:
15040:
15013:
15009:
15005:
14890:
14883:
14880:
14869:
14857:
14842:CorrelationTest
14841:
14835:
14824:
14811:
14795:
14790:
14783:
14745:
14741:
14737:
14727:
14726:
14722:
14708:
14705:
14704:
14674:
14670:
14660:
14646:
14643:
14642:
14606:represents the
14602:
14598:
14595:
14593:
14564:
14560:
14556:
14546:
14545:
14541:
14527:
14524:
14523:
14496:
14492:
14482:
14468:
14465:
14464:
14410:
14406:
14404:
14401:
14400:
14369:
14365:
14363:
14360:
14359:
14340:
14334:
14288:
14259:
14257:
14254:
14253:
14216:
14214:
14211:
14210:
14191:
14188:
14187:
14162:
14160:
14157:
14156:
14138:
14135:
14134:
14109:
14107:
14104:
14103:
14079:
14076:
14075:
14044:
14042:
14039:
14038:
14020:
14017:
14016:
13991:
13989:
13986:
13985:
13967:
13964:
13963:
13938:
13936:
13933:
13932:
13894:
13877:
13861:
13844:
13821:
13820:
13818:
13789:
13787:
13784:
13783:
13764:
13761:
13760:
13744:
13741:
13740:
13737:
13724:
13718:
13679:
13678:
13676:
13673:
13672:
13650:
13649:
13647:
13644:
13643:
13618:
13614:
13603:
13602:
13593:
13589:
13574:
13563:
13557:
13549:
13545:
13534:
13533:
13524:
13520:
13505:
13494:
13488:
13487:
13472:
13471:
13462:
13458:
13435:
13434:
13425:
13421:
13406:
13395:
13390:
13388:
13379:
13375:
13373:
13370:
13369:
13350:
13348:
13339:
13328:
13319:
13307:
13301:
13280:
13268:
13264:
13259:
13238:
13234:
13232:
13229:
13228:
13191:
13187:
13166:
13162:
13160:
13157:
13156:
13138:
13117:
13114:
13113:
13094:
13091:
13090:
13073:
13069:
13067:
13064:
13063:
13040:
13036:
13030:
13019:
13005:
12996:
12985:
12984:
12983:
12981:
12978:
12977:
12957:
12946:
12945:
12944:
12942:
12939:
12938:
12907:
12903:
12889:
12886:
12885:
12866:
12863:
12862:
12846:
12843:
12842:
12826:
12823:
12822:
12812:
12806:
12775:
12770:
12760:
12756:
12741:
12736:
12726:
12722:
12708:
12704:
12698:
12694:
12688:
12684:
12680:
12678:
12660:
12656:
12651:
12648:
12647:
12615:
12610:
12591:
12586:
12568:
12564:
12558:
12554:
12550:
12548:
12536:
12532:
12527:
12524:
12523:
12444:
12440:
12410:
12406:
12379:
12375:
12348:
12344:
12342:
12339:
12338:
12305:
12301:
12288:
12287:
12274:
12270:
12257:
12256:
12230:
12229:
12228:
12226:
12199:
12195:
12193:
12190:
12189:
12183:
12077:
12075:
12043:
12040:
12039:
12014:
12010:
12004:
11999:
11965:
11961:
11925:
11921:
11909:
11905:
11899:
11894:
11892:
11860:
11857:
11856:
11831:
11827:
11821:
11816:
11809:
11805:
11799:
11795:
11789:
11784:
11782:
11756:
11753:
11752:
11751:Weighted mean:
11725:
11716:
11709:
11703:
11666:
11641:
11637:
11627:
11625:
11617:
11608:
11604:
11602:
11599:
11598:
11581:
11577:
11576:
11575:
11572:
11566:
11560:
11557:
11551:
11538:
11532:
11527:
11521:
11497:
11494:
11493:
11439:
11432:
11428:
11421:
11419:
11412:
11408:
11396:
11392:
11390:
11387:
11386:
11335:
11323:
11318:
11307:
11303:
11297:
11293:
11292:
11290:
11281:
11277:
11256:
11255:
11247:
11244:
11243:
11234:
11231:
11225:
11172:
11168:
11162:
11159:
11158:
11156:
11153:
11152:
11128:
11125:
11124:
11080:
11076:
11051:
11049:
11036:
11023:
11022:
11018:
11011:
11007:
11001:
10998:
10997:
10984:
10980:
10978:
10975:
10974:
10966:
10960:
10938:
10935:
10934:
10930:
10899:
10887:
10883:
10876:
10872:
10868:
10866:
10846:
10837:
10836:
10834:
10831:
10830:
10823:
10819:
10811:
10807:
10804:
10796:
10790:
10763:exchangeability
10702:
10641:
10595:
10590:
10584:
10554:
10549:
10548:
10546:
10543:
10542:
10521:
10516:
10515:
10513:
10510:
10509:
10488:
10484:
10473:
10472:
10463:
10459:
10450:
10437:
10432:
10431:
10429:
10426:
10425:
10407:
10403:
10392:
10391:
10382:
10371:
10370:
10369:
10360:
10347:
10342:
10341:
10339:
10336:
10335:
10310:
10305:
10304:
10298:
10293:
10292:
10290:
10281:
10277:
10266:
10265:
10251:
10248:
10247:
10223:
10219:
10213:
10202:
10201:
10200:
10191:
10187:
10178:
10166:
10164:
10161:
10160:
10155:
10148:
10139:
10101:
10100:
10091:
10080:
10079:
10078:
10066:
10055:
10054:
10053:
10044:
10040:
10031:
10025:
10022:
10021:
9990:
9986:
9975:
9974:
9960:
9957:
9956:
9933:
9929:
9918:
9917:
9908:
9904:
9895:
9890:
9883:
9879:
9868:
9867:
9858:
9847:
9846:
9845:
9836:
9831:
9829:
9820:
9816:
9805:
9804:
9790:
9787:
9786:
9766:
9765:
9752:
9748:
9737:
9736:
9727:
9723:
9714:
9709:
9702:
9698:
9687:
9686:
9677:
9666:
9665:
9664:
9655:
9650:
9647:
9638:
9637:
9628:
9624:
9613:
9612:
9603:
9592:
9591:
9590:
9581:
9568:
9564:
9553:
9552:
9543:
9539:
9530:
9518:
9514:
9503:
9502:
9493:
9482:
9481:
9480:
9471:
9466:
9464:
9455:
9454:
9445:
9441:
9430:
9429:
9420:
9409:
9408:
9407:
9398:
9385:
9381:
9370:
9369:
9360:
9356:
9347:
9332:
9328:
9317:
9316:
9307:
9296:
9295:
9294:
9274:
9273:
9264:
9253:
9252:
9251:
9239:
9228:
9227:
9226:
9217:
9213:
9201:
9196:
9194:
9185:
9184:
9175:
9171:
9160:
9159:
9150:
9139:
9138:
9137:
9128:
9115:
9111:
9100:
9099:
9090:
9086:
9077:
9057:
9056:
9047:
9036:
9035:
9034:
9017:
9016:
9007:
8996:
8995:
8994:
8985:
8974:
8973:
8972:
8963:
8959:
8950:
8945:
8943:
8934:
8933:
8924:
8920:
8909:
8908:
8899:
8888:
8887:
8886:
8877:
8864:
8860:
8849:
8848:
8839:
8835:
8826:
8806:
8805:
8796:
8785:
8784:
8783:
8766:
8765:
8756:
8752:
8743:
8738:
8736:
8729:
8715:
8714:
8698:
8696:
8693:
8692:
8672:
8661:
8660:
8659:
8650:
8646:
8644:
8641:
8640:
8623:
8612:
8611:
8610:
8608:
8605:
8604:
8559:
8555:
8544:
8543:
8534:
8530:
8521:
8516:
8509:
8505:
8494:
8493:
8484:
8473:
8472:
8471:
8462:
8457:
8455:
8443:
8439:
8428:
8427:
8418:
8414:
8405:
8400:
8393:
8389:
8383:
8372:
8371:
8370:
8361:
8357:
8348:
8343:
8341:
8333:
8330:
8329:
8309:
8298:
8297:
8296:
8294:
8291:
8290:
8267:
8263:
8252:
8251:
8242:
8231:
8230:
8229:
8220:
8207:
8203:
8197:
8186:
8185:
8184:
8175:
8171:
8162:
8149:
8145:
8134:
8133:
8124:
8120:
8111:
8105:
8102:
8101:
8096:
8072:
8061:
8060:
8059:
8044:
8033:
8032:
8031:
8029:
8026:
8025:
8008:
8004:
7989:
7985:
7983:
7980:
7979:
7956:
7949:
7921:
7913:
7910:
7909:
7881:
7873:
7870:
7869:
7832:
7822:
7818:
7814:
7776:
7766:
7762:
7758:
7714:
7691:
7688:
7687:
7662:
7652:
7648:
7644:
7597:
7574:
7571:
7570:
7550:
7547:
7546:
7530:
7508:
7505:
7504:
7471:
7467:
7459:
7456:
7455:
7452:null hypothesis
7424:
7412:
7408:
7370:
7363:
7361:
7353:
7350:
7349:
7322:
7318:
7316:
7313:
7312:
7296:
7293:
7292:
7276:
7273:
7272:
7233:
7225:
7220:
7217:
7216:
7209:
7161:
7159:
7156:
7155:
7092:
7081:
7079:
7075:
7056:
7039:
7036:
7035:
7014:
7011:
7010:
6987:
6981:
6942:
6939:
6938:
6922:
6919:
6918:
6880:
6877:
6862:
6841:
6823:
6822:
6818:
6792:
6790:
6772:
6768:
6767:
6747:
6745:
6734:
6730:
6723:
6719:
6718:
6698:
6696:
6685:
6681:
6674:
6670:
6669:
6651:
6644:
6640:
6627:
6626:
6588:
6586:
6563:
6560:
6559:
6546:
6517:
6515:
6512:
6511:
6467:
6464:
6449:
6448:
6444:
6443:
6442:
6433:
6432:
6431:
6414:
6412:
6401:
6397:
6390:
6386:
6385:
6383:
6366:
6363:
6362:
6329:
6326:
6325:
6274:
6269:
6268:
6262:
6260:
6259:
6257:
6254:
6253:
6233:
6230:
6229:
6178:
6145:
6130:
6115:
6114:
6110:
6109:
6108:
6102:
6097:
6096:
6090:
6088:
6087:
6072:
6065:
6061:
6027:
6020:
6016:
6015:
6014:
6006:
5995:
5994:
5976:
5974:
5963:
5959:
5952:
5948:
5947:
5930:
5928:
5917:
5913:
5906:
5902:
5901:
5881:
5864:
5862:
5845:
5842:
5841:
5819:
5774:
5770:
5752:
5744:
5741:
5740:
5705:
5701:
5694:
5683:
5680:
5666:
5662:
5657:
5649:
5646:
5645:
5607:
5582:
5579:
5578:
5562:
5559:
5558:
5530:
5523:
5519:
5512:
5509:
5500:
5496:
5494:
5491:
5490:
5467:
5464:
5463:
5447:
5444:
5443:
5440:
5401:
5392:
5374:
5295:
5286:
5277:
5268:
5251:
5220:null hypothesis
5212:
5151:
5147:
5139:
5131:
5128:
5127:
5108:
5077:
5073:
5054:
5047:
5046:
5041:
5026:
5022:
5013:
5009:
5008:
5002:
4994:
4993:
4991:
4977:
4974:
4973:
4963:
4956:
4948:
4936:
4922:
4888:
4881:
4880:
4875:
4860:
4856:
4847:
4843:
4842:
4836:
4828:
4827:
4825:
4811:
4808:
4807:
4782:
4775:
4718:
4711:
4704:
4676:
4664:
4656:
4644:
4629:
4617:
4609:
4597:
4590:
4535:
4526:
4513:
4504:
4495:
4486:
4471:
4469:
4456:
4454:
4445:
4407:
4385:
4359:
4345:
4310:
4276:
4253:
4252:
4246:
4241:
4235:
4229:
4225:
4219:
4215:
4203:
4199:
4196:
4195:
4189:
4185:
4179:
4175:
4163:
4159:
4157:
4151:
4146:
4135:
4134:
4126:
4123:
4122:
4106:
4103:
4102:
4064:
4061:
4060:
4057:
4034:
4030:
4028:
4025:
4024:
4001:
3997:
3986:
3985:
3976:
3972:
3963:
3952:
3935:
3930:
3928:
3919:
3915:
3913:
3910:
3909:
3885:
3884:
3870:
3869:
3860:
3856:
3847:
3843:
3835:
3832:
3831:
3805:
3801:
3795:
3791:
3775:
3763:
3762:
3751:
3750:
3738:
3734:
3728:
3724:
3720:
3718:
3706:
3702:
3700:
3697:
3696:
3673:
3669:
3667:
3664:
3663:
3643:
3639:
3637:
3634:
3633:
3613:
3610:
3609:
3586:
3582:
3570:
3569:
3560:
3556:
3555:
3553:
3549:
3547:
3544:
3543:
3524:
3520:
3511:
3507:
3505:
3502:
3501:
3479:
3478:
3464:
3463:
3454:
3450:
3441:
3437:
3429:
3426:
3425:
3396:
3392:
3380:
3379:
3370:
3366:
3365:
3363:
3359:
3347:
3343:
3331:
3330:
3321:
3317:
3316:
3314:
3310:
3304:
3293:
3276:
3271:
3259:
3255:
3253:
3250:
3249:
3243:standard scores
3222:
3218:
3216:
3213:
3212:
3185:
3181:
3172:
3168:
3160:
3157:
3156:
3128:
3117:
3113:
3109:
3105:
3104:
3095:
3090:
3078:
3067:
3056:
3052:
3048:
3044:
3043:
3034:
3029:
3017:
3016:
3009:
3005:
2996:
2992:
2980:
2976:
2970:
2966:
2959:
2957:
2945:
2941:
2939:
2936:
2935:
2912:
2908:
2906:
2903:
2902:
2877:
2876:
2862:
2861:
2852:
2848:
2839:
2835:
2827:
2824:
2823:
2795:
2784:
2783:
2782:
2770:
2765:
2755:
2749:
2738:
2727:
2726:
2725:
2713:
2708:
2698:
2692:
2691:
2679:
2678:
2667:
2666:
2654:
2650:
2644:
2640:
2634:
2629:
2627:
2615:
2611:
2609:
2606:
2605:
2582:
2578:
2576:
2573:
2572:
2546:
2545:
2543:
2540:
2539:
2522:
2518:
2512:
2501:
2487:
2473:
2472:
2470:
2467:
2466:
2444:
2440:
2431:
2427:
2425:
2422:
2421:
2403:
2400:
2399:
2372:
2368:
2357:
2356:
2347:
2343:
2334:
2323:
2317:
2309:
2305:
2294:
2293:
2284:
2280:
2271:
2260:
2254:
2253:
2238:
2237:
2228:
2224:
2207:
2206:
2197:
2193:
2184:
2173:
2168:
2166:
2154:
2150:
2148:
2145:
2144:
2122:
2118:
2116:
2113:
2112:
2096:
2093:
2092:
2067:
2063:
2054:
2050:
2029:
2025:
2016:
2012:
2008:
2004:
2002:
1999:
1998:
1978:
1974:
1972:
1969:
1968:
1940:
1936:
1934:
1931:
1930:
1923:
1894:
1869:
1868:
1867:
1863:
1862:
1847:
1843:
1841:
1837:
1828:
1827:
1825:
1814:
1789:
1788:
1787:
1783:
1782:
1767:
1763:
1761:
1757:
1748:
1747:
1745:
1744:
1723:
1722:
1702:
1701:
1674:
1673:
1672:
1670:
1655:
1651:
1649:
1646:
1645:
1629:
1626:
1625:
1608:
1607:
1583:
1582:
1562:
1561:
1534:
1533:
1501:
1500:
1493:
1489:
1464:
1463:
1456:
1452:
1439:
1438:
1420:
1416:
1409:
1405:
1394:
1390:
1383:
1379:
1366:
1365:
1361:
1360:
1354:
1329:
1328:
1326:
1322:
1321:
1306:
1302:
1300:
1296:
1287:
1286:
1271:
1248:
1247:
1240:
1236:
1235:
1233:
1229:
1220:
1219:
1217:
1215:
1206:
1201:
1194:
1193:
1187:
1162:
1161:
1160:
1156:
1155:
1140:
1136:
1134:
1130:
1121:
1120:
1105:
1082:
1081:
1074:
1070:
1069:
1067:
1063:
1054:
1053:
1051:
1049:
1040:
1035:
1028:
1027:
1007:
1006:
1004:
1002:
993:
989:
986:
985:
965:
964:
962:
960:
951:
947:
943:
941:
938:
937:
918:
915:
914:
893:
892:
890:
887:
886:
869:
866:
865:
864:is the mean of
848:
844:
842:
839:
838:
821:
818:
817:
816:is the mean of
800:
796:
794:
791:
790:
771:
767:
765:
762:
761:
744:
740:
738:
735:
734:
709:
705:
699:
695:
694:
681:
677:
659:
655:
634:
633:
632:
630:
615:
611:
609:
606:
605:
587:
584:
583:
554:
550:
532:
528:
507:
506:
480:
477:
476:
431:
428:
427:
407:
404:
403:
386:
382:
380:
377:
376:
359:
356:
355:
334:
330:
328:
325:
324:
303:
300:
299:
274:
270:
264:
260:
259:
236:
234:
219:
215:
213:
210:
209:
175:
172:
171:
152:
132:
120:Auguste Bravais
108:
24:
17:
12:
11:
5:
19305:
19295:
19294:
19289:
19284:
19267:
19266:
19264:
19263:
19257:
19254:
19253:
19251:
19250:
19245:
19240:
19234:
19232:
19228:
19227:
19225:
19224:
19219:
19213:
19211:
19205:
19204:
19202:
19201:
19196:
19190:
19188:
19184:
19183:
19181:
19180:
19175:
19169:
19167:
19161:
19160:
19158:
19157:
19152:
19147:
19141:
19139:
19133:
19132:
19130:
19129:
19124:
19119:
19113:
19111:
19105:
19104:
19102:
19101:
19096:
19091:
19086:
19081:
19076:
19071:
19066:
19064:Davies-Bouldin
19061:
19056:
19050:
19048:
19042:
19041:
19039:
19038:
19033:
19028:
19023:
19018:
19013:
19008:
19003:
18998:
18993:
18988:
18982:
18980:
18978:Classification
18974:
18973:
18971:
18970:
18965:
18960:
18955:
18950:
18945:
18940:
18935:
18930:
18925:
18920:
18914:
18912:
18906:
18905:
18897:
18896:
18889:
18882:
18874:
18865:
18864:
18862:
18861:
18849:
18837:
18823:
18810:
18807:
18806:
18803:
18802:
18799:
18798:
18796:
18795:
18790:
18785:
18780:
18775:
18769:
18767:
18761:
18760:
18758:
18757:
18752:
18747:
18742:
18737:
18732:
18727:
18722:
18717:
18712:
18706:
18704:
18698:
18697:
18695:
18694:
18689:
18684:
18675:
18670:
18665:
18659:
18657:
18651:
18650:
18648:
18647:
18642:
18637:
18628:
18626:Bioinformatics
18622:
18620:
18610:
18609:
18597:
18596:
18593:
18592:
18589:
18588:
18585:
18584:
18582:
18581:
18575:
18573:
18569:
18568:
18566:
18565:
18559:
18557:
18551:
18550:
18548:
18547:
18542:
18537:
18532:
18526:
18524:
18515:
18509:
18508:
18505:
18504:
18502:
18501:
18496:
18491:
18486:
18481:
18475:
18473:
18467:
18466:
18464:
18463:
18458:
18453:
18445:
18440:
18435:
18434:
18433:
18431:partial (PACF)
18422:
18420:
18414:
18413:
18411:
18410:
18405:
18400:
18392:
18387:
18381:
18379:
18378:Specific tests
18375:
18374:
18372:
18371:
18366:
18361:
18356:
18351:
18346:
18341:
18336:
18330:
18328:
18321:
18315:
18314:
18312:
18311:
18310:
18309:
18308:
18307:
18292:
18291:
18290:
18280:
18278:Classification
18275:
18270:
18265:
18260:
18255:
18250:
18244:
18242:
18236:
18235:
18233:
18232:
18227:
18225:McNemar's test
18222:
18217:
18212:
18207:
18201:
18199:
18189:
18188:
18164:
18163:
18160:
18159:
18156:
18155:
18153:
18152:
18147:
18142:
18137:
18131:
18129:
18123:
18122:
18120:
18119:
18103:
18097:
18095:
18089:
18088:
18086:
18085:
18080:
18075:
18070:
18065:
18063:Semiparametric
18060:
18055:
18049:
18047:
18043:
18042:
18040:
18039:
18034:
18029:
18024:
18018:
18016:
18010:
18009:
18007:
18006:
18001:
17996:
17991:
17986:
17980:
17978:
17972:
17971:
17969:
17968:
17963:
17958:
17953:
17947:
17945:
17935:
17934:
17931:
17930:
17925:
17919:
17911:
17910:
17907:
17906:
17903:
17902:
17900:
17899:
17898:
17897:
17887:
17882:
17877:
17876:
17875:
17870:
17859:
17857:
17851:
17850:
17847:
17846:
17844:
17843:
17838:
17837:
17836:
17828:
17820:
17804:
17801:(Mann–Whitney)
17796:
17795:
17794:
17781:
17780:
17779:
17768:
17766:
17760:
17759:
17757:
17756:
17755:
17754:
17749:
17744:
17734:
17729:
17726:(Shapiro–Wilk)
17721:
17716:
17711:
17706:
17701:
17693:
17687:
17685:
17679:
17678:
17676:
17675:
17667:
17658:
17646:
17640:
17638:Specific tests
17634:
17633:
17630:
17629:
17627:
17626:
17621:
17616:
17610:
17608:
17602:
17601:
17599:
17598:
17593:
17592:
17591:
17581:
17580:
17579:
17569:
17563:
17561:
17555:
17554:
17552:
17551:
17550:
17549:
17544:
17534:
17529:
17524:
17519:
17514:
17508:
17506:
17500:
17499:
17497:
17496:
17491:
17490:
17489:
17484:
17483:
17482:
17477:
17462:
17461:
17460:
17455:
17450:
17445:
17434:
17432:
17423:
17417:
17416:
17414:
17413:
17408:
17403:
17402:
17401:
17391:
17386:
17385:
17384:
17374:
17373:
17372:
17367:
17362:
17352:
17347:
17342:
17341:
17340:
17335:
17330:
17314:
17313:
17312:
17307:
17302:
17292:
17291:
17290:
17285:
17275:
17274:
17273:
17263:
17262:
17261:
17251:
17246:
17241:
17235:
17233:
17223:
17222:
17210:
17209:
17206:
17205:
17202:
17201:
17199:
17198:
17193:
17188:
17183:
17177:
17175:
17169:
17168:
17166:
17165:
17160:
17155:
17149:
17147:
17143:
17142:
17140:
17139:
17134:
17129:
17124:
17119:
17114:
17109:
17103:
17101:
17095:
17094:
17092:
17091:
17089:Standard error
17086:
17081:
17076:
17075:
17074:
17069:
17058:
17056:
17050:
17049:
17047:
17046:
17041:
17036:
17031:
17026:
17021:
17019:Optimal design
17016:
17011:
17005:
17003:
16993:
16992:
16980:
16979:
16976:
16975:
16972:
16971:
16969:
16968:
16963:
16958:
16953:
16948:
16943:
16938:
16933:
16928:
16923:
16918:
16913:
16908:
16903:
16898:
16892:
16890:
16884:
16883:
16881:
16880:
16875:
16874:
16873:
16868:
16858:
16853:
16847:
16845:
16839:
16838:
16836:
16835:
16830:
16825:
16819:
16817:
16816:Summary tables
16813:
16812:
16810:
16809:
16803:
16801:
16795:
16794:
16791:
16790:
16788:
16787:
16786:
16785:
16780:
16775:
16765:
16759:
16757:
16751:
16750:
16748:
16747:
16742:
16737:
16732:
16727:
16722:
16717:
16711:
16709:
16703:
16702:
16700:
16699:
16694:
16689:
16688:
16687:
16682:
16677:
16672:
16667:
16662:
16657:
16652:
16650:Contraharmonic
16647:
16642:
16631:
16629:
16620:
16610:
16609:
16597:
16596:
16594:
16593:
16588:
16582:
16579:
16578:
16571:
16570:
16563:
16556:
16548:
16542:
16541:
16532:
16531:– large table.
16516:
16504:
16491:
16476:
16475:External links
16473:
16470:
16469:
16462:
16444:
16423:(13): 130401.
16403:
16392:(2): 913–923.
16372:
16358:
16338:
16282:
16262:
16212:
16198:
16180:
16158:(1): 201–211.
16138:
16119:(2): 193–232.
16103:
16075:
16068:
16040:
16025:
16006:(3): 531–545.
15987:
15969:
15927:
15918:|journal=
15881:
15862:
15847:
15828:(2): 193–232.
15812:
15759:
15748:(4): 328–413.
15723:
15702:
15689:
15664:
15637:(161): 31–34.
15617:
15599:
15592:
15574:
15559:
15540:(4): 311–313.
15524:
15482:
15457:
15432:
15421:(3): 281–288.
15405:
15398:
15370:
15344:
15322:
15303:
15281:
15240:
15209:
15170:
15147:
15093:
15075:
15060:
15059:
15057:
15054:
15052:
15051:
15038:
15014:Also known as
15006:
15004:
15001:
15000:
14999:
14994:
14992:RV coefficient
14989:
14984:
14979:
14974:
14969:
14964:
14959:
14954:
14949:
14947:Disattenuation
14944:
14939:
14934:
14929:
14924:
14923:
14922:
14917:
14907:
14902:
14896:
14895:
14879:
14876:
14875:
14874:
14862:
14846:
14828:
14816:
14812:pearsonr(x, y)
14800:
14796:cor.test(x, y)
14782:
14779:
14771:
14770:
14759:
14752:
14749:
14744:
14740:
14736:
14730:
14725:
14721:
14718:
14715:
14712:
14702:
14691:
14688:
14683:
14680:
14677:
14673:
14667:
14664:
14659:
14656:
14653:
14650:
14590:
14589:
14578:
14571:
14568:
14563:
14559:
14555:
14549:
14544:
14540:
14537:
14534:
14531:
14521:
14510:
14505:
14502:
14499:
14495:
14489:
14486:
14481:
14478:
14475:
14472:
14419:
14416:
14413:
14409:
14378:
14375:
14372:
14368:
14336:Main article:
14333:
14326:
14313:
14310:
14307:
14304:
14301:
14297:
14294:
14291:
14287:
14284:
14281:
14278:
14275:
14272:
14268:
14265:
14262:
14241:
14238:
14235:
14232:
14229:
14225:
14222:
14219:
14208:
14207:
14195:
14175:
14172:
14169:
14165:
14154:
14142:
14122:
14119:
14116:
14112:
14101:
14089:
14086:
14083:
14063:
14060:
14057:
14054:
14051:
14047:
14036:
14024:
14004:
14001:
13998:
13994:
13983:
13971:
13951:
13948:
13945:
13941:
13926:
13925:
13914:
13907:
13904:
13901:
13897:
13893:
13890:
13887:
13884:
13880:
13874:
13871:
13868:
13864:
13860:
13857:
13854:
13851:
13847:
13843:
13840:
13837:
13834:
13831:
13828:
13824:
13817:
13814:
13811:
13808:
13805:
13802:
13798:
13795:
13792:
13768:
13748:
13736:
13733:
13720:Main article:
13717:
13714:
13702:circular means
13686:
13683:
13657:
13654:
13640:
13639:
13621:
13617:
13610:
13607:
13601:
13596:
13592:
13588:
13585:
13582:
13577:
13572:
13569:
13566:
13562:
13552:
13548:
13541:
13538:
13532:
13527:
13523:
13519:
13516:
13513:
13508:
13503:
13500:
13497:
13493:
13485:
13479:
13476:
13470:
13465:
13461:
13457:
13454:
13451:
13448:
13442:
13439:
13433:
13428:
13424:
13420:
13417:
13414:
13409:
13404:
13401:
13398:
13394:
13387:
13378:
13344:
13337:
13324:
13317:
13309:For variables
13300:
13297:
13283:
13277:
13274:
13271:
13267:
13262:
13258:
13255:
13252:
13247:
13244:
13241:
13237:
13217:
13216:
13205:
13200:
13197:
13194:
13190:
13186:
13183:
13180:
13175:
13172:
13169:
13165:
13137:
13134:
13121:
13098:
13076:
13072:
13060:
13059:
13048:
13043:
13039:
13033:
13028:
13025:
13022:
13018:
13012:
13009:
13004:
12999:
12992:
12989:
12960:
12953:
12950:
12935:
12934:
12923:
12919:
12914:
12911:
12906:
12902:
12899:
12896:
12893:
12870:
12850:
12830:
12808:Main article:
12805:
12802:
12801:
12800:
12789:
12783:
12778:
12773:
12769:
12763:
12759:
12755:
12752:
12749:
12744:
12739:
12735:
12729:
12725:
12721:
12718:
12711:
12707:
12701:
12697:
12691:
12687:
12683:
12677:
12672:
12669:
12666:
12663:
12659:
12655:
12641:
12640:
12629:
12623:
12618:
12613:
12609:
12605:
12602:
12599:
12594:
12589:
12585:
12581:
12578:
12571:
12567:
12561:
12557:
12553:
12547:
12542:
12539:
12535:
12531:
12513:
12512:
12501:
12498:
12495:
12492:
12489:
12486:
12483:
12479:
12476:
12473:
12470:
12467:
12464:
12461:
12458:
12455:
12452:
12447:
12443:
12439:
12436:
12433:
12430:
12427:
12424:
12421:
12418:
12413:
12409:
12405:
12402:
12399:
12396:
12393:
12390:
12387:
12382:
12378:
12374:
12371:
12368:
12365:
12362:
12359:
12356:
12351:
12347:
12332:
12331:
12320:
12314:
12308:
12304:
12299:
12296:
12291:
12286:
12283:
12277:
12273:
12268:
12265:
12260:
12253:
12249:
12245:
12241:
12238:
12233:
12225:
12222:
12219:
12216:
12213:
12210:
12207:
12202:
12198:
12182:
12179:
12178:
12177:
12166:
12160:
12157:
12154:
12151:
12148:
12145:
12142:
12139:
12136:
12133:
12130:
12127:
12124:
12121:
12118:
12115:
12112:
12109:
12104:
12101:
12098:
12095:
12092:
12089:
12086:
12083:
12080:
12074:
12071:
12068:
12065:
12062:
12059:
12056:
12053:
12050:
12047:
12036:
12025:
12017:
12013:
12007:
12003:
11997:
11994:
11991:
11988:
11985:
11982:
11979:
11976:
11973:
11968:
11964:
11960:
11957:
11954:
11951:
11948:
11945:
11942:
11939:
11936:
11933:
11928:
11924:
11920:
11917:
11912:
11908:
11902:
11898:
11891:
11888:
11885:
11882:
11879:
11876:
11873:
11870:
11867:
11864:
11853:
11842:
11834:
11830:
11824:
11820:
11812:
11808:
11802:
11798:
11792:
11788:
11781:
11778:
11775:
11772:
11769:
11766:
11763:
11760:
11724:
11721:
11707:
11701:
11700:
11689:
11681:
11678:
11675:
11672:
11669:
11664:
11661:
11658:
11655:
11652:
11649:
11644:
11640:
11636:
11633:
11630:
11624:
11621:
11616:
11607:
11592:
11591:
11570:
11564:
11555:
11549:
11536:
11530:
11525:
11519:
11507:
11504:
11501:
11479:
11478:
11469:
11467:
11456:
11452:
11445:
11442:
11435:
11431:
11427:
11424:
11418:
11415:
11411:
11407:
11404:
11395:
11370:
11369:
11360:
11358:
11347:
11341:
11338:
11332:
11326:
11317:
11313:
11310:
11306:
11296:
11289:
11280:
11276:
11273:
11270:
11267:
11264:
11259:
11254:
11251:
11229:
11222:
11221:
11205:
11202:
11199:
11196:
11193:
11190:
11187:
11184:
11181:
11175:
11171:
11165:
11161:
11150:
11138:
11135:
11132:
11116:
11115:
11106:
11104:
11093:
11089:
11083:
11079:
11075:
11072:
11069:
11064:
11060:
11057:
11054:
11048:
11043:
11040:
11035:
11030:
11027:
11021:
11014:
11010:
11004:
11000:
10995:
10992:
10983:
10964:
10957:
10956:
10945:
10942:
10917:
10914:
10911:
10905:
10902:
10896:
10890:
10886:
10882:
10879:
10875:
10871:
10865:
10862:
10859:
10855:
10852:
10849:
10845:
10840:
10803:
10800:
10789:
10786:
10759:non-parametric
10701:
10698:
10697:
10696:
10689:
10678:
10667:
10664:
10654:asymptotically
10640:
10637:
10605:for which the
10594:
10591:
10583:
10580:
10578:of the data).
10506:
10505:
10491:
10487:
10480:
10477:
10471:
10466:
10462:
10458:
10453:
10449:
10445:
10423:
10410:
10406:
10399:
10396:
10390:
10385:
10378:
10375:
10368:
10363:
10359:
10355:
10329:
10328:
10289:
10284:
10280:
10273:
10270:
10264:
10261:
10258:
10255:
10241:
10240:
10226:
10222:
10216:
10209:
10206:
10199:
10194:
10190:
10186:
10181:
10177:
10173:
10153:
10146:
10132:
10131:
10120:
10117:
10114:
10108:
10105:
10099:
10094:
10087:
10084:
10077:
10074:
10069:
10062:
10059:
10052:
10047:
10043:
10039:
10034:
10030:
9993:
9989:
9982:
9979:
9973:
9970:
9967:
9964:
9953:
9952:
9936:
9932:
9925:
9922:
9916:
9911:
9907:
9903:
9898:
9894:
9886:
9882:
9875:
9872:
9866:
9861:
9854:
9851:
9844:
9839:
9835:
9828:
9823:
9819:
9812:
9809:
9803:
9800:
9797:
9794:
9780:
9779:
9764:
9755:
9751:
9744:
9741:
9735:
9730:
9726:
9722:
9717:
9713:
9705:
9701:
9694:
9691:
9685:
9680:
9673:
9670:
9663:
9658:
9654:
9646:
9643:
9641:
9639:
9631:
9627:
9620:
9617:
9611:
9606:
9599:
9596:
9589:
9584:
9580:
9576:
9571:
9567:
9560:
9557:
9551:
9546:
9542:
9538:
9533:
9529:
9521:
9517:
9510:
9507:
9501:
9496:
9489:
9486:
9479:
9474:
9470:
9463:
9460:
9458:
9456:
9448:
9444:
9437:
9434:
9428:
9423:
9416:
9413:
9406:
9401:
9397:
9393:
9388:
9384:
9377:
9374:
9368:
9363:
9359:
9355:
9350:
9346:
9340:
9335:
9331:
9324:
9321:
9315:
9310:
9303:
9300:
9293:
9290:
9287:
9281:
9278:
9272:
9267:
9260:
9257:
9250:
9247:
9242:
9235:
9232:
9225:
9220:
9216:
9212:
9209:
9204:
9200:
9193:
9190:
9188:
9186:
9178:
9174:
9167:
9164:
9158:
9153:
9146:
9143:
9136:
9131:
9127:
9123:
9118:
9114:
9107:
9104:
9098:
9093:
9089:
9085:
9080:
9076:
9070:
9064:
9061:
9055:
9050:
9043:
9040:
9033:
9030:
9024:
9021:
9015:
9010:
9003:
9000:
8993:
8988:
8981:
8978:
8971:
8966:
8962:
8958:
8953:
8949:
8942:
8939:
8937:
8935:
8927:
8923:
8916:
8913:
8907:
8902:
8895:
8892:
8885:
8880:
8876:
8872:
8867:
8863:
8856:
8853:
8847:
8842:
8838:
8834:
8829:
8825:
8819:
8813:
8810:
8804:
8799:
8792:
8789:
8782:
8779:
8773:
8770:
8764:
8759:
8755:
8751:
8746:
8742:
8735:
8732:
8730:
8728:
8722:
8719:
8713:
8710:
8707:
8704:
8701:
8700:
8675:
8668:
8665:
8658:
8653:
8649:
8626:
8619:
8616:
8582:
8581:
8570:
8562:
8558:
8551:
8548:
8542:
8537:
8533:
8529:
8524:
8520:
8512:
8508:
8501:
8498:
8492:
8487:
8480:
8477:
8470:
8465:
8461:
8454:
8446:
8442:
8435:
8432:
8426:
8421:
8417:
8413:
8408:
8404:
8396:
8392:
8386:
8379:
8376:
8369:
8364:
8360:
8356:
8351:
8347:
8340:
8337:
8312:
8305:
8302:
8287:
8286:
8275:
8270:
8266:
8259:
8256:
8250:
8245:
8238:
8235:
8228:
8223:
8219:
8215:
8210:
8206:
8200:
8193:
8190:
8183:
8178:
8174:
8170:
8165:
8161:
8157:
8152:
8148:
8141:
8138:
8132:
8127:
8123:
8119:
8114:
8110:
8092:
8075:
8068:
8065:
8058:
8055:
8052:
8047:
8040:
8037:
8011:
8007:
8003:
8000:
7997:
7992:
7988:
7948:
7945:
7929:
7925:
7920:
7917:
7897:
7894:
7890:
7887:
7884:
7880:
7877:
7854:
7853:
7842:
7839:
7829:
7825:
7821:
7817:
7813:
7810:
7807:
7804:
7801:
7798:
7795:
7792:
7789:
7786:
7783:
7773:
7769:
7765:
7761:
7757:
7754:
7751:
7748:
7745:
7742:
7739:
7736:
7733:
7730:
7727:
7724:
7721:
7713:
7710:
7707:
7704:
7701:
7698:
7695:
7681:
7680:
7669:
7659:
7655:
7651:
7647:
7643:
7640:
7637:
7634:
7631:
7628:
7625:
7622:
7619:
7616:
7613:
7610:
7607:
7604:
7596:
7593:
7590:
7587:
7584:
7581:
7578:
7554:
7518:
7515:
7512:
7474:
7470:
7466:
7463:
7448:
7447:
7434:
7431:
7428:
7423:
7420:
7415:
7411:
7407:
7404:
7401:
7398:
7395:
7392:
7389:
7386:
7383:
7369:
7366:
7360:
7357:
7325:
7321:
7300:
7280:
7265:
7264:
7253:
7247:
7244:
7241:
7237:
7232:
7224:
7214:standard error
7198:
7195:
7192:
7189:
7186:
7183:
7180:
7177:
7174:
7171:
7168:
7138:
7137:
7126:
7123:
7120:
7117:
7114:
7111:
7107:
7101:
7098:
7095:
7090:
7087:
7084:
7078:
7074:
7071:
7064:
7061:
7055:
7052:
7049:
7046:
7043:
7018:
6983:Main article:
6980:
6977:
6964:
6961:
6958:
6955:
6952:
6949:
6946:
6926:
6903:
6896:
6892:
6889:
6886:
6883:
6876:
6870:
6867:
6861:
6858:
6855:
6849:
6846:
6840:
6837:
6831:
6828:
6821:
6817:
6814:
6808:
6804:
6801:
6798:
6795:
6788:
6784:
6781:
6778:
6775:
6771:
6766:
6760:
6756:
6753:
6750:
6743:
6737:
6733:
6729:
6726:
6722:
6717:
6711:
6707:
6704:
6701:
6694:
6688:
6684:
6680:
6677:
6673:
6664:
6658:
6655:
6650:
6647:
6643:
6639:
6634:
6631:
6624:
6621:
6618:
6615:
6612:
6609:
6606:
6603:
6600:
6597:
6594:
6591:
6585:
6582:
6579:
6576:
6573:
6570:
6567:
6545:
6542:
6520:
6508:
6507:
6496:
6487:
6480:
6476:
6473:
6470:
6463:
6457:
6454:
6447:
6441:
6436:
6427:
6423:
6420:
6417:
6410:
6404:
6400:
6396:
6393:
6389:
6382:
6379:
6376:
6373:
6370:
6339:
6336:
6333:
6306:
6303:
6300:
6297:
6294:
6291:
6288:
6285:
6282:
6277:
6272:
6265:
6250:gamma function
6237:
6226:
6225:
6211:
6207:
6204:
6201:
6198:
6195:
6192:
6186:
6183:
6177:
6174:
6171:
6168:
6165:
6162:
6159:
6153:
6150:
6144:
6138:
6135:
6129:
6123:
6120:
6113:
6105:
6100:
6093:
6079:
6076:
6071:
6068:
6064:
6060:
6057:
6054:
6051:
6048:
6042:
6035:
6032:
6026:
6023:
6019:
6013:
6009:
6002:
5999:
5989:
5985:
5982:
5979:
5972:
5966:
5962:
5958:
5955:
5951:
5943:
5939:
5936:
5933:
5926:
5920:
5916:
5912:
5909:
5905:
5900:
5897:
5894:
5891:
5888:
5884:
5879:
5876:
5873:
5870:
5867:
5861:
5858:
5855:
5852:
5849:
5818:
5815:
5797:
5796:
5785:
5777:
5773:
5769:
5766:
5763:
5760:
5756:
5751:
5748:
5726:
5725:
5708:
5704:
5700:
5697:
5692:
5689:
5686:
5679:
5676:
5669:
5665:
5661:
5656:
5653:
5606:
5599:
5586:
5566:
5555:
5554:
5539:
5536:
5533:
5526:
5522:
5518:
5515:
5508:
5503:
5499:
5484:standard error
5471:
5451:
5439:
5438:Standard error
5436:
5397:
5388:
5373:
5370:
5349:
5348:
5341:
5291:
5282:
5273:
5264:
5250:
5247:
5243:
5242:
5231:
5211:
5208:
5154:
5150:
5146:
5143:
5138:
5135:
5107:
5104:
5100:
5099:
5088:
5083:
5080:
5076:
5072:
5069:
5066:
5058:
5051:
5045:
5040:
5033:
5029:
5025:
5020:
5016:
5012:
5005:
5001:
4997:
4990:
4987:
4984:
4981:
4926:= 0.10 + 0.01
4915:
4914:
4903:
4900:
4892:
4885:
4879:
4874:
4867:
4863:
4859:
4854:
4850:
4846:
4839:
4835:
4831:
4824:
4821:
4818:
4815:
4672:
4652:
4625:
4605:
4589:
4586:
4585:
4584:
4581:
4578:
4575:
4572:
4569:
4566:
4563:
4560:
4557:
4554:
4551:
4548:
4538:absolute value
4531:
4522:
4509:
4500:
4491:
4482:
4465:
4450:
4406:
4405:Interpretation
4403:
4354:and transform
4309:
4306:
4275:
4272:
4257:
4249:
4244:
4240:
4236:
4232:
4228:
4222:
4218:
4212:
4209:
4206:
4202:
4198:
4197:
4192:
4188:
4182:
4178:
4172:
4169:
4166:
4162:
4158:
4154:
4149:
4145:
4141:
4140:
4138:
4133:
4130:
4110:
4080:
4077:
4074:
4071:
4068:
4056:
4053:
4052:
4051:
4037:
4033:
4004:
4000:
3993:
3990:
3984:
3979:
3975:
3971:
3966:
3961:
3958:
3955:
3951:
3944:
3941:
3938:
3934:
3927:
3922:
3918:
3907:
3892:
3889:
3883:
3877:
3874:
3868:
3863:
3859:
3855:
3850:
3846:
3842:
3839:
3825:
3824:
3808:
3804:
3798:
3794:
3790:
3787:
3784:
3781:
3778:
3770:
3767:
3758:
3755:
3749:
3746:
3741:
3737:
3731:
3727:
3723:
3717:
3712:
3709:
3705:
3679:
3676:
3672:
3649:
3646:
3642:
3630:
3629:
3617:
3596:
3589:
3585:
3577:
3574:
3568:
3563:
3559:
3552:
3541:
3527:
3523:
3519:
3514:
3510:
3486:
3483:
3477:
3471:
3468:
3462:
3457:
3453:
3449:
3444:
3440:
3436:
3433:
3419:
3418:
3406:
3399:
3395:
3387:
3384:
3378:
3373:
3369:
3362:
3357:
3350:
3346:
3338:
3335:
3329:
3324:
3320:
3313:
3307:
3302:
3299:
3296:
3292:
3285:
3282:
3279:
3275:
3270:
3265:
3262:
3258:
3228:
3225:
3221:
3188:
3184:
3180:
3175:
3171:
3167:
3164:
3153:
3152:
3141:
3131:
3126:
3120:
3116:
3112:
3108:
3103:
3098:
3093:
3089:
3085:
3082:
3070:
3065:
3059:
3055:
3051:
3047:
3042:
3037:
3032:
3028:
3024:
3021:
3012:
3008:
3004:
2999:
2995:
2991:
2988:
2983:
2979:
2973:
2969:
2965:
2962:
2956:
2951:
2948:
2944:
2918:
2915:
2911:
2884:
2881:
2875:
2869:
2866:
2860:
2855:
2851:
2847:
2842:
2838:
2834:
2831:
2820:
2819:
2808:
2798:
2791:
2788:
2781:
2778:
2773:
2768:
2764:
2758:
2754:
2741:
2734:
2731:
2724:
2721:
2716:
2711:
2707:
2701:
2697:
2686:
2683:
2674:
2671:
2665:
2662:
2657:
2653:
2647:
2643:
2637:
2633:
2626:
2621:
2618:
2614:
2588:
2585:
2581:
2569:
2568:
2553:
2550:
2525:
2521:
2515:
2510:
2507:
2504:
2500:
2494:
2491:
2486:
2480:
2477:
2464:
2447:
2443:
2439:
2434:
2430:
2419:
2418:is sample size
2407:
2375:
2371:
2364:
2361:
2355:
2350:
2346:
2342:
2337:
2332:
2329:
2326:
2322:
2312:
2308:
2301:
2298:
2292:
2287:
2283:
2279:
2274:
2269:
2266:
2263:
2259:
2251:
2245:
2242:
2236:
2231:
2227:
2223:
2220:
2214:
2211:
2205:
2200:
2196:
2192:
2187:
2182:
2179:
2176:
2172:
2165:
2160:
2157:
2153:
2141:is defined as
2128:
2125:
2121:
2100:
2091:consisting of
2079:
2075:
2070:
2066:
2062:
2057:
2053:
2049:
2046:
2043:
2040:
2037:
2032:
2028:
2024:
2019:
2015:
2011:
2007:
1984:
1981:
1977:
1946:
1943:
1939:
1922:
1919:
1907:
1897:
1892:
1888:
1884:
1880:
1877:
1872:
1866:
1861:
1857:
1850:
1846:
1840:
1836:
1831:
1817:
1812:
1808:
1804:
1800:
1797:
1792:
1786:
1781:
1777:
1770:
1766:
1760:
1756:
1751:
1742:
1738:
1734:
1731:
1726:
1721:
1717:
1713:
1710:
1705:
1700:
1697:
1693:
1689:
1685:
1682:
1677:
1669:
1664:
1661:
1658:
1654:
1633:
1622:
1621:
1606:
1602:
1598:
1594:
1591:
1586:
1581:
1577:
1573:
1570:
1565:
1560:
1557:
1553:
1549:
1545:
1542:
1537:
1532:
1529:
1524:
1520:
1516:
1512:
1509:
1504:
1499:
1496:
1492:
1487:
1483:
1479:
1475:
1472:
1467:
1462:
1459:
1455:
1450:
1447:
1442:
1437:
1434:
1429:
1423:
1419:
1415:
1412:
1408:
1403:
1397:
1393:
1389:
1386:
1382:
1377:
1374:
1369:
1364:
1362:
1357:
1352:
1348:
1344:
1340:
1337:
1332:
1325:
1320:
1316:
1309:
1305:
1299:
1295:
1290:
1285:
1281:
1274:
1269:
1265:
1262:
1259:
1256:
1251:
1246:
1243:
1239:
1232:
1228:
1223:
1218:
1214:
1209:
1204:
1200:
1196:
1195:
1190:
1185:
1181:
1177:
1173:
1170:
1165:
1159:
1154:
1150:
1143:
1139:
1133:
1129:
1124:
1119:
1115:
1108:
1103:
1099:
1096:
1093:
1090:
1085:
1080:
1077:
1073:
1066:
1062:
1057:
1052:
1048:
1043:
1038:
1034:
1030:
1029:
1026:
1022:
1018:
1015:
1010:
1005:
1001:
996:
992:
988:
987:
984:
980:
976:
973:
968:
963:
959:
954:
950:
946:
945:
922:
911:
910:
896:
884:
873:
851:
847:
836:
825:
803:
799:
788:
774:
770:
747:
743:
712:
708:
702:
698:
692:
689:
684:
680:
676:
673:
670:
667:
662:
658:
654:
651:
648:
645:
642:
637:
629:
624:
621:
618:
614:
591:
580:
579:
568:
565:
562:
557:
553:
549:
546:
543:
540:
535:
531:
527:
524:
521:
518:
515:
510:
505:
502:
499:
496:
493:
490:
487:
484:
453:
450:
447:
444:
441:
438:
435:
424:
423:
411:
389:
385:
374:
363:
337:
333:
322:
307:
277:
273:
267:
263:
257:
254:
251:
248:
245:
242:
239:
233:
228:
225:
222:
218:
191:
188:
185:
182:
179:
151:
148:
144:product-moment
131:
128:
116:Francis Galton
107:
104:
85:that measures
15:
9:
6:
4:
3:
2:
19304:
19293:
19290:
19288:
19285:
19283:
19280:
19279:
19277:
19262:
19259:
19258:
19255:
19249:
19246:
19244:
19241:
19239:
19236:
19235:
19233:
19229:
19223:
19220:
19218:
19215:
19214:
19212:
19210:
19206:
19200:
19197:
19195:
19192:
19191:
19189:
19185:
19179:
19176:
19174:
19171:
19170:
19168:
19166:
19162:
19156:
19153:
19151:
19148:
19146:
19143:
19142:
19140:
19138:
19134:
19128:
19125:
19123:
19120:
19118:
19115:
19114:
19112:
19110:
19106:
19100:
19097:
19095:
19092:
19090:
19087:
19085:
19082:
19080:
19079:Jaccard index
19077:
19075:
19072:
19070:
19067:
19065:
19062:
19060:
19057:
19055:
19052:
19051:
19049:
19047:
19043:
19037:
19034:
19032:
19029:
19027:
19024:
19022:
19019:
19017:
19014:
19012:
19009:
19007:
19004:
19002:
18999:
18997:
18994:
18992:
18989:
18987:
18984:
18983:
18981:
18979:
18975:
18969:
18966:
18964:
18961:
18959:
18956:
18954:
18951:
18949:
18946:
18944:
18941:
18939:
18936:
18934:
18931:
18929:
18926:
18924:
18921:
18919:
18916:
18915:
18913:
18911:
18907:
18902:
18895:
18890:
18888:
18883:
18881:
18876:
18875:
18872:
18860:
18859:
18850:
18848:
18847:
18838:
18836:
18835:
18830:
18824:
18822:
18821:
18812:
18811:
18808:
18794:
18791:
18789:
18788:Geostatistics
18786:
18784:
18781:
18779:
18776:
18774:
18771:
18770:
18768:
18766:
18762:
18756:
18755:Psychometrics
18753:
18751:
18748:
18746:
18743:
18741:
18738:
18736:
18733:
18731:
18728:
18726:
18723:
18721:
18718:
18716:
18713:
18711:
18708:
18707:
18705:
18703:
18699:
18693:
18690:
18688:
18685:
18683:
18679:
18676:
18674:
18671:
18669:
18666:
18664:
18661:
18660:
18658:
18656:
18652:
18646:
18643:
18641:
18638:
18636:
18632:
18629:
18627:
18624:
18623:
18621:
18619:
18618:Biostatistics
18615:
18611:
18607:
18602:
18598:
18580:
18579:Log-rank test
18577:
18576:
18574:
18570:
18564:
18561:
18560:
18558:
18556:
18552:
18546:
18543:
18541:
18538:
18536:
18533:
18531:
18528:
18527:
18525:
18523:
18519:
18516:
18514:
18510:
18500:
18497:
18495:
18492:
18490:
18487:
18485:
18482:
18480:
18477:
18476:
18474:
18472:
18468:
18462:
18459:
18457:
18454:
18452:
18450:(Box–Jenkins)
18446:
18444:
18441:
18439:
18436:
18432:
18429:
18428:
18427:
18424:
18423:
18421:
18419:
18415:
18409:
18406:
18404:
18403:Durbin–Watson
18401:
18399:
18393:
18391:
18388:
18386:
18385:Dickey–Fuller
18383:
18382:
18380:
18376:
18370:
18367:
18365:
18362:
18360:
18359:Cointegration
18357:
18355:
18352:
18350:
18347:
18345:
18342:
18340:
18337:
18335:
18334:Decomposition
18332:
18331:
18329:
18325:
18322:
18320:
18316:
18306:
18303:
18302:
18301:
18298:
18297:
18296:
18293:
18289:
18286:
18285:
18284:
18281:
18279:
18276:
18274:
18271:
18269:
18266:
18264:
18261:
18259:
18256:
18254:
18251:
18249:
18246:
18245:
18243:
18241:
18237:
18231:
18228:
18226:
18223:
18221:
18218:
18216:
18213:
18211:
18208:
18206:
18205:Cohen's kappa
18203:
18202:
18200:
18198:
18194:
18190:
18186:
18182:
18178:
18174:
18169:
18165:
18151:
18148:
18146:
18143:
18141:
18138:
18136:
18133:
18132:
18130:
18128:
18124:
18118:
18114:
18110:
18104:
18102:
18099:
18098:
18096:
18094:
18090:
18084:
18081:
18079:
18076:
18074:
18071:
18069:
18066:
18064:
18061:
18059:
18058:Nonparametric
18056:
18054:
18051:
18050:
18048:
18044:
18038:
18035:
18033:
18030:
18028:
18025:
18023:
18020:
18019:
18017:
18015:
18011:
18005:
18002:
18000:
17997:
17995:
17992:
17990:
17987:
17985:
17982:
17981:
17979:
17977:
17973:
17967:
17964:
17962:
17959:
17957:
17954:
17952:
17949:
17948:
17946:
17944:
17940:
17936:
17929:
17926:
17924:
17921:
17920:
17916:
17912:
17896:
17893:
17892:
17891:
17888:
17886:
17883:
17881:
17878:
17874:
17871:
17869:
17866:
17865:
17864:
17861:
17860:
17858:
17856:
17852:
17842:
17839:
17835:
17829:
17827:
17821:
17819:
17813:
17812:
17811:
17808:
17807:Nonparametric
17805:
17803:
17797:
17793:
17790:
17789:
17788:
17782:
17778:
17777:Sample median
17775:
17774:
17773:
17770:
17769:
17767:
17765:
17761:
17753:
17750:
17748:
17745:
17743:
17740:
17739:
17738:
17735:
17733:
17730:
17728:
17722:
17720:
17717:
17715:
17712:
17710:
17707:
17705:
17702:
17700:
17698:
17694:
17692:
17689:
17688:
17686:
17684:
17680:
17674:
17672:
17668:
17666:
17664:
17659:
17657:
17652:
17648:
17647:
17644:
17641:
17639:
17635:
17625:
17622:
17620:
17617:
17615:
17612:
17611:
17609:
17607:
17603:
17597:
17594:
17590:
17587:
17586:
17585:
17582:
17578:
17575:
17574:
17573:
17570:
17568:
17565:
17564:
17562:
17560:
17556:
17548:
17545:
17543:
17540:
17539:
17538:
17535:
17533:
17530:
17528:
17525:
17523:
17520:
17518:
17515:
17513:
17510:
17509:
17507:
17505:
17501:
17495:
17492:
17488:
17485:
17481:
17478:
17476:
17473:
17472:
17471:
17468:
17467:
17466:
17463:
17459:
17456:
17454:
17451:
17449:
17446:
17444:
17441:
17440:
17439:
17436:
17435:
17433:
17431:
17427:
17424:
17422:
17418:
17412:
17409:
17407:
17404:
17400:
17397:
17396:
17395:
17392:
17390:
17387:
17383:
17382:loss function
17380:
17379:
17378:
17375:
17371:
17368:
17366:
17363:
17361:
17358:
17357:
17356:
17353:
17351:
17348:
17346:
17343:
17339:
17336:
17334:
17331:
17329:
17323:
17320:
17319:
17318:
17315:
17311:
17308:
17306:
17303:
17301:
17298:
17297:
17296:
17293:
17289:
17286:
17284:
17281:
17280:
17279:
17276:
17272:
17269:
17268:
17267:
17264:
17260:
17257:
17256:
17255:
17252:
17250:
17247:
17245:
17242:
17240:
17237:
17236:
17234:
17232:
17228:
17224:
17220:
17215:
17211:
17197:
17194:
17192:
17189:
17187:
17184:
17182:
17179:
17178:
17176:
17174:
17170:
17164:
17161:
17159:
17156:
17154:
17151:
17150:
17148:
17144:
17138:
17135:
17133:
17130:
17128:
17125:
17123:
17120:
17118:
17115:
17113:
17110:
17108:
17105:
17104:
17102:
17100:
17096:
17090:
17087:
17085:
17084:Questionnaire
17082:
17080:
17077:
17073:
17070:
17068:
17065:
17064:
17063:
17060:
17059:
17057:
17055:
17051:
17045:
17042:
17040:
17037:
17035:
17032:
17030:
17027:
17025:
17022:
17020:
17017:
17015:
17012:
17010:
17007:
17006:
17004:
17002:
16998:
16994:
16990:
16985:
16981:
16967:
16964:
16962:
16959:
16957:
16954:
16952:
16949:
16947:
16944:
16942:
16939:
16937:
16934:
16932:
16929:
16927:
16924:
16922:
16919:
16917:
16914:
16912:
16911:Control chart
16909:
16907:
16904:
16902:
16899:
16897:
16894:
16893:
16891:
16889:
16885:
16879:
16876:
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16821:
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16678:
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16671:
16668:
16666:
16663:
16661:
16658:
16656:
16653:
16651:
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16641:
16638:
16637:
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16633:
16632:
16630:
16628:
16624:
16621:
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16615:
16611:
16607:
16602:
16598:
16592:
16589:
16587:
16584:
16583:
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16576:
16569:
16564:
16562:
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16555:
16550:
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16546:
16537:
16533:
16528:
16521:
16517:
16513:
16509:
16505:
16500:
16499:nagysandor.eu
16496:
16495:"Correlation"
16492:
16487:
16483:
16479:
16478:
16465:
16463:0-412-12420-3
16459:
16455:
16448:
16440:
16436:
16431:
16426:
16422:
16418:
16414:
16407:
16399:
16395:
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16327:
16323:
16319:
16315:
16310:
16305:
16301:
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16293:
16286:
16280:
16279:1-4020-8879-5
16276:
16272:
16266:
16258:
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16230:
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16149:
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16107:
16101:
16100:0-521-54985-X
16097:
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16089:
16085:
16079:
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16065:
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16044:
16036:
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16001:
15997:
15991:
15983:
15976:
15974:
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15778:
15774:
15770:
15763:
15755:
15751:
15747:
15743:
15742:
15737:
15733:
15727:
15720:
15719:0-85264-215-6
15716:
15712:
15706:
15699:
15693:
15678:
15674:
15668:
15660:
15656:
15652:
15648:
15644:
15640:
15636:
15632:
15628:
15621:
15613:
15606:
15604:
15595:
15593:9788391527290
15589:
15585:
15578:
15570:
15563:
15555:
15551:
15547:
15543:
15539:
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15512:
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15471:
15470:opentextbc.ca
15467:
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15428:
15424:
15420:
15416:
15409:
15401:
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15387:
15383:
15382:
15374:
15359:
15355:
15348:
15341:
15335:
15333:
15331:
15329:
15327:
15319:(7): 557–585.
15318:
15314:
15307:
15299:
15295:
15291:
15285:
15277:
15273:
15268:
15263:
15259:
15255:
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15232:
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14901:
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14703:
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14613:
14609:
14576:
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14542:
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14529:
14522:
14508:
14503:
14500:
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14484:
14479:
14476:
14473:
14470:
14463:
14462:
14461:
14459:
14455:
14451:
14447:
14443:
14439:
14435:
14417:
14414:
14411:
14407:
14398:
14394:
14376:
14373:
14370:
14366:
14357:
14353:
14349:
14344:
14339:
14338:Decorrelation
14331:
14325:
14308:
14305:
14302:
14285:
14279:
14276:
14273:
14236:
14233:
14230:
14193:
14170:
14155:
14140:
14117:
14102:
14087:
14084:
14081:
14058:
14055:
14052:
14037:
14022:
13999:
13984:
13969:
13946:
13931:
13930:
13929:
13912:
13902:
13891:
13885:
13869:
13858:
13852:
13841:
13835:
13832:
13829:
13815:
13809:
13806:
13803:
13782:
13781:
13780:
13766:
13746:
13732:
13729:
13723:
13713:
13711:
13707:
13703:
13681:
13652:
13619:
13605:
13599:
13594:
13590:
13583:
13580:
13575:
13570:
13567:
13564:
13560:
13550:
13536:
13530:
13525:
13521:
13514:
13511:
13506:
13501:
13498:
13495:
13491:
13474:
13468:
13463:
13459:
13452:
13449:
13437:
13431:
13426:
13422:
13415:
13412:
13407:
13402:
13399:
13396:
13392:
13385:
13376:
13368:
13367:
13366:
13364:
13360:
13356:
13347:
13343:
13336:
13332:
13327:
13323:
13316:
13312:
13306:
13296:
13275:
13272:
13269:
13265:
13256:
13253:
13250:
13245:
13242:
13239:
13235:
13224:
13222:
13203:
13198:
13195:
13192:
13188:
13184:
13181:
13178:
13173:
13170:
13167:
13163:
13155:
13154:
13153:
13151:
13147:
13143:
13133:
13119:
13110:
13096:
13074:
13070:
13046:
13041:
13037:
13031:
13026:
13023:
13020:
13010:
13007:
13002:
12997:
12987:
12976:
12975:
12974:
12958:
12948:
12921:
12917:
12912:
12909:
12904:
12900:
12897:
12894:
12891:
12884:
12883:
12882:
12868:
12848:
12828:
12819:
12817:
12811:
12787:
12776:
12771:
12767:
12761:
12757:
12753:
12742:
12737:
12733:
12727:
12723:
12719:
12709:
12705:
12699:
12695:
12689:
12685:
12681:
12675:
12670:
12667:
12664:
12661:
12657:
12653:
12646:
12645:
12644:
12627:
12616:
12611:
12607:
12603:
12592:
12587:
12583:
12579:
12569:
12565:
12559:
12555:
12551:
12545:
12540:
12537:
12533:
12529:
12522:
12521:
12520:
12518:
12499:
12496:
12493:
12490:
12487:
12484:
12481:
12477:
12471:
12468:
12465:
12462:
12459:
12456:
12450:
12445:
12441:
12437:
12431:
12428:
12425:
12422:
12416:
12411:
12407:
12403:
12397:
12394:
12391:
12385:
12380:
12376:
12372:
12366:
12363:
12360:
12354:
12349:
12345:
12337:
12336:
12335:
12318:
12306:
12302:
12294:
12284:
12275:
12271:
12263:
12247:
12243:
12236:
12223:
12217:
12214:
12211:
12205:
12200:
12196:
12188:
12187:
12186:
12164:
12155:
12152:
12149:
12146:
12143:
12137:
12134:
12128:
12125:
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12119:
12116:
12110:
12107:
12099:
12096:
12093:
12090:
12087:
12081:
12078:
12072:
12066:
12063:
12060:
12057:
12054:
12048:
12045:
12037:
12023:
12015:
12011:
12005:
12001:
11989:
11986:
11983:
11977:
11971:
11966:
11962:
11949:
11946:
11943:
11937:
11931:
11926:
11922:
11915:
11910:
11906:
11900:
11896:
11889:
11883:
11880:
11877:
11874:
11871:
11865:
11862:
11854:
11840:
11832:
11828:
11822:
11818:
11810:
11806:
11800:
11796:
11790:
11786:
11779:
11773:
11770:
11767:
11761:
11750:
11749:
11748:
11746:
11742:
11738:
11734:
11730:
11720:
11713:
11706:
11687:
11676:
11673:
11670:
11659:
11656:
11653:
11642:
11638:
11634:
11631:
11622:
11619:
11614:
11605:
11597:
11596:
11595:
11585:
11569:
11565:
11554:
11550:
11547:
11543:
11535:
11531:
11524:
11520:
11505:
11502:
11499:
11492:
11491:
11490:
11488:
11487:
11477:
11470:
11468:
11454:
11450:
11443:
11440:
11433:
11429:
11425:
11422:
11416:
11413:
11409:
11405:
11402:
11393:
11385:
11384:
11381:
11379:
11378:
11368:
11361:
11359:
11345:
11339:
11336:
11330:
11324:
11315:
11311:
11308:
11304:
11294:
11287:
11278:
11274:
11268:
11262:
11252:
11249:
11242:
11241:
11238:
11228:
11219:
11200:
11197:
11194:
11191:
11188:
11185:
11182:
11160:
11151:
11136:
11133:
11130:
11123:
11122:
11121:
11114:
11107:
11105:
11091:
11087:
11081:
11077:
11073:
11070:
11067:
11062:
11058:
11055:
11052:
11046:
11041:
11038:
11033:
11028:
11025:
11019:
10999:
10993:
10990:
10981:
10973:
10972:
10969:
10963:
10943:
10940:
10915:
10912:
10909:
10903:
10900:
10894:
10888:
10884:
10880:
10877:
10873:
10869:
10863:
10860:
10857:
10853:
10850:
10847:
10843:
10829:
10828:
10827:
10817:
10799:
10795:
10785:
10783:
10779:
10775:
10771:
10766:
10764:
10760:
10756:
10752:
10748:
10743:
10741:
10736:
10732:
10728:
10724:
10723:
10718:
10714:
10710:
10707:
10694:
10690:
10687:
10683:
10679:
10676:
10672:
10668:
10665:
10662:
10658:
10655:
10651:
10647:
10643:
10642:
10636:
10634:
10630:
10626:
10622:
10618:
10615:
10611:
10608:
10604:
10600:
10589:
10579:
10577:
10573:
10540:
10489:
10475:
10469:
10464:
10460:
10451:
10447:
10443:
10424:
10408:
10394:
10388:
10383:
10373:
10361:
10357:
10353:
10334:
10333:
10332:
10287:
10282:
10268:
10262:
10259:
10253:
10246:
10245:
10244:
10224:
10214:
10204:
10197:
10192:
10188:
10179:
10175:
10171:
10159:
10158:
10157:
10152:
10145:
10137:
10118:
10115:
10103:
10097:
10092:
10082:
10067:
10057:
10050:
10045:
10041:
10032:
10028:
10020:
10019:
10018:
10015:
10013:
10009:
9991:
9977:
9971:
9968:
9962:
9934:
9920:
9914:
9909:
9905:
9896:
9892:
9884:
9870:
9864:
9859:
9849:
9837:
9833:
9826:
9821:
9807:
9801:
9798:
9792:
9785:
9784:
9783:
9762:
9753:
9739:
9733:
9728:
9724:
9715:
9711:
9703:
9689:
9683:
9678:
9668:
9656:
9652:
9644:
9642:
9629:
9615:
9609:
9604:
9594:
9582:
9578:
9574:
9569:
9555:
9549:
9544:
9540:
9531:
9527:
9519:
9505:
9499:
9494:
9484:
9472:
9468:
9461:
9459:
9446:
9432:
9426:
9421:
9411:
9399:
9395:
9391:
9386:
9372:
9366:
9361:
9357:
9348:
9344:
9333:
9319:
9313:
9308:
9298:
9288:
9276:
9270:
9265:
9255:
9240:
9230:
9223:
9218:
9214:
9202:
9198:
9191:
9189:
9176:
9162:
9156:
9151:
9141:
9129:
9125:
9121:
9116:
9102:
9096:
9091:
9087:
9078:
9074:
9059:
9053:
9048:
9038:
9019:
9013:
9008:
8998:
8991:
8986:
8976:
8969:
8964:
8960:
8951:
8947:
8940:
8938:
8925:
8911:
8905:
8900:
8890:
8878:
8874:
8870:
8865:
8851:
8845:
8840:
8836:
8827:
8823:
8808:
8802:
8797:
8787:
8768:
8762:
8757:
8753:
8744:
8740:
8733:
8731:
8717:
8711:
8708:
8702:
8691:
8690:
8689:
8673:
8663:
8656:
8651:
8647:
8624:
8614:
8602:
8601:least squares
8597:
8595:
8591:
8587:
8568:
8560:
8546:
8540:
8535:
8531:
8522:
8518:
8510:
8496:
8490:
8485:
8475:
8463:
8459:
8452:
8444:
8430:
8424:
8419:
8415:
8406:
8402:
8394:
8384:
8374:
8367:
8362:
8358:
8349:
8345:
8338:
8335:
8328:
8327:
8326:
8310:
8300:
8273:
8268:
8254:
8248:
8243:
8233:
8221:
8217:
8213:
8208:
8198:
8188:
8181:
8176:
8172:
8163:
8159:
8155:
8150:
8136:
8130:
8125:
8121:
8112:
8108:
8100:
8099:
8098:
8095:
8091:
8073:
8063:
8056:
8053:
8050:
8045:
8035:
8009:
8005:
8001:
7998:
7995:
7990:
7986:
7977:
7973:
7969:
7965:
7961:
7954:
7944:
7927:
7923:
7918:
7915:
7895:
7892:
7888:
7885:
7882:
7878:
7875:
7867:
7863:
7859:
7827:
7823:
7819:
7815:
7811:
7805:
7799:
7796:
7790:
7787:
7784:
7771:
7767:
7763:
7759:
7755:
7749:
7743:
7740:
7734:
7731:
7725:
7722:
7719:
7705:
7702:
7699:
7693:
7686:
7685:
7684:
7657:
7653:
7649:
7645:
7641:
7635:
7629:
7626:
7620:
7614:
7608:
7605:
7602:
7588:
7585:
7582:
7576:
7569:
7568:
7567:
7565:
7552:
7543:
7538:
7536:
7516:
7513:
7510:
7502:
7498:
7494:
7491:and follow a
7490:
7472:
7468:
7464:
7461:
7453:
7432:
7429:
7426:
7413:
7409:
7402:
7399:
7393:
7387:
7381:
7367:
7364:
7358:
7355:
7348:
7347:
7346:
7344:
7339:
7323:
7319:
7298:
7278:
7270:
7251:
7245:
7242:
7239:
7235:
7230:
7222:
7215:
7193:
7187:
7184:
7181:
7175:
7169:
7166:
7154:
7153:
7152:
7150:
7146:
7142:
7121:
7115:
7112:
7109:
7105:
7099:
7096:
7093:
7088:
7085:
7082:
7076:
7072:
7069:
7062:
7059:
7053:
7047:
7041:
7034:
7033:
7032:
7031:
7016:
7008:
7004:
7000:
6996:
6992:
6989:In practice,
6986:
6976:
6962:
6959:
6956:
6953:
6950:
6947:
6944:
6915:
6901:
6894:
6890:
6887:
6884:
6881:
6874:
6868:
6865:
6859:
6856:
6853:
6847:
6844:
6838:
6835:
6829:
6826:
6819:
6815:
6806:
6802:
6799:
6796:
6793:
6786:
6782:
6779:
6776:
6773:
6769:
6764:
6758:
6754:
6751:
6748:
6741:
6735:
6731:
6727:
6724:
6720:
6715:
6709:
6705:
6702:
6699:
6692:
6686:
6682:
6678:
6675:
6671:
6662:
6656:
6653:
6648:
6645:
6641:
6632:
6629:
6619:
6616:
6613:
6601:
6598:
6595:
6589:
6583:
6577:
6574:
6571:
6565:
6557:
6555:
6551:
6541:
6539:
6535:
6534:beta function
6494:
6485:
6478:
6474:
6471:
6468:
6461:
6455:
6452:
6445:
6439:
6425:
6421:
6418:
6415:
6408:
6402:
6398:
6394:
6391:
6387:
6380:
6374:
6368:
6361:
6360:
6359:
6357:
6353:
6337:
6334:
6331:
6322:
6320:
6301:
6298:
6295:
6292:
6289:
6286:
6283:
6275:
6263:
6251:
6209:
6202:
6199:
6196:
6193:
6184:
6181:
6175:
6169:
6166:
6163:
6160:
6151:
6148:
6142:
6136:
6133:
6127:
6121:
6118:
6111:
6103:
6091:
6077:
6074:
6069:
6066:
6058:
6055:
6052:
6049:
6040:
6033:
6030:
6024:
6021:
6017:
6011:
6000:
5997:
5987:
5983:
5980:
5977:
5970:
5964:
5960:
5956:
5953:
5949:
5941:
5937:
5934:
5931:
5924:
5918:
5914:
5910:
5907:
5903:
5895:
5892:
5889:
5874:
5871:
5868:
5859:
5853:
5847:
5840:
5839:
5838:
5836:
5832:
5828:
5824:
5814:
5812:
5807:
5805:
5800:
5783:
5775:
5771:
5767:
5764:
5761:
5758:
5754:
5749:
5746:
5739:
5738:
5737:
5735:
5731:
5706:
5702:
5698:
5695:
5690:
5687:
5684:
5677:
5674:
5667:
5663:
5659:
5654:
5651:
5644:
5643:
5642:
5640:
5636:
5635:-distribution
5634:
5628:
5624:
5620:
5611:
5605:-distribution
5604:
5598:
5584:
5564:
5537:
5534:
5531:
5524:
5520:
5516:
5513:
5506:
5501:
5497:
5489:
5488:
5487:
5485:
5469:
5449:
5435:
5433:
5429:
5425:
5421:
5417:
5413:
5409:
5405:
5400:
5396:
5391:
5387:
5383:
5379:
5369:
5367:
5363:
5358:
5354:
5346:
5342:
5339:
5335:
5331:
5327:
5326:bootstrapping
5323:
5319:
5315:
5311:
5307:
5303:
5299:
5296:), where the
5294:
5290:
5285:
5281:
5276:
5272:
5267:
5263:
5259:
5258:
5257:
5255:
5246:
5240:
5236:
5232:
5229:
5225:
5221:
5217:
5216:
5215:
5207:
5200:
5196:
5192:
5188:
5184:
5180:
5176:
5172:
5152:
5148:
5144:
5141:
5136:
5133:
5125:
5121:
5117:
5112:
5103:
5102:as expected.
5086:
5081:
5078:
5074:
5070:
5067:
5064:
5056:
5049:
5043:
5038:
4999:
4988:
4985:
4982:
4979:
4972:
4971:
4970:
4969:, from which
4966:
4959:
4952:
4946:
4940:
4934:
4929:
4925:
4920:
4901:
4898:
4890:
4883:
4877:
4872:
4833:
4822:
4819:
4816:
4813:
4806:
4805:
4804:
4802:
4798:
4794:
4789:
4785:
4778:
4773:
4769:
4763:
4761:
4757:
4753:
4749:
4746:
4742:
4736:
4734:
4729:
4725:
4721:
4714:
4707:
4702:
4698:
4694:
4690:
4686:
4680:
4675:
4671:
4667:
4660:
4655:
4651:
4647:
4642:
4633:
4628:
4624:
4620:
4613:
4608:
4604:
4600:
4594:
4582:
4579:
4576:
4573:
4570:
4567:
4564:
4561:
4558:
4555:
4552:
4549:
4546:
4545:
4544:
4541:
4539:
4534:
4530:
4525:
4521:
4517:
4512:
4508:
4503:
4499:
4494:
4490:
4485:
4481:
4474:
4468:
4464:
4459:
4453:
4449:
4442:
4440:
4436:
4432:
4429:increases as
4428:
4424:
4420:
4416:
4412:
4402:
4400:
4399:
4392:
4388:
4383:
4379:
4375:
4371:
4366:
4362:
4357:
4352:
4348:
4343:
4339:
4334:
4332:
4328:
4324:
4320:
4316:
4305:
4303:
4300:other than a
4299:
4294:
4292:
4287:
4285:
4281:
4271:
4255:
4247:
4242:
4238:
4230:
4226:
4220:
4216:
4210:
4207:
4204:
4200:
4190:
4186:
4180:
4176:
4170:
4167:
4164:
4160:
4152:
4147:
4143:
4136:
4131:
4101:
4097:
4094:
4075:
4072:
4069:
4035:
4031:
4022:
4002:
3988:
3982:
3977:
3973:
3964:
3959:
3956:
3953:
3949:
3942:
3939:
3936:
3932:
3925:
3920:
3916:
3908:
3887:
3881:
3872:
3866:
3861:
3857:
3853:
3848:
3844:
3840:
3837:
3830:
3829:
3828:
3806:
3802:
3796:
3792:
3785:
3782:
3779:
3765:
3753:
3747:
3744:
3739:
3735:
3729:
3725:
3721:
3715:
3710:
3707:
3703:
3695:
3694:
3693:
3677:
3674:
3670:
3647:
3644:
3640:
3615:
3594:
3587:
3583:
3572:
3566:
3561:
3557:
3550:
3542:
3525:
3521:
3517:
3512:
3508:
3481:
3475:
3466:
3460:
3455:
3451:
3447:
3442:
3438:
3434:
3431:
3424:
3423:
3422:
3404:
3397:
3393:
3382:
3376:
3371:
3367:
3360:
3355:
3348:
3344:
3333:
3327:
3322:
3318:
3311:
3305:
3300:
3297:
3294:
3290:
3283:
3280:
3277:
3273:
3268:
3263:
3260:
3256:
3248:
3247:
3246:
3244:
3226:
3223:
3219:
3209:
3207:
3202:
3186:
3182:
3178:
3173:
3169:
3165:
3162:
3139:
3129:
3124:
3118:
3114:
3110:
3106:
3101:
3096:
3091:
3087:
3083:
3080:
3068:
3063:
3057:
3053:
3049:
3045:
3040:
3035:
3030:
3026:
3022:
3019:
3010:
3006:
3002:
2997:
2993:
2989:
2986:
2981:
2977:
2971:
2967:
2963:
2960:
2954:
2949:
2946:
2942:
2934:
2933:
2932:
2916:
2913:
2909:
2899:
2879:
2873:
2864:
2858:
2853:
2849:
2845:
2840:
2836:
2832:
2829:
2806:
2796:
2786:
2779:
2776:
2771:
2766:
2762:
2756:
2752:
2739:
2729:
2722:
2719:
2714:
2709:
2705:
2699:
2695:
2681:
2669:
2663:
2660:
2655:
2651:
2645:
2641:
2635:
2631:
2624:
2619:
2616:
2612:
2604:
2603:
2602:
2586:
2583:
2579:
2548:
2523:
2519:
2513:
2508:
2505:
2502:
2498:
2492:
2489:
2484:
2475:
2465:
2463:
2445:
2441:
2437:
2432:
2428:
2420:
2405:
2398:
2397:
2396:
2393:
2373:
2359:
2353:
2348:
2344:
2335:
2330:
2327:
2324:
2320:
2310:
2296:
2290:
2285:
2281:
2272:
2267:
2264:
2261:
2257:
2240:
2234:
2229:
2225:
2209:
2203:
2198:
2194:
2185:
2180:
2177:
2174:
2170:
2163:
2158:
2155:
2151:
2142:
2126:
2123:
2119:
2098:
2077:
2068:
2064:
2060:
2055:
2051:
2044:
2041:
2038:
2030:
2026:
2022:
2017:
2013:
2005:
1982:
1979:
1975:
1966:
1962:
1944:
1941:
1937:
1928:
1918:
1905:
1895:
1890:
1882:
1875:
1864:
1859:
1855:
1848:
1844:
1838:
1834:
1815:
1810:
1802:
1795:
1784:
1779:
1775:
1768:
1764:
1758:
1754:
1736:
1729:
1715:
1708:
1698:
1691:
1687:
1680:
1667:
1662:
1659:
1656:
1652:
1631:
1604:
1596:
1589:
1575:
1568:
1558:
1551:
1547:
1540:
1530:
1522:
1514:
1507:
1497:
1494:
1490:
1485:
1477:
1470:
1460:
1457:
1453:
1445:
1435:
1427:
1421:
1417:
1413:
1410:
1406:
1401:
1395:
1391:
1387:
1384:
1380:
1372:
1355:
1350:
1342:
1335:
1323:
1318:
1314:
1307:
1303:
1297:
1293:
1283:
1279:
1272:
1267:
1260:
1254:
1244:
1241:
1237:
1230:
1226:
1212:
1207:
1202:
1198:
1188:
1183:
1175:
1168:
1157:
1152:
1148:
1141:
1137:
1131:
1127:
1117:
1113:
1106:
1101:
1094:
1088:
1078:
1075:
1071:
1064:
1060:
1046:
1041:
1036:
1032:
1020:
1013:
999:
994:
990:
978:
971:
957:
952:
948:
936:
935:
934:
920:
885:
871:
849:
845:
837:
823:
801:
797:
789:
772:
768:
745:
741:
733:
732:
731:
728:
710:
706:
700:
696:
682:
678:
674:
671:
660:
656:
652:
649:
640:
627:
622:
619:
616:
612:
603:
589:
566:
555:
551:
547:
544:
533:
529:
525:
522:
513:
503:
497:
494:
491:
485:
482:
475:
474:
473:
471:
467:
448:
445:
442:
436:
433:
409:
387:
383:
375:
361:
353:
335:
331:
323:
321:
305:
298:
297:
296:
293:
275:
271:
265:
261:
252:
249:
246:
240:
237:
231:
226:
223:
220:
216:
207:
205:
186:
183:
180:
169:
165:
161:
157:
147:
146:in the name.
145:
141:
137:
127:
125:
124:Stigler's Law
121:
117:
113:
103:
100:
96:
92:
88:
84:
80:
76:
72:
64:
59:
55:
51:
47:
42:
35:
30:
26:
22:
19247:
18856:
18844:
18825:
18818:
18730:Econometrics
18680: /
18663:Chemometrics
18640:Epidemiology
18633: /
18606:Applications
18448:ARIMA model
18395:Q-statistic
18344:Stationarity
18240:Multivariate
18183: /
18179: /
18177:Multivariate
18175: /
18115: /
18111: /
17885:Bayes factor
17784:Signed rank
17696:
17670:
17662:
17650:
17345:Completeness
17181:Cohort study
17079:Opinion poll
17014:Missing data
17001:Study design
16956:Scatter plot
16878:Scatter plot
16871:Spearman's ρ
16855:
16833:Grouped data
16526:
16512:hackmath.net
16511:
16498:
16485:
16453:
16447:
16420:
16416:
16406:
16389:
16385:
16375:
16365:21 September
16363:. Retrieved
16348:
16341:
16329:. Retrieved
16299:
16295:
16285:
16270:
16265:
16232:
16228:
16215:
16201:
16192:
16183:
16155:
16151:
16141:
16116:
16112:
16106:
16083:
16078:
16050:
16043:
16034:
16028:
16003:
15999:
15990:
15981:
15947:
15943:
15930:
15909:cite journal
15884:
15875:
15865:
15856:
15850:
15825:
15821:
15815:
15772:
15768:
15762:
15745:
15739:
15726:
15710:
15705:
15697:
15692:
15680:. Retrieved
15676:
15667:
15634:
15630:
15620:
15611:
15583:
15577:
15562:
15537:
15533:
15527:
15505:(1): 59–66.
15502:
15498:
15485:
15473:. Retrieved
15469:
15460:
15448:. Retrieved
15444:
15435:
15418:
15414:
15408:
15379:
15373:
15361:. Retrieved
15357:
15347:
15316:
15312:
15306:
15297:
15293:
15284:
15260:(2): 73–79.
15257:
15253:
15243:
15226:
15222:
15212:
15187:
15183:
15173:
15164:
15160:
15150:
15142:
15110:
15106:
15096:
15087:
15078:
15064:
15046:
15041:
15034:
15030:
15026:
15022:
15017:
15015:
15010:
14809:library via
14772:
14635:
14631:
14627:
14623:
14619:
14615:
14591:
14453:
14445:
14441:
14437:
14433:
14396:
14392:
14355:
14351:
14347:
14345:
14341:
14329:
14209:
13927:
13738:
13725:
13709:
13705:
13641:
13358:
13354:
13345:
13341:
13334:
13330:
13325:
13321:
13314:
13310:
13308:
13225:
13218:
13149:
13145:
13141:
13139:
13111:
13061:
12936:
12820:
12813:
12642:
12514:
12333:
12184:
11744:
11740:
11736:
11732:
11728:
11726:
11711:
11704:
11702:
11593:
11583:
11567:
11552:
11545:
11541:
11533:
11522:
11484:
11482:
11471:
11375:
11373:
11362:
11226:
11223:
11119:
11108:
10968:is given by
10961:
10958:
10805:
10797:
10781:
10777:
10769:
10767:
10744:
10734:
10730:
10720:
10708:
10703:
10685:
10681:
10628:
10624:
10596:
10507:
10330:
10242:
10150:
10143:
10133:
10016:
10011:
10007:
9954:
9781:
8598:
8593:
8589:
8585:
8583:
8288:
8093:
8089:
7971:
7967:
7959:
7957:
7865:
7861:
7857:
7855:
7682:
7545:
7541:
7539:
7500:
7449:
7340:
7268:
7266:
7144:
7140:
7139:
7029:
6998:
6997:relating to
6988:
6916:
6558:
6553:
6547:
6509:
6355:
6351:
6323:
6227:
5834:
5830:
5826:
5820:
5810:
5808:
5803:
5801:
5798:
5733:
5729:
5727:
5638:
5632:
5616:
5602:
5556:
5441:
5431:
5423:
5411:
5407:
5403:
5398:
5394:
5389:
5385:
5381:
5375:
5356:
5350:
5344:
5337:
5333:
5329:
5321:
5317:
5313:
5309:
5305:
5297:
5292:
5288:
5283:
5279:
5274:
5270:
5265:
5261:
5252:
5244:
5238:
5227:
5223:
5213:
5204:
5198:
5194:
5190:
5186:
5182:
5178:
5170:
5123:
5119:
5115:
5101:
4964:
4957:
4950:
4944:
4938:
4932:
4927:
4923:
4916:
4902:0.920814711.
4800:
4792:
4790:
4783:
4776:
4771:
4767:
4764:
4759:
4755:
4747:
4737:
4727:
4723:
4719:
4712:
4705:
4700:
4696:
4692:
4688:
4684:
4678:
4673:
4669:
4665:
4658:
4653:
4649:
4645:
4640:
4638:
4631:
4626:
4622:
4618:
4611:
4606:
4602:
4598:
4542:
4532:
4528:
4523:
4519:
4510:
4506:
4501:
4497:
4492:
4488:
4483:
4479:
4472:
4466:
4462:
4457:
4451:
4447:
4443:
4438:
4434:
4430:
4426:
4414:
4410:
4408:
4396:
4390:
4386:
4381:
4377:
4373:
4369:
4364:
4360:
4355:
4350:
4346:
4341:
4335:
4330:
4326:
4322:
4318:
4311:
4295:
4288:
4277:
4058:
3826:
3631:
3420:
3245:as follows:
3210:
3203:
3154:
2900:
2821:
2570:
2461:
2394:
2143:
1964:
1960:
1924:
1921:For a sample
1623:
912:
729:
604:
581:
425:
294:
208:
203:
167:
163:
159:
153:
143:
133:
112:Karl Pearson
109:
78:
74:
68:
62:
57:
53:
49:
45:
33:
25:
18858:WikiProject
18773:Cartography
18735:Jurimetrics
18687:Reliability
18418:Time domain
18397:(Ljung–Box)
18319:Time-series
18197:Categorical
18181:Time-series
18173:Categorical
18108:(Bernoulli)
17943:Correlation
17923:Correlation
17719:Jarque–Bera
17691:Chi-squared
17453:M-estimator
17406:Asymptotics
17350:Sufficiency
17117:Interaction
17029:Replication
17009:Effect size
16966:Violin plot
16946:Radar chart
16926:Forest plot
16916:Correlogram
16866:Kendall's τ
16331:11 February
16235:(5): 1–21.
15790:11343/44035
15775:: 728–740.
15732:Soper, H.E.
15713:, Griffin.
15229:: 240–242.
15190:: 246–263.
14836:Correlation
14458:independent
14354:times. Let
13351:[0, 2π)
12816:time series
10727:scatterplot
10693:dichotomous
10639:Sample size
10508:The symbol
6538:studentized
5627:studentized
5302:permutation
4797:dot product
4293:estimator.
470:expectation
99:correlation
19276:Categories
19231:Similarity
19173:Perplexity
19084:Rand index
19069:Dunn index
19054:Silhouette
19046:Clustering
18910:Regression
18725:Demography
18443:ARMA model
18248:Regression
17825:(Friedman)
17786:(Wilcoxon)
17724:Normality
17714:Lilliefors
17661:Student's
17537:Resampling
17411:Robustness
17399:divergence
17389:Efficiency
17327:(monotone)
17322:Likelihood
17239:Population
17072:Stratified
17024:Population
16843:Dependence
16799:Count data
16730:Percentile
16707:Dispersion
16640:Arithmetic
16575:Statistics
16000:Biometrika
15769:NeuroImage
15741:Biometrika
15056:References
15016:Pearson's
14972:Odds ratio
11483:where in (
10929:therefore
10792:See also:
10700:Robustness
10610:covariance
10607:population
8289:where the
7450:under the
7291:and small
5631:Student's
5428:percentile
4801:uncentered
320:covariance
156:population
136:covariance
130:Definition
91:covariance
71:statistics
19001:Precision
18953:RMSE/RMSD
18106:Logistic
17873:posterior
17799:Rank sum
17547:Jackknife
17542:Bootstrap
17360:Bootstrap
17295:Parameter
17244:Statistic
17039:Statistic
16951:Run chart
16936:Pie chart
16931:Histogram
16921:Fan chart
16896:Bar chart
16778:L-moments
16665:Geometric
16430:1408.6851
16304:CiteSeerX
15950:: 58–77.
15807:207184701
15651:0162-1459
15475:21 August
15388:pp.
15363:22 August
15003:Footnotes
14861:function.
14791:cor(x, y)
14743:−
14658:−
14562:−
14480:−
14085:⊗
14056:⊗
13892:⋅
13859:⋅
13842:−
13833:⊗
13708:and
13685:¯
13656:¯
13609:¯
13600:−
13584:
13561:∑
13540:¯
13531:−
13515:
13492:∑
13478:¯
13469:−
13453:
13441:¯
13432:−
13416:
13393:∑
13266:ρ
13257:−
13189:ρ
13185:−
13148:known as
13017:∑
12991:¯
12952:¯
12901:
12754:∑
12720:∑
12682:∑
12604:∑
12580:∑
12552:∑
12485:≠
12451:
12438:≠
12417:
12386:
12355:
12295:
12285:⋅
12264:
12237:
12206:
12138:
12111:
12082:
12049:
12002:∑
11978:
11972:−
11938:
11932:−
11916:⋅
11897:∑
11866:
11819:∑
11787:∑
11762:
11674:−
11657:−
11635:−
11623:−
11426:−
11403:≈
11312:−
11288:−
11275:≈
11263:
11074:−
11056:−
10941:ρ
10913:⋯
10885:ρ
10881:−
10870:ρ
10864:−
10861:ρ
10844:
10751:bootstrap
10706:statistic
10661:efficient
10593:Existence
10479:¯
10470:−
10448:∑
10398:¯
10389:−
10377:^
10358:∑
10272:^
10208:^
10198:−
10176:∑
10107:¯
10098:−
10086:^
10061:^
10051:−
10029:∑
9981:^
9924:¯
9915:−
9893:∑
9874:¯
9865:−
9853:^
9834:∑
9811:^
9743:¯
9734:−
9712:∑
9693:¯
9684:−
9672:^
9653:∑
9619:¯
9610:−
9598:^
9579:∑
9575:⋅
9559:¯
9550:−
9528:∑
9509:¯
9500:−
9488:^
9469:∑
9436:¯
9427:−
9415:^
9396:∑
9392:⋅
9376:¯
9367:−
9345:∑
9323:¯
9314:−
9302:^
9280:¯
9271:−
9259:^
9234:^
9224:−
9199:∑
9166:¯
9157:−
9145:^
9126:∑
9122:⋅
9106:¯
9097:−
9075:∑
9063:¯
9054:−
9042:^
9023:¯
9014:−
9002:^
8980:^
8970:−
8948:∑
8915:¯
8906:−
8894:^
8875:∑
8871:⋅
8855:¯
8846:−
8824:∑
8812:¯
8803:−
8791:^
8772:¯
8763:−
8741:∑
8721:^
8667:^
8657:−
8618:^
8550:¯
8541:−
8519:∑
8500:¯
8491:−
8479:^
8460:∑
8434:¯
8425:−
8403:∑
8378:^
8368:−
8346:∑
8304:^
8258:¯
8249:−
8237:^
8218:∑
8192:^
8182:−
8160:∑
8140:¯
8131:−
8109:∑
8067:^
8054:…
8039:^
7999:…
7919:±
7879:
7820:α
7800:
7791:
7764:α
7756:−
7744:
7735:
7726:∈
7723:ρ
7712:%
7706:α
7703:−
7650:α
7642:±
7630:
7621:∈
7615:ρ
7609:
7595:%
7589:α
7586:−
7553:ρ
7511:ρ
7469:ρ
7462:ρ
7430:−
7410:ρ
7400:−
7368:−
7320:ρ
7243:−
7194:ρ
7188:
7176:ρ
7116:
7097:−
7073:
7054:≡
6954:−
6945:ν
6891:ρ
6857:ν
6839:−
6816:
6803:ν
6797:−
6783:ρ
6777:−
6765:⋅
6752:−
6749:ν
6732:ρ
6728:−
6716:⋅
6703:−
6700:ν
6679:−
6646:ν
6638:Γ
6633:π
6617:−
6614:ν
6608:Γ
6599:−
6596:ν
6590:ν
6575:∣
6572:ρ
6566:π
6472:−
6440:
6419:−
6395:−
6332:ρ
6236:Γ
6194:ρ
6167:−
6070:−
6056:ρ
6053:−
6025:−
6012:
6008:Γ
6001:π
5981:−
5957:−
5935:−
5915:ρ
5911:−
5893:−
5883:Γ
5872:−
5762:−
5699:−
5688:−
5664:σ
5535:−
5517:−
5498:σ
5378:bootstrap
5366:one-sided
5362:two-sided
5210:Inference
5149:ρ
5145:−
5137:−
5075:ρ
5000:⋅
4986:θ
4983:
4955:) yields
4953:) = 0.138
4834:⋅
4820:θ
4817:
4338:invariant
4315:supported
4239:σ
4227:σ
4217:σ
4201:ρ
4187:σ
4177:σ
4161:ρ
4144:σ
4129:Σ
4109:Σ
3992:¯
3983:−
3950:∑
3940:−
3891:¯
3876:¯
3783:−
3769:¯
3757:¯
3745:−
3722:∑
3576:¯
3567:−
3485:¯
3470:¯
3386:¯
3377:−
3337:¯
3328:−
3291:∑
3281:−
3111:∑
3102:−
3084:∑
3050:∑
3041:−
3023:∑
3003:∑
2990:∑
2987:−
2964:∑
2883:¯
2868:¯
2790:¯
2777:−
2753:∑
2733:¯
2720:−
2696:∑
2685:¯
2673:¯
2661:−
2632:∑
2552:¯
2499:∑
2479:¯
2363:¯
2354:−
2321:∑
2300:¯
2291:−
2258:∑
2244:¯
2235:−
2213:¯
2204:−
2171:∑
2042:…
1876:
1860:−
1835:
1796:
1780:−
1755:
1730:
1709:
1699:−
1681:
1653:ρ
1632:ρ
1590:
1569:
1559:−
1541:
1508:
1498:−
1471:
1461:−
1446:
1418:μ
1414:−
1392:μ
1388:−
1373:
1336:
1319:−
1294:
1255:
1245:−
1227:
1199:σ
1169:
1153:−
1128:
1089:
1079:−
1061:
1033:σ
1014:
991:μ
972:
949:μ
921:ρ
846:μ
798:μ
769:σ
742:σ
707:σ
697:σ
679:μ
675:−
657:μ
653:−
641:
613:ρ
590:ρ
552:μ
548:−
530:μ
526:−
514:
486:
437:
384:σ
332:σ
272:σ
262:σ
241:
217:ρ
19217:Coverage
18996:Accuracy
18820:Category
18513:Survival
18390:Johansen
18113:Binomial
18068:Isotonic
17655:(normal)
17300:location
17107:Blocking
17062:Sampling
16941:Q–Q plot
16906:Box plot
16888:Graphics
16783:Skewness
16773:Kurtosis
16745:Variance
16675:Heronian
16670:Harmonic
16249:22324876
16037:. Wiley.
15964:52878443
15799:22939874
15554:27528906
15445:STAT 462
14920:Yule's Y
14915:Yule's Q
14878:See also
14833:via the
13700:are the
13381:circular
10788:Variants
10774:stratify
10729:between
10717:outliers
10657:unbiased
10614:marginal
10576:variance
8596:(left).
5434:values.
5334:i′
5332:and the
5318:i′
5310:i′
5298:i′
5293:i′
5032:‖
5024:‖
5019:‖
5011:‖
4866:‖
4858:‖
4853:‖
4845:‖
4368:, where
4100:variance
4096:gaussian
472:. Since
65:is zero.
19109:Ranking
19099:SimHash
18986:F-score
18846:Commons
18793:Kriging
18678:Process
18635:studies
18494:Wavelet
18327:General
17494:Plug-in
17288:L space
17067:Cluster
16768:Moments
16586:Outline
16482:"cocor"
16326:1027502
16257:4694570
16174:2237306
16133:2983768
16020:2335508
15842:2983768
15682:30 July
15659:2277400
15519:2685263
15450:10 July
15390:223–260
15276:2245329
15231:Bibcode
15204:2841583
15137:4136393
15115:Bibcode
15029:), the
14612:inverse
14610:of the
14601:⁄
14391:is the
13361:with a
11580:⁄
11216:is the
11120:where:
10711:is not
10599:moments
10570:is the
10142:) over
7876:arctanh
7497:p-value
7343:z-score
6532:is the
6317:is the
6248:is the
5625:of the
5393:,
5384:pairs (
5353:p-value
5324:}. In
5287:,
5269:,
5057:0.00308
4941:) = 3.8
4799:), the
4752:vectors
4743:of the
4121:, then
4093:jointly
2111:pairs,
1963:or the
350:is the
318:is the
166:or the
81:) is a
48:,
19006:Recall
18715:Census
18305:Normal
18253:Manova
18073:Robust
17823:2-way
17815:1-way
17653:-test
17324:
16901:Biplot
16692:Median
16685:Lehmer
16627:Center
16460:
16356:
16324:
16306:
16277:
16255:
16247:
16172:
16131:
16098:
16090:
16066:
16018:
15962:
15840:
15805:
15797:
15717:
15657:
15649:
15590:
15552:
15517:
15396:
15274:
15202:
15161:Nature
15135:
15107:Nature
15021:, the
14820:Pandas
14807:Python
14432:be an
14399:. Let
13928:where
13642:where
13329:} and
13062:where
10713:robust
10541:, and
10331:where
9955:where
7916:0.8673
7896:0.8673
7797:artanh
7741:artanh
7627:artanh
7606:artanh
7267:where
7185:artanh
7113:artanh
6917:where
6510:where
6228:where
5621:, the
5557:where
5300:are a
5193:|
4891:0.0983
4741:cosine
4726:− tan
4722:= sec
4715:< 0
4708:> 0
4393:> 0
4380:, and
3827:where
3421:where
3155:where
3076:
2822:where
2747:
2395:where
1927:sample
1823:
730:where
295:where
140:moment
87:linear
73:, the
19011:Kappa
18928:sMAPE
18339:Trend
17868:prior
17810:anova
17699:-test
17673:-test
17665:-test
17572:Power
17517:Pivot
17310:shape
17305:scale
16755:Shape
16735:Range
16680:Heinz
16655:Cubic
16591:Index
16523:(PDF)
16425:arXiv
16322:S2CID
16253:S2CID
16225:(PDF)
16170:JSTOR
16129:JSTOR
16016:JSTOR
15960:S2CID
15940:(PDF)
15838:JSTOR
15803:S2CID
15655:JSTOR
15550:JSTOR
15515:JSTOR
15495:(PDF)
15272:JSTOR
15200:JSTOR
15133:S2CID
15027:PPMCC
14865:Excel
14850:Boost
14804:SciPy
14153:, and
13340:,...,
13320:,...,
12898:round
11380:) is
9782:Thus
7974:in a
7454:that
7151:with
5044:0.308
4745:angle
4518:) if
4019:(the
19178:BLEU
19150:SSIM
19145:PSNR
19122:NDCG
18943:MSPE
18938:MASE
18933:MAPE
18572:Test
17772:Sign
17624:Wald
16697:Mode
16635:Mean
16458:ISBN
16367:2016
16354:ISBN
16333:2018
16275:ISBN
16245:PMID
16096:ISBN
16088:ISBN
16064:ISBN
15922:help
15795:PMID
15715:ISBN
15684:2021
15647:ISSN
15588:ISBN
15477:2020
15452:2021
15394:ISBN
15365:2020
14848:The
14818:The
14802:The
14634:and
13759:and
13671:and
13363:sine
13357:and
13144:and
12821:Let
12497:>
12442:corr
12408:corr
12377:corr
12346:corr
12197:corr
12046:corr
11735:and
11586:− 1)
10733:and
10659:and
10149:and
8639:and
7924:1.96
7788:tanh
7732:tanh
7372:mean
7311:and
7212:and
7163:mean
6993:and
6960:>
6252:and
5462:and
5422:for
5376:The
5177:for
5050:30.8
4962:and
4943:and
4878:2.93
4781:and
4770:and
4691:and
4663:and
4616:and
4527:and
4505:and
4487:and
4419:line
4413:and
760:and
468:and
466:mean
354:of
56:and
19199:FID
19165:NLP
19155:IoU
19117:MRR
19094:SMC
19026:ROC
19021:AUC
19016:MCC
18968:MAD
18963:MDA
18948:RMS
18923:MAE
18918:MSE
17752:BIC
17747:AIC
16435:doi
16421:114
16394:doi
16314:doi
16237:doi
16160:doi
16121:doi
16056:doi
16008:doi
15952:doi
15948:470
15895:doi
15830:doi
15785:hdl
15777:doi
15750:doi
15639:doi
15542:doi
15507:doi
15423:doi
15262:doi
15192:doi
15123:doi
14853:C++
14452:of
14436:by
13704:of
13581:sin
13512:sin
13450:sin
13413:sin
13333:= {
13313:= {
12135:cov
12108:cov
12079:cov
11863:cov
11747:),
11708:adj
11610:adj
11571:adj
11556:adj
11548:)),
11537:adj
11526:adj
11398:adj
11320:adj
11299:adj
11283:adj
11230:adj
10986:adj
10965:adj
10627:or
10556:tot
10523:reg
10439:tot
10349:reg
10312:tot
10300:reg
10168:RSS
10140:RSS
7694:100
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5878:)
5875:2
5869:n
5866:(
5860:=
5857:)
5854:r
5851:(
5848:f
5835:r
5831:r
5829:(
5827:f
5811:t
5804:ρ
5784:.
5776:2
5772:t
5768:+
5765:2
5759:n
5755:t
5750:=
5747:r
5734:r
5730:t
5707:2
5703:r
5696:1
5691:2
5685:n
5678:r
5675:=
5668:r
5660:r
5655:=
5652:t
5639:n
5633:t
5603:t
5585:n
5565:r
5538:2
5532:n
5525:2
5521:r
5514:1
5507:=
5502:r
5470:y
5450:x
5432:r
5424:ρ
5412:r
5408:r
5404:n
5399:i
5395:y
5390:i
5386:x
5382:n
5357:r
5345:r
5338:n
5330:i
5322:n
5314:n
5306:n
5289:y
5284:i
5280:x
5275:i
5271:y
5266:i
5262:x
5241:.
5239:ρ
5230:.
5228:r
5224:ρ
5201:.
5199:Y
5195:X
5191:Y
5187:ρ
5183:X
5179:Y
5171:ρ
5153:2
5142:1
5134:1
5124:ρ
5120:Y
5116:X
5087:,
5082:y
5079:x
5071:=
5068:1
5065:=
5039:=
5028:y
5015:x
5004:y
4996:x
4989:=
4965:y
4958:x
4951:y
4945:y
4939:x
4933:x
4928:x
4924:y
4899:=
4873:=
4862:y
4849:x
4838:y
4830:x
4823:=
4793:θ
4784:y
4777:x
4772:y
4768:x
4760:N
4756:N
4748:θ
4728:φ
4724:φ
4720:r
4713:r
4706:r
4701:φ
4697:y
4693:x
4689:x
4685:y
4681:)
4679:y
4677:(
4674:Y
4670:g
4666:x
4661:)
4659:x
4657:(
4654:X
4650:g
4646:y
4641:φ
4634:)
4632:y
4630:(
4627:Y
4623:g
4619:x
4614:)
4612:x
4610:(
4607:X
4603:g
4599:y
4533:i
4529:Y
4524:i
4520:X
4511:i
4507:Y
4502:i
4498:X
4493:i
4489:Y
4484:i
4480:X
4476:)
4473:Y
4467:i
4463:Y
4458:X
4452:i
4448:X
4446:(
4439:X
4435:Y
4431:X
4427:Y
4415:Y
4411:X
4391:d
4387:b
4382:d
4378:c
4374:b
4370:a
4361:c
4356:Y
4347:a
4342:X
4331:X
4329:,
4327:Y
4323:Y
4321:,
4319:X
4256:]
4248:2
4243:Y
4231:Y
4221:X
4211:Y
4208:,
4205:X
4191:Y
4181:X
4171:Y
4168:,
4165:X
4153:2
4148:X
4137:[
4132:=
4079:)
4076:Y
4073:,
4070:X
4067:(
4050:.
4036:y
4032:s
4003:2
3999:)
3989:x
3978:i
3974:x
3970:(
3965:n
3960:1
3957:=
3954:i
3943:1
3937:n
3933:1
3926:=
3921:x
3917:s
3888:y
3882:,
3873:x
3867:,
3862:i
3858:y
3854:,
3849:i
3845:x
3841:,
3838:n
3807:y
3803:s
3797:x
3793:s
3789:)
3786:1
3780:n
3777:(
3766:y
3754:x
3748:n
3740:i
3736:y
3730:i
3726:x
3716:=
3711:y
3708:x
3704:r
3678:y
3675:x
3671:r
3648:y
3645:x
3641:r
3616:y
3595:)
3588:x
3584:s
3573:x
3562:i
3558:x
3551:(
3526:y
3522:s
3518:,
3513:x
3509:s
3482:y
3476:,
3467:x
3461:,
3456:i
3452:y
3448:,
3443:i
3439:x
3435:,
3432:n
3405:)
3398:y
3394:s
3383:y
3372:i
3368:y
3361:(
3356:)
3349:x
3345:s
3334:x
3323:i
3319:x
3312:(
3306:n
3301:1
3298:=
3295:i
3284:1
3278:n
3274:1
3269:=
3264:y
3261:x
3257:r
3227:y
3224:x
3220:r
3187:i
3183:y
3179:,
3174:i
3170:x
3166:,
3163:n
3140:,
3130:2
3125:)
3119:i
3115:y
3107:(
3097:2
3092:i
3088:y
3081:n
3069:2
3064:)
3058:i
3054:x
3046:(
3036:2
3031:i
3027:x
3020:n
3011:i
3007:y
2998:i
2994:x
2982:i
2978:y
2972:i
2968:x
2961:n
2955:=
2950:y
2947:x
2943:r
2917:y
2914:x
2910:r
2880:y
2874:,
2865:x
2859:,
2854:i
2850:y
2846:,
2841:i
2837:x
2833:,
2830:n
2807:,
2797:2
2787:y
2780:n
2772:2
2767:i
2763:y
2757:i
2740:2
2730:x
2723:n
2715:2
2710:i
2706:x
2700:i
2682:y
2670:x
2664:n
2656:i
2652:y
2646:i
2642:x
2636:i
2625:=
2620:y
2617:x
2613:r
2587:y
2584:x
2580:r
2567:.
2549:y
2524:i
2520:x
2514:n
2509:1
2506:=
2503:i
2493:n
2490:1
2485:=
2476:x
2462:i
2446:i
2442:y
2438:,
2433:i
2429:x
2406:n
2374:2
2370:)
2360:y
2349:i
2345:y
2341:(
2336:n
2331:1
2328:=
2325:i
2311:2
2307:)
2297:x
2286:i
2282:x
2278:(
2273:n
2268:1
2265:=
2262:i
2250:)
2241:y
2230:i
2226:y
2222:(
2219:)
2210:x
2199:i
2195:x
2191:(
2186:n
2181:1
2178:=
2175:i
2164:=
2159:y
2156:x
2152:r
2127:y
2124:x
2120:r
2099:n
2078:}
2074:)
2069:n
2065:y
2061:,
2056:n
2052:x
2048:(
2045:,
2039:,
2036:)
2031:1
2027:y
2023:,
2018:1
2014:x
2010:(
2006:{
1983:y
1980:x
1976:r
1945:y
1942:x
1938:r
1906:.
1896:2
1891:)
1887:]
1883:Y
1879:[
1871:E
1865:(
1856:]
1849:2
1845:Y
1839:[
1830:E
1816:2
1811:)
1807:]
1803:X
1799:[
1791:E
1785:(
1776:]
1769:2
1765:X
1759:[
1750:E
1741:]
1737:Y
1733:[
1725:E
1720:]
1716:X
1712:[
1704:E
1696:]
1692:Y
1688:X
1684:[
1676:E
1668:=
1663:Y
1660:,
1657:X
1605:,
1601:]
1597:Y
1593:[
1585:E
1580:]
1576:X
1572:[
1564:E
1556:]
1552:Y
1548:X
1544:[
1536:E
1531:=
1528:]
1523:)
1519:]
1515:Y
1511:[
1503:E
1495:Y
1491:(
1486:)
1482:]
1478:X
1474:[
1466:E
1458:X
1454:(
1449:[
1441:E
1436:=
1433:]
1428:)
1422:Y
1411:Y
1407:(
1402:)
1396:X
1385:X
1381:(
1376:[
1368:E
1356:2
1351:)
1347:]
1343:Y
1339:[
1331:E
1324:(
1315:]
1308:2
1304:Y
1298:[
1289:E
1284:=
1280:]
1273:2
1268:)
1264:]
1261:Y
1258:[
1250:E
1242:Y
1238:(
1231:[
1222:E
1213:=
1208:2
1203:Y
1189:2
1184:)
1180:]
1176:X
1172:[
1164:E
1158:(
1149:]
1142:2
1138:X
1132:[
1123:E
1118:=
1114:]
1107:2
1102:)
1098:]
1095:X
1092:[
1084:E
1076:X
1072:(
1065:[
1056:E
1047:=
1042:2
1037:X
1025:]
1021:Y
1017:[
1009:E
1000:=
995:Y
983:]
979:X
975:[
967:E
958:=
953:X
895:E
872:Y
850:Y
824:X
802:X
773:X
746:Y
711:Y
701:X
691:]
688:)
683:Y
672:Y
669:(
666:)
661:X
650:X
647:(
644:[
636:E
628:=
623:Y
620:,
617:X
567:,
564:]
561:)
556:Y
545:Y
542:(
539:)
534:X
523:X
520:(
517:[
509:E
504:=
501:)
498:Y
495:,
492:X
489:(
452:)
449:Y
446:,
443:X
440:(
422:.
410:Y
388:Y
362:X
336:X
276:Y
266:X
256:)
253:Y
250:,
247:X
244:(
232:=
227:Y
224:,
221:X
204:ρ
190:)
187:Y
184:,
181:X
178:(
160:ρ
77:(
63:Y
58:y
54:x
50:y
46:x
36:)
34:ρ
23:.
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