162:
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283:, who had been developing inverse probability methods, had his own questions about the validity of the process. While fiducial inference was developed in the early twentieth century, the late twentieth century believed that the method was inferior to the frequentist and Bayesian approaches but held an important place in historical context for statistical inference. However, modern-day approaches have generalized the fiducial interval into Generalized Fiducial Inference (GFI), which can be used to estimate discrete and continuous data sets.
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interval estimates can be formulated. In this regard confidence intervals and credible intervals have a similar standing but there two differences. First, credible intervals can readily deal with prior information, while confidence intervals cannot. Secondly, confidence intervals are more flexible and can be used practically in more situations than credible intervals: one area where credible intervals suffer in comparison is in dealing with
4158:
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makes this is straightforward in the case of confidence intervals, but it is somewhat more problematic for credible intervals where prior information needs to be taken properly into account. Checking of credible intervals can be done for situations representing no-prior-information but the check involves checking the long-run frequency properties of the procedures.
1164:
guidelines towards using them. In manufacturing, it is also common to find interval estimates estimating a product life, or to evaluate the tolerances of a product. Meeker and
Escobar (1998) present methods to analyze reliability data under parametric and nonparametric estimation, including the prediction of future, random variables (prediction intervals).
122:. A confidence interval states there is a 100Îł% confidence that the parameter of interest is within a lower and upper bound. A common misconception of confidence intervals is 100Îł% of the data set fits within or above/below the bounds, this is referred to as a tolerance interval, which is discussed below.
1121:. After experimenting, a typical first step in creating interval estimates is plotting using various graphical methods. From this, one can determine the distribution of samples from the data set. Producing interval boundaries with incorrect assumptions based on distribution makes a prediction faulty.
294:
use collected data set population to obtain an interval, within tolerance limits, containing 100Îł% values. Examples typically used to describe tolerance intervals include manufacturing. In this context, a percentage of an existing product set is evaluated to ensure that a percentage of the population
1163:
Applications of confidence intervals are used to solve a variety of problems dealing with uncertainty. Katz (1975) proposes various challenges and benefits for utilizing interval estimates in legal proceedings. For use in medical research, Altmen (1990) discusses the use of confidence intervals and
1136:
There should be ways of testing the performance of interval estimation procedures. This arises because many such procedures involve approximations of various kinds and there is a need to check that the actual performance of a procedure is close to what is claimed. The use of stochastic simulations
964:
Differentiating from the two-sided interval, the one-sided interval utilizes a level of confidence, Îł, to construct a minimum or maximum bound which predicts the parameter of interest to Îł*100% probability. Typically, a one-sided interval is required when the estimate's minimum or maximum bound is
259:
Utilizes the principles of a likelihood function to estimate the parameter of interest. Utilizing the likelihood-based method, confidence intervals can be found for exponential, Weibull, and lognormal means. Additionally, likelihood-based approaches can give confidence intervals for the standard
1128:
In commonly occurring situations there should be sets of standard procedures that can be used, subject to the checking and validity of any required assumptions. This applies for both confidence intervals and credible intervals. However, in more novel situations there should be guidance on how
899:). Examples may include estimating the average height of males in a geographic region or lengths of a particular desk made by a manufacturer. These cases tend to estimate the central value of a parameter. Typically, this is presented in a form similar to the equation below.
237:
While a prior assumption is helpful towards providing more data towards building an interval, it removes the objectivity of a confidence interval. A prior will be used to inform a posterior, if unchallenged this prior can lead to incorrect predictions.
268:
Fiducial inference utilizes a data set, carefully removes the noise and recovers a distribution estimator, Generalized
Fiducial Distribution (GFD). Without the use of Bayes' Theorem, there is no assumption of a prior, much like confidence intervals.
663:
1116:
When determining the significance of a parameter, it is best to understand the data and its collection methods. Before collecting data, an experiment should be planned such that the uncertainty of the data is sample variability, as opposed to a
241:
The credible interval's bounds are variable, unlike the confidence interval. There are multiple methods to determine where the correct upper and lower limits should be located. Common techniques to adjust the bounds of the interval include
233:
1124:
When interval estimates are reported, they should have a commonly held interpretation within and beyond the scientific community. Interval estimates derived from fuzzy logic have much more application-specific meanings.
1151:, which is a common approach to and justification for Bayesian statistics, interval estimation is not of direct interest. The outcome is a decision, not an interval estimate, and thus Bayesian decision theorists use a
1044:) will increase. Likewise, when concerned with finding only an upper bound of a parameter's estimate, the upper bound will decrease. A one-sided interval is a commonly found in material production's
960:
810:
contexts. These intervals are typically used in regression data sets, but prediction intervals are not used for extrapolation beyond the previous data's experimentally controlled parameters.
1815:
and has discussion comparing the three approaches. Note that this work predates modern computationally intensive methodologies. In addition, Chapter 21 discusses the
BehrensâFisher problem.
965:
not of interest. When concerned about the minimum predicted value of Î, one is no longer required to find an upper bounds of the estimate, leading to a form reduced form of the two-sided.
391:
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498:
448:
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is used to handle decision-making in a non-binary fashion for artificial intelligence, medical decisions, and other fields. In general, it takes inputs, maps them through
129:, one uses the z-table to create an interval where a confidence level of 100Îł% can be obtained centered around the sample mean from a data set of n measurements, . For a
825:, and produces an output decision. This process involves fuzzification, fuzzy logic rule evaluation, and defuzzification. When looking at fuzzy logic rule evaluation,
295:
is included within tolerance limits. When creating tolerance intervals, the bounds can be written in terms of an upper and lower tolerance limit, utilizing the sample
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There are multiple methods used to build a confidence interval, the correct choice depends on the data being analyzed. For a normal distribution with a known
194:
1075:) with some confidence (100Îł%). In this case, the manufacturer is not concerned with producing a product that is too strong, there is no upper-bound (
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convert our non-binary input information into tangible variables. These membership functions are essential to predict the uncertainty of the system.
1140:
Severini discusses conditions under which credible intervals and confidence intervals will produce similar results, and also discusses both the
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Hannig, Jan; Iyer, Hari; Lai, Randy C. S.; Lee, Thomas C. M. (2016-07-02). "Generalized
Fiducial Inference: A Review and New Results".
260:
deviation. It is also possible to create a prediction interval by combining the likelihood function and the future random variable.
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134:
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1155:: they minimize expected loss of a loss function with respect to the entire posterior distribution, not a specific interval.
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estimates the interval containing future samples with some confidence, Îł. Prediction intervals can be used for both
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1776:. Wiley series in probability and statistics Applied probability and statistics section. New York Weinheim: Wiley.
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This has played an important role in the development of the theory behind applicable statistical methodologies.
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And in the case of one-sided intervals where the tolerance is required only above or below a critical value,
1838:
https://web.archive.org/web/20061205114153/http://blog.peltarion.com/2006/10/25/fuzzy-math-part-1-the-theory
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Confidence intervals are used to estimate the parameter of interest from a sampled data set, commonly the
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1895:
1329:
Severini, Thomas A. (1991). "On the
Relationship between Bayesian and Non-Bayesian Interval Estimates".
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2019:
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Philosophical
Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
1234:
845:
Two-sided intervals estimate a parameter of interest, Î, with a level of confidence, Îł, using a lower (
658:{\displaystyle k_{2}=z_{\alpha /2}{\sqrt {\frac {\nu (1+{\frac {1}{N}})}{\chi _{1-\alpha ,\nu }^{2}}}}}
528:
varies by distribution and the number of sides, i, in the interval estimate. In a normal distribution,
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In the above
Chapter 20 covers confidence intervals, while Chapter 21 covers fiducial intervals and
1748:
Statistics with confidence: confidence intervals and statistical guidelines; [includes disk]
185:
the parameter of interest is included, as opposed to the confidence interval where one can be 100Îł%
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Differentiating between two-sided and one-sided intervals on a standard normal distribution curve.
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2011:
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37:
1400:
Hespanhol, Luiz; Vallio, Caio Sain; Costa, LucĂola
Menezes; Saragiotto, Bruno T (2019-07-01).
1048:, where an expected value of a material's strength, Î, must be above a certain minimum value (
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42:
1260:"Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability"
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of credible intervals and the posterior probabilities associated with confidence intervals.
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1402:"Understanding and interpreting confidence and credible intervals around effect estimates"
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As a result of removing the upper bound and maintaining the confidence, the lower-bound (
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228:{\displaystyle {\text{Posterior}}\ \propto \ {\text{Likelihood}}\times {\text{Prior}}}
165:
Bayesian
Distribution: Adjusting a prior distribution to form a posterior probability.
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246:(HPDI), equal-tailed interval, or choosing the center the interval around the mean.
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1708:"Presentation of a Confidence Interval Estimate as Evidence in a Legal Proceeding"
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1979:
1974:
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1989:
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1984:
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1879:
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97:. For a non-statistical method, interval estimates can be deduced from
32:
20:
1519:"Two-Sided Tolerance Limits for Normal Populations, Some Improvements"
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2928:
2548:
2343:
2255:
2240:
2235:
2200:
1634:
Hahn, Gerald J.; Doganaksoy, Necip; Meeker, William Q. (2019-08-01).
1518:
1301:
145:. The Jeffrey method can also be used to approximate intervals for a
1802:
The
Advanced Theory of Statistics. Vol 2: Inference and Relationship
1723:
1612:
1573:
1534:
1367:
Meeker, William Q.; Hahn, Gerald J.; Escobar, Luis A. (2017-03-27).
1259:
169:
As opposed to a confidence interval, a credible interval requires a
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2210:
2087:
2082:
2077:
1681:
Journal of the Royal Statistical Society. Series B (Methodological)
1331:
Journal of the Royal Statistical Society, Series B (Methodological)
126:
1371:. Wiley Series in Probability and Statistics (1 ed.). Wiley.
181:. Utilizing the posterior distribution, one can determine a 100Îł%
4097:
3798:
1677:"Bayesian Interval Estimates which are also Confidence Intervals"
1824:
Statistical Intervals: A Guide for Practitioners and Researchers
1369:
Statistical Intervals: A Guide for Practitioners and Researchers
4019:
3000:
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2954:
2205:
1996:
713:
is the critical value of the chi-square distribution utilizing
1399:
790:
is the critical values obtained from the normal distribution.
1848:
149:. If the underlying distribution is unknown, one can utilize
1939:
296:
115:
16:
Interval bounded by an upper and a lower limit statistics
1105:
1636:"Statistical Intervals, Not Statistical Significance"
1112:
Tolerance interval § Relation to other intervals
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1023:
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739:
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degrees of freedom that is exceeded with probability
719:
675:
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507:
457:
407:
331:
305:
197:
133:, confidence intervals can be approximated using the
3761:
Autoregressive conditional heteroskedasticity (ARCH)
1633:
1171:
955:{\displaystyle P(l_{b}<\Theta <u_{b})=\gamma }
52:
The most prevalent forms of interval estimation are
1822:Meeker, W.Q., Hahn, G.J. and Escobar, L.A. (2017).
153:to create bounds about the median of the data set.
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189:that an estimate is included within an interval.
173:assumption, modifying the assumption utilizing a
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1481:
3309:Multivariate adaptive regression splines (MARS)
1523:Journal of the American Statistical Association
1484:Journal of the American Statistical Association
1461:(4. ed., 1. publ ed.). Chichester: Wiley.
104:
1864:
1772:Meeker, William Q.; Escobar, Luis A. (1998).
1771:
1595:Hahn, Gerald J.; Meeker, William Q. (1993).
386:{\displaystyle (l_{b},u_{b})=\mu \pm k_{2}s}
1844:https://www.youtube.com/watch?v=__0nZuG4sTw
1322:
1008:{\displaystyle P(l_{b}<\Theta )=\gamma }
1909:
1871:
1857:
1594:
832:
706:{\displaystyle \chi _{1-\alpha ,\nu }^{2}}
2522:
1651:
1433:
1283:
1248:
1774:Statistical methods for reliability data
1751:(2. ed., ed.). London: BMJ Books.
1674:
1555:
1328:
836:
160:
1597:"Assumptions for Statistical Inference"
109:
4177:
3835:KaplanâMeier estimator (product limit)
1744:
1254:
3908:
3475:
3222:
2521:
2291:
1908:
1852:
1826:(2nd Edition). John Wiley & Sons.
1800:Kendall, M.G. and Stuart, A. (1973).
1406:Brazilian Journal of Physical Therapy
156:
4145:
3845:Accelerated failure time (AFT) model
1705:
1516:
1459:Bayesian statistics: an introduction
1362:
1360:
1106:Caution using and building estimates
249:
45:of interest. This is in contrast to
4157:
3440:Analysis of variance (ANOVA, anova)
2292:
1456:
1270:(767). The Royal Society: 333â380.
254:
13:
3535:CochranâMantelâHaenszel statistics
2161:Pearson product-moment correlation
1343:10.1111/j.2517-6161.1991.tb01849.x
993:
927:
244:highest posterior density interval
14:
4196:
1830:
1558:"What about the Other Intervals?"
1357:
493:{\displaystyle u_{b}=\mu +k_{1}s}
443:{\displaystyle l_{b}=\mu -k_{1}s}
4156:
4144:
4132:
4119:
4118:
3909:
1745:Altman, Douglas G., ed. (2011).
1653:10.1111/j.1740-9713.2019.01298.x
1174:
3794:Least-squares spectral analysis
1804:(3rd Edition). Griffin, London.
1794:
1765:
1738:
1699:
1668:
1627:
1158:
2775:Mean-unbiased minimum-variance
1878:
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1450:
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996:
977:
943:
911:
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602:
358:
332:
49:, which gives a single value.
1:
4088:Geographic information system
3304:Simultaneous equations models
1556:Vardeman, Stephen B. (1992).
1496:10.1080/01621459.2016.1165102
1241:
793:
783:{\displaystyle z_{\alpha /2}}
72:). Less common forms include
3271:Coefficient of determination
2882:Uniformly most powerful test
1675:Severini, Thomas A. (1993).
286:
105:Types of interval estimation
7:
3840:Proportional hazards models
3784:Spectral density estimation
3766:Vector autoregression (VAR)
3200:Maximum posterior estimator
2432:Randomized controlled trial
1167:
555: can be expressed as
263:
10:
4201:
3600:Multivariate distributions
2020:Average absolute deviation
1418:10.1016/j.bjpt.2018.12.006
1109:
4114:
4068:
4005:
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3904:
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3816:
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3721:
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3622:
3588:Structural equation model
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2924:Score/Lagrange multiplier
2909:
2862:
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2724:
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2517:
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2450:
2402:
2357:
2339:Sample size determination
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2191:
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2120:
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2058:
2010:
1930:
1921:
1917:
1904:
1886:
1836:Fuzzy Math Introductions
1712:The American Statistician
1601:The American Statistician
1562:The American Statistician
1517:Howe, W. G. (June 1969).
275:is a less common form of
4083:Environmental statistics
3605:Elliptical distributions
3398:Generalized linear model
3327:Simple linear regression
3097:HodgesâLehmann estimator
2554:Probability distribution
2463:Stochastic approximation
2025:Coefficient of variation
1225:Philosophy of statistics
396:for two-sided intervals
393:for two-sided intervals
143:Clopper-Pearson interval
41:of possible values of a
3743:Cross-correlation (XCF)
3351:Non-standard predictors
2785:LehmannâScheffĂ© theorem
2458:Adaptive clinical trial
833:One-sided vs. two-sided
823:fuzzy inference systems
746:{\displaystyle \alpha }
135:Wald Approximate Method
4139:Mathematics portal
3960:Engineering statistics
3868:NelsonâAalen estimator
3445:Analysis of covariance
3332:Ordinary least squares
3256:Pearson product-moment
2660:Statistical functional
2571:Empirical distribution
2404:Controlled experiments
2133:Frequency distribution
1911:Descriptive statistics
1457:Lee, Peter M. (2012).
1285:10.1098/rsta.1937.0005
1235:BehrensâFisher problem
1210:Induction (philosophy)
1142:coverage probabilities
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1069:
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387:
313:
229:
179:posterior distribution
166:
4185:Statistical intervals
4055:Population statistics
3997:System identification
3731:Autocorrelation (ACF)
3659:Exponential smoothing
3573:Discriminant analysis
3568:Canonical correlation
3432:Partition of variance
3294:Regression validation
3138:(JonckheereâTerpstra)
3037:Likelihood-ratio test
2726:Frequentist inference
2638:Locationâscale family
2559:Sampling distribution
2524:Statistical inference
2491:Cross-sectional study
2478:Observational studies
2437:Randomized experiment
2266:Stem-and-leaf display
2068:Central limit theorem
1842:What is Fuzzy Logic?
1377:10.1002/9781118594841
1337:(3). Wiley: 611â618.
1205:Estimation statistics
1195:Algorithmic inference
1131:non-parametric models
1097:
1095:{\displaystyle u_{b}}
1070:
1068:{\displaystyle l_{b}}
1039:
1037:{\displaystyle l_{b}}
1010:
957:
894:
892:{\displaystyle u_{b}}
867:
865:{\displaystyle l_{b}}
840:
785:
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728:
708:
660:
550:
548:{\displaystyle k_{2}}
523:
521:{\displaystyle k_{i}}
495:
445:
388:
314:
277:statistical inference
230:
164:
131:Binomial distribution
3978:Probabilistic design
3563:Principal components
3406:Exponential families
3358:Nonlinear regression
3337:General linear model
3299:Mixed effects models
3289:Errors and residuals
3266:Confounding variable
3168:Bayesian probability
3146:Van der Waerden test
3136:Ordered alternative
2901:Multiple comparisons
2780:RaoâBlackwellization
2743:Estimating equations
2699:Statistical distance
2417:Factorial experiment
1950:Arithmetic-Geometric
1230:Predictive inference
1220:Multiple comparisons
1200:Coverage probability
1079:
1052:
1021:
971:
905:
876:
849:
827:membership functions
759:
737:
726:{\displaystyle \nu }
717:
673:
561:
532:
505:
455:
405:
329:
312:{\displaystyle \mu }
303:
195:
177:, and determining a
147:Poisson distribution
110:Confidence intervals
94:prediction intervals
75:likelihood intervals
55:confidence intervals
4050:Official statistics
3973:Methods engineering
3654:Seasonal adjustment
3422:Poisson regressions
3342:Bayesian regression
3281:Regression analysis
3261:Partial correlation
3233:Regression analysis
2832:Prediction interval
2827:Likelihood interval
2817:Confidence interval
2809:Interval estimation
2770:Unbiased estimators
2588:Model specification
2468:Up-and-down designs
2156:Partial correlation
2112:Index of dispersion
2030:Interquartile range
1276:1937RSPTA.236..333N
872:) and upper bound (
800:prediction interval
702:
651:
292:Tolerance intervals
87:tolerance intervals
25:interval estimation
4070:Spatial statistics
3950:Medical statistics
3850:First hitting time
3804:Whittle likelihood
3455:Degrees of freedom
3450:Multivariate ANOVA
3383:Heteroscedasticity
3195:Bayesian estimator
3160:Bayesian inference
3009:KolmogorovâSmirnov
2894:Randomization test
2864:Testing hypotheses
2837:Tolerance interval
2748:Maximum likelihood
2643:Exponential family
2576:Density estimation
2536:Statistical theory
2496:Natural experiment
2442:Scientific control
2359:Survey methodology
2045:Standard deviation
1813:Bayesian intervals
1706:Katz, Leo (1975).
1490:(515): 1346â1361.
1182:Mathematics portal
1092:
1065:
1034:
1005:
952:
889:
862:
843:
780:
743:
723:
703:
676:
655:
625:
545:
518:
490:
440:
383:
321:standard deviation
309:
273:Fiducial inference
225:
167:
157:Credible intervals
120:standard deviation
81:fiducial intervals
65:credible intervals
4172:
4171:
4110:
4109:
4106:
4105:
4045:National accounts
4015:Actuarial science
4007:Social statistics
3900:
3899:
3896:
3895:
3892:
3891:
3827:Survival function
3812:
3811:
3674:Granger causality
3515:Contingency table
3490:Survival analysis
3467:
3466:
3463:
3462:
3319:Linear regression
3214:
3213:
3210:
3209:
3185:Credible interval
3154:
3153:
2937:
2936:
2753:Method of moments
2622:Parametric family
2583:Statistical model
2513:
2512:
2509:
2508:
2427:Random assignment
2349:Statistical power
2283:
2282:
2279:
2278:
2128:Contingency table
2098:
2097:
1965:Generalized/power
1783:978-0-471-14328-4
1758:978-0-7279-1375-3
1468:978-1-118-33257-3
1386:978-0-471-68717-7
1046:quality assurance
653:
652:
619:
319:, and the sample
250:Less common forms
223:
215:
211:
205:
201:
139:Jeffreys interval
4192:
4160:
4159:
4148:
4147:
4137:
4136:
4122:
4121:
4025:Crime statistics
3919:
3918:
3906:
3905:
3823:
3822:
3789:Fourier analysis
3776:Frequency domain
3756:
3703:
3669:Structural break
3629:
3628:
3578:Cluster analysis
3525:Log-linear model
3498:
3497:
3473:
3472:
3414:
3388:Homoscedasticity
3244:
3243:
3220:
3219:
3139:
3131:
3123:
3122:(KruskalâWallis)
3107:
3092:
3047:Cross validation
3032:
3014:AndersonâDarling
2961:
2948:
2947:
2919:Likelihood-ratio
2911:Parametric tests
2889:Permutation test
2872:1- & 2-tails
2763:Minimum distance
2735:Point estimation
2731:
2730:
2682:Optimal decision
2633:
2532:
2531:
2519:
2518:
2501:Quasi-experiment
2451:Adaptive designs
2302:
2301:
2289:
2288:
2166:Rank correlation
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1119:statistical bias
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255:Likelihood-based
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47:point estimation
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4189:
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4168:
4131:
4102:
4064:
4001:
3987:quality control
3954:
3936:Clinical trials
3913:
3888:
3872:
3860:Hazard function
3854:
3808:
3770:
3754:
3717:
3713:BreuschâGodfrey
3701:
3678:
3618:
3593:Factor analysis
3539:
3520:Graphical model
3492:
3459:
3426:
3412:
3392:
3346:
3313:
3275:
3238:
3237:
3206:
3150:
3137:
3129:
3121:
3105:
3090:
3069:Rank statistics
3063:
3042:Model selection
3030:
2988:Goodness of fit
2982:
2959:
2933:
2905:
2858:
2803:
2792:Median unbiased
2720:
2631:
2564:Order statistic
2526:
2505:
2472:
2446:
2398:
2353:
2296:
2294:Data collection
2275:
2187:
2142:
2116:
2094:
2054:
2006:
1923:Continuous data
1913:
1900:
1882:
1877:
1833:
1797:
1792:
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1784:
1770:
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1759:
1743:
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1724:10.2307/2683480
1704:
1700:
1673:
1669:
1632:
1628:
1613:10.2307/2684774
1593:
1589:
1574:10.2307/2685212
1554:
1550:
1535:10.2307/2283644
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1365:
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1253:
1249:
1244:
1215:Margin of error
1190:68â95â99.7 rule
1180:
1173:
1170:
1161:
1149:decision theory
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1086:
1082:
1080:
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289:
279:. The founder,
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107:
70:Bayesian method
17:
12:
11:
5:
4198:
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4154:
4142:
4128:
4115:
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4000:
3999:
3994:
3989:
3980:
3975:
3970:
3964:
3962:
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3953:
3952:
3947:
3942:
3933:
3931:Bioinformatics
3927:
3925:
3915:
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3901:
3898:
3897:
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3807:
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3796:
3791:
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3778:
3772:
3771:
3769:
3768:
3763:
3758:
3750:
3745:
3740:
3739:
3738:
3736:partial (PACF)
3727:
3725:
3719:
3718:
3716:
3715:
3710:
3705:
3697:
3692:
3686:
3684:
3683:Specific tests
3680:
3679:
3677:
3676:
3671:
3666:
3661:
3656:
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3646:
3641:
3635:
3633:
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3617:
3616:
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3612:
3597:
3596:
3595:
3585:
3583:Classification
3580:
3575:
3570:
3565:
3560:
3555:
3549:
3547:
3541:
3540:
3538:
3537:
3532:
3530:McNemar's test
3527:
3522:
3517:
3512:
3506:
3504:
3494:
3493:
3469:
3468:
3465:
3464:
3461:
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3436:
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3428:
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3424:
3408:
3402:
3400:
3394:
3393:
3391:
3390:
3385:
3380:
3375:
3370:
3368:Semiparametric
3365:
3360:
3354:
3352:
3348:
3347:
3345:
3344:
3339:
3334:
3329:
3323:
3321:
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3258:
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3208:
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3192:
3187:
3182:
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3180:
3175:
3164:
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3156:
3155:
3152:
3151:
3149:
3148:
3143:
3142:
3141:
3133:
3125:
3109:
3106:(MannâWhitney)
3101:
3100:
3099:
3086:
3085:
3084:
3073:
3071:
3065:
3064:
3062:
3061:
3060:
3059:
3054:
3049:
3039:
3034:
3031:(ShapiroâWilk)
3026:
3021:
3016:
3011:
3006:
2998:
2992:
2990:
2984:
2983:
2981:
2980:
2972:
2963:
2951:
2945:
2943:Specific tests
2939:
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2932:
2931:
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2921:
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2913:
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2906:
2904:
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2885:
2884:
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2860:
2859:
2857:
2856:
2855:
2854:
2849:
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2834:
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2824:
2819:
2813:
2811:
2805:
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2802:
2801:
2796:
2795:
2794:
2789:
2788:
2787:
2782:
2767:
2766:
2765:
2760:
2755:
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2728:
2722:
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2538:
2528:
2527:
2515:
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2507:
2506:
2504:
2503:
2498:
2493:
2488:
2482:
2480:
2474:
2473:
2471:
2470:
2465:
2460:
2454:
2452:
2448:
2447:
2445:
2444:
2439:
2434:
2429:
2424:
2419:
2414:
2408:
2406:
2400:
2399:
2397:
2396:
2394:Standard error
2391:
2386:
2381:
2380:
2379:
2374:
2363:
2361:
2355:
2354:
2352:
2351:
2346:
2341:
2336:
2331:
2326:
2324:Optimal design
2321:
2316:
2310:
2308:
2298:
2297:
2285:
2284:
2281:
2280:
2277:
2276:
2274:
2273:
2268:
2263:
2258:
2253:
2248:
2243:
2238:
2233:
2228:
2223:
2218:
2213:
2208:
2203:
2197:
2195:
2189:
2188:
2186:
2185:
2180:
2179:
2178:
2173:
2163:
2158:
2152:
2150:
2144:
2143:
2141:
2140:
2135:
2130:
2124:
2122:
2121:Summary tables
2118:
2117:
2115:
2114:
2108:
2106:
2100:
2099:
2096:
2095:
2093:
2092:
2091:
2090:
2085:
2080:
2070:
2064:
2062:
2056:
2055:
2053:
2052:
2047:
2042:
2037:
2032:
2027:
2022:
2016:
2014:
2008:
2007:
2005:
2004:
1999:
1994:
1993:
1992:
1987:
1982:
1977:
1972:
1967:
1962:
1957:
1955:Contraharmonic
1952:
1947:
1936:
1934:
1925:
1915:
1914:
1902:
1901:
1899:
1898:
1893:
1887:
1884:
1883:
1876:
1875:
1868:
1861:
1853:
1847:
1846:
1840:
1832:
1831:External links
1829:
1828:
1827:
1819:
1818:
1817:
1816:
1806:
1805:
1796:
1793:
1790:
1789:
1782:
1764:
1757:
1737:
1718:(4): 138â142.
1698:
1687:(2): 533â540.
1667:
1626:
1587:
1568:(3): 193â197.
1548:
1509:
1474:
1467:
1449:
1412:(4): 290â301.
1392:
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27:is the use of
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9:
6:
4:
3:
2:
4197:
4186:
4183:
4182:
4180:
4165:
4164:
4155:
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4143:
4141:
4140:
4135:
4129:
4127:
4126:
4117:
4116:
4113:
4099:
4096:
4094:
4093:Geostatistics
4091:
4089:
4086:
4084:
4081:
4079:
4076:
4075:
4073:
4071:
4067:
4061:
4060:Psychometrics
4058:
4056:
4053:
4051:
4048:
4046:
4043:
4041:
4038:
4036:
4033:
4031:
4028:
4026:
4023:
4021:
4018:
4016:
4013:
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4010:
4008:
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3998:
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3990:
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3926:
3924:
3923:Biostatistics
3920:
3916:
3912:
3907:
3903:
3885:
3884:Log-rank test
3882:
3881:
3879:
3875:
3869:
3866:
3865:
3863:
3861:
3857:
3851:
3848:
3846:
3843:
3841:
3838:
3836:
3833:
3832:
3830:
3828:
3824:
3821:
3819:
3815:
3805:
3802:
3800:
3797:
3795:
3792:
3790:
3787:
3785:
3782:
3781:
3779:
3777:
3773:
3767:
3764:
3762:
3759:
3757:
3755:(BoxâJenkins)
3751:
3749:
3746:
3744:
3741:
3737:
3734:
3733:
3732:
3729:
3728:
3726:
3724:
3720:
3714:
3711:
3709:
3708:DurbinâWatson
3706:
3704:
3698:
3696:
3693:
3691:
3690:DickeyâFuller
3688:
3687:
3685:
3681:
3675:
3672:
3670:
3667:
3665:
3664:Cointegration
3662:
3660:
3657:
3655:
3652:
3650:
3647:
3645:
3642:
3640:
3639:Decomposition
3637:
3636:
3634:
3630:
3627:
3625:
3621:
3611:
3608:
3607:
3606:
3603:
3602:
3601:
3598:
3594:
3591:
3590:
3589:
3586:
3584:
3581:
3579:
3576:
3574:
3571:
3569:
3566:
3564:
3561:
3559:
3556:
3554:
3551:
3550:
3548:
3546:
3542:
3536:
3533:
3531:
3528:
3526:
3523:
3521:
3518:
3516:
3513:
3511:
3510:Cohen's kappa
3508:
3507:
3505:
3503:
3499:
3495:
3491:
3487:
3483:
3479:
3474:
3470:
3456:
3453:
3451:
3448:
3446:
3443:
3441:
3438:
3437:
3435:
3433:
3429:
3423:
3419:
3415:
3409:
3407:
3404:
3403:
3401:
3399:
3395:
3389:
3386:
3384:
3381:
3379:
3376:
3374:
3371:
3369:
3366:
3364:
3363:Nonparametric
3361:
3359:
3356:
3355:
3353:
3349:
3343:
3340:
3338:
3335:
3333:
3330:
3328:
3325:
3324:
3322:
3320:
3316:
3310:
3307:
3305:
3302:
3300:
3297:
3295:
3292:
3290:
3287:
3286:
3284:
3282:
3278:
3272:
3269:
3267:
3264:
3262:
3259:
3257:
3254:
3253:
3251:
3249:
3245:
3241:
3234:
3231:
3229:
3226:
3225:
3221:
3217:
3201:
3198:
3197:
3196:
3193:
3191:
3188:
3186:
3183:
3179:
3176:
3174:
3171:
3170:
3169:
3166:
3165:
3163:
3161:
3157:
3147:
3144:
3140:
3134:
3132:
3126:
3124:
3118:
3117:
3116:
3113:
3112:Nonparametric
3110:
3108:
3102:
3098:
3095:
3094:
3093:
3087:
3083:
3082:Sample median
3080:
3079:
3078:
3075:
3074:
3072:
3070:
3066:
3058:
3055:
3053:
3050:
3048:
3045:
3044:
3043:
3040:
3038:
3035:
3033:
3027:
3025:
3022:
3020:
3017:
3015:
3012:
3010:
3007:
3005:
3003:
2999:
2997:
2994:
2993:
2991:
2989:
2985:
2979:
2977:
2973:
2971:
2969:
2964:
2962:
2957:
2953:
2952:
2949:
2946:
2944:
2940:
2930:
2927:
2925:
2922:
2920:
2917:
2916:
2914:
2912:
2908:
2902:
2899:
2895:
2892:
2891:
2890:
2887:
2883:
2880:
2879:
2878:
2875:
2873:
2870:
2869:
2867:
2865:
2861:
2853:
2850:
2848:
2845:
2844:
2843:
2840:
2838:
2835:
2833:
2830:
2828:
2825:
2823:
2820:
2818:
2815:
2814:
2812:
2810:
2806:
2800:
2797:
2793:
2790:
2786:
2783:
2781:
2778:
2777:
2776:
2773:
2772:
2771:
2768:
2764:
2761:
2759:
2756:
2754:
2751:
2749:
2746:
2745:
2744:
2741:
2740:
2738:
2736:
2732:
2729:
2727:
2723:
2717:
2714:
2712:
2709:
2705:
2702:
2701:
2700:
2697:
2695:
2692:
2688:
2687:loss function
2685:
2684:
2683:
2680:
2676:
2673:
2671:
2668:
2666:
2663:
2662:
2661:
2658:
2656:
2653:
2651:
2648:
2644:
2641:
2639:
2636:
2634:
2628:
2625:
2624:
2623:
2620:
2616:
2613:
2611:
2608:
2606:
2603:
2602:
2601:
2598:
2594:
2591:
2589:
2586:
2585:
2584:
2581:
2577:
2574:
2573:
2572:
2569:
2565:
2562:
2561:
2560:
2557:
2555:
2552:
2550:
2547:
2545:
2542:
2541:
2539:
2537:
2533:
2529:
2525:
2520:
2516:
2502:
2499:
2497:
2494:
2492:
2489:
2487:
2484:
2483:
2481:
2479:
2475:
2469:
2466:
2464:
2461:
2459:
2456:
2455:
2453:
2449:
2443:
2440:
2438:
2435:
2433:
2430:
2428:
2425:
2423:
2420:
2418:
2415:
2413:
2410:
2409:
2407:
2405:
2401:
2395:
2392:
2390:
2389:Questionnaire
2387:
2385:
2382:
2378:
2375:
2373:
2370:
2369:
2368:
2365:
2364:
2362:
2360:
2356:
2350:
2347:
2345:
2342:
2340:
2337:
2335:
2332:
2330:
2327:
2325:
2322:
2320:
2317:
2315:
2312:
2311:
2309:
2307:
2303:
2299:
2295:
2290:
2286:
2272:
2269:
2267:
2264:
2262:
2259:
2257:
2254:
2252:
2249:
2247:
2244:
2242:
2239:
2237:
2234:
2232:
2229:
2227:
2224:
2222:
2219:
2217:
2216:Control chart
2214:
2212:
2209:
2207:
2204:
2202:
2199:
2198:
2196:
2194:
2190:
2184:
2181:
2177:
2174:
2172:
2169:
2168:
2167:
2164:
2162:
2159:
2157:
2154:
2153:
2151:
2149:
2145:
2139:
2136:
2134:
2131:
2129:
2126:
2125:
2123:
2119:
2113:
2110:
2109:
2107:
2105:
2101:
2089:
2086:
2084:
2081:
2079:
2076:
2075:
2074:
2071:
2069:
2066:
2065:
2063:
2061:
2057:
2051:
2048:
2046:
2043:
2041:
2038:
2036:
2033:
2031:
2028:
2026:
2023:
2021:
2018:
2017:
2015:
2013:
2009:
2003:
2000:
1998:
1995:
1991:
1988:
1986:
1983:
1981:
1978:
1976:
1973:
1971:
1968:
1966:
1963:
1961:
1958:
1956:
1953:
1951:
1948:
1946:
1943:
1942:
1941:
1938:
1937:
1935:
1933:
1929:
1926:
1924:
1920:
1916:
1912:
1907:
1903:
1897:
1894:
1892:
1889:
1888:
1885:
1881:
1874:
1869:
1867:
1862:
1860:
1855:
1854:
1851:
1845:
1841:
1839:
1835:
1834:
1825:
1821:
1820:
1814:
1810:
1809:
1808:
1807:
1803:
1799:
1798:
1785:
1779:
1775:
1768:
1760:
1754:
1750:
1749:
1741:
1733:
1729:
1725:
1721:
1717:
1713:
1709:
1702:
1694:
1690:
1686:
1682:
1678:
1671:
1663:
1659:
1654:
1649:
1645:
1641:
1637:
1630:
1622:
1618:
1614:
1610:
1606:
1602:
1598:
1591:
1583:
1579:
1575:
1571:
1567:
1563:
1559:
1552:
1544:
1540:
1536:
1532:
1528:
1524:
1520:
1513:
1505:
1501:
1497:
1493:
1489:
1485:
1478:
1470:
1464:
1460:
1453:
1445:
1441:
1436:
1431:
1427:
1423:
1419:
1415:
1411:
1407:
1403:
1396:
1388:
1382:
1378:
1374:
1370:
1363:
1361:
1352:
1348:
1344:
1340:
1336:
1332:
1325:
1311:
1307:
1303:
1299:
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1277:
1273:
1269:
1265:
1261:
1257:
1251:
1247:
1236:
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1231:
1228:
1226:
1223:
1221:
1218:
1216:
1213:
1211:
1208:
1206:
1203:
1201:
1198:
1196:
1193:
1191:
1188:
1187:
1183:
1177:
1172:
1165:
1156:
1154:
1150:
1145:
1143:
1138:
1134:
1132:
1126:
1122:
1120:
1113:
1103:
1087:
1083:
1060:
1056:
1047:
1029:
1025:
1015:
1002:
999:
990:
985:
981:
974:
966:
962:
949:
946:
938:
934:
930:
924:
919:
915:
908:
900:
884:
880:
857:
853:
839:
830:
828:
824:
820:
811:
809:
805:
801:
791:
775:
771:
767:
763:
754:
740:
720:
698:
693:
690:
687:
684:
681:
677:
668:
665:
647:
642:
639:
636:
633:
630:
626:
616:
613:
608:
605:
599:
590:
586:
582:
578:
574:
569:
565:
556:
540:
536:
513:
509:
500:
487:
482:
478:
474:
471:
468:
463:
459:
450:
437:
432:
428:
424:
421:
418:
413:
409:
400:
397:
394:
380:
375:
371:
367:
364:
361:
353:
349:
345:
340:
336:
324:
322:
306:
298:
293:
284:
282:
278:
274:
270:
261:
247:
245:
239:
235:
217:
206:
190:
188:
184:
180:
176:
172:
163:
154:
152:
151:bootstrapping
148:
144:
140:
136:
132:
128:
123:
121:
117:
102:
100:
96:
95:
90:
88:
84:
82:
78:
76:
71:
67:
66:
62:method) and
61:
57:
56:
50:
48:
44:
40:
39:
34:
30:
26:
22:
4161:
4149:
4130:
4123:
4035:Econometrics
3985: /
3968:Chemometrics
3945:Epidemiology
3938: /
3911:Applications
3753:ARIMA model
3700:Q-statistic
3649:Stationarity
3545:Multivariate
3488: /
3484: /
3482:Multivariate
3480: /
3420: /
3416: /
3190:Bayes factor
3089:Signed rank
3001:
2975:
2967:
2955:
2808:
2650:Completeness
2486:Cohort study
2384:Opinion poll
2319:Missing data
2306:Study design
2261:Scatter plot
2183:Scatter plot
2176:Spearman's Ï
2138:Grouped data
1823:
1801:
1795:Bibliography
1773:
1767:
1747:
1740:
1715:
1711:
1701:
1684:
1680:
1670:
1646:(4): 20â22.
1643:
1640:Significance
1639:
1629:
1604:
1600:
1590:
1565:
1561:
1551:
1529:(326): 610.
1526:
1522:
1512:
1487:
1483:
1477:
1458:
1452:
1409:
1405:
1395:
1368:
1334:
1330:
1324:
1313:. Retrieved
1267:
1263:
1250:
1162:
1159:Applications
1153:Bayes action
1146:
1139:
1135:
1127:
1123:
1115:
1016:
967:
963:
901:
844:
817:
797:
755:
669:
666:
557:
501:
451:
401:
398:
395:
325:
290:
271:
267:
258:
240:
236:
191:
186:
182:
175:Bayes factor
168:
124:
113:
92:
85:
79:
73:
63:
53:
51:
36:
24:
18:
4163:WikiProject
4078:Cartography
4040:Jurimetrics
3992:Reliability
3723:Time domain
3702:(LjungâBox)
3624:Time-series
3502:Categorical
3486:Time-series
3478:Categorical
3413:(Bernoulli)
3248:Correlation
3228:Correlation
3024:JarqueâBera
2996:Chi-squared
2758:M-estimator
2711:Asymptotics
2655:Sufficiency
2422:Interaction
2334:Replication
2314:Effect size
2271:Violin plot
2251:Radar chart
2231:Forest plot
2221:Correlogram
2171:Kendall's Ï
1607:(1): 1â11.
819:Fuzzy logic
814:Fuzzy logic
808:frequentist
281:R.A. Fisher
183:probability
99:fuzzy logic
60:frequentist
29:sample data
4030:Demography
3748:ARMA model
3553:Regression
3130:(Friedman)
3091:(Wilcoxon)
3029:Normality
3019:Lilliefors
2966:Student's
2842:Resampling
2716:Robustness
2704:divergence
2694:Efficiency
2632:(monotone)
2627:Likelihood
2544:Population
2377:Stratified
2329:Population
2148:Dependence
2104:Count data
2035:Percentile
2012:Dispersion
1945:Arithmetic
1880:Statistics
1315:2021-07-15
1256:Neyman, J.
1242:References
1110:See also:
794:Prediction
214:Likelihood
21:statistics
3411:Logistic
3178:posterior
3104:Rank sum
2852:Jackknife
2847:Bootstrap
2665:Bootstrap
2600:Parameter
2549:Statistic
2344:Statistic
2256:Run chart
2241:Pie chart
2236:Histogram
2226:Fan chart
2201:Bar chart
2083:L-moments
1970:Geometric
1732:0003-1305
1693:0035-9246
1662:1740-9705
1621:0003-1305
1582:0003-1305
1543:0162-1459
1504:0162-1459
1426:1413-3555
1351:0035-9246
1294:0080-4614
1003:γ
994:Θ
950:γ
928:Θ
768:α
741:α
721:ν
694:ν
688:α
685:−
678:χ
643:ν
637:α
634:−
627:χ
600:ν
583:α
472:μ
425:−
422:μ
368:±
365:μ
307:μ
287:Tolerance
218:×
207:∝
200:Posterior
187:confident
43:parameter
4179:Category
4125:Category
3818:Survival
3695:Johansen
3418:Binomial
3373:Isotonic
2960:(normal)
2605:location
2412:Blocking
2367:Sampling
2246:QâQ plot
2211:Box plot
2193:Graphics
2088:Skewness
2078:Kurtosis
2050:Variance
1980:Heronian
1975:Harmonic
1444:30638956
1310:19584450
1258:(1937).
1168:See also
804:Bayesian
264:Fiducial
127:variance
38:interval
33:estimate
4151:Commons
4098:Kriging
3983:Process
3940:studies
3799:Wavelet
3632:General
2799:Plug-in
2593:L space
2372:Cluster
2073:Moments
1891:Outline
1435:6630113
1272:Bibcode
667:Where,
4020:Census
3610:Normal
3558:Manova
3378:Robust
3128:2-way
3120:1-way
2958:-test
2629:
2206:Biplot
1997:Median
1990:Lehmer
1932:Center
1780:
1755:
1730:
1691:
1660:
1619:
1580:
1541:
1502:
1465:
1442:
1432:
1424:
1383:
1349:
1308:
1300:
1292:
210:
204:
141:, and
3644:Trend
3173:prior
3115:anova
3004:-test
2978:-test
2970:-test
2877:Power
2822:Pivot
2615:shape
2610:scale
2060:Shape
2040:Range
1985:Heinz
1960:Cubic
1896:Index
1306:S2CID
1302:91337
1298:JSTOR
323:, s.
222:Prior
171:prior
3877:Test
3077:Sign
2929:Wald
2002:Mode
1940:Mean
1778:ISBN
1753:ISBN
1728:ISSN
1689:ISSN
1658:ISSN
1617:ISSN
1578:ISSN
1539:ISSN
1500:ISSN
1463:ISBN
1440:PMID
1422:ISSN
1381:ISBN
1347:ISSN
1290:ISSN
991:<
931:<
925:<
806:and
297:mean
116:mean
91:and
3057:BIC
3052:AIC
1720:doi
1648:doi
1609:doi
1570:doi
1531:doi
1492:doi
1488:111
1430:PMC
1414:doi
1373:doi
1339:doi
1280:doi
1268:236
1147:In
1102:).
118:or
68:(a
58:(a
35:an
31:to
19:In
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1716:29
1714:.
1710:.
1685:55
1683:.
1679:.
1656:.
1644:16
1642:.
1638:.
1615:.
1605:47
1603:.
1599:.
1576:.
1566:46
1564:.
1560:.
1537:.
1527:64
1525:.
1521:.
1498:.
1486:.
1438:.
1428:.
1420:.
1410:23
1408:.
1404:.
1379:.
1359:^
1345:.
1335:53
1333:.
1304:.
1296:.
1288:.
1278:.
1266:.
1262:.
1133:.
798:A
753:.
299:,
137:,
101:.
23:,
3002:G
2976:F
2968:t
2956:Z
2675:V
2670:U
1872:e
1865:t
1858:v
1786:.
1761:.
1734:.
1722::
1695:.
1664:.
1650::
1623:.
1611::
1584:.
1572::
1545:.
1533::
1506:.
1494::
1471:.
1446:.
1416::
1389:.
1375::
1353:.
1341::
1318:.
1282::
1274::
1088:b
1084:u
1061:b
1057:l
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1000:=
997:)
986:b
982:l
978:(
975:P
947:=
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939:b
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912:(
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858:b
854:l
776:2
772:/
764:z
699:2
691:,
682:1
648:2
640:,
631:1
622:)
617:N
614:1
609:+
606:1
603:(
591:2
587:/
579:z
575:=
570:2
566:k
541:2
537:k
514:i
510:k
488:s
483:1
479:k
475:+
469:=
464:b
460:u
438:s
433:1
429:k
419:=
414:b
410:l
381:s
376:2
372:k
362:=
359:)
354:b
350:u
346:,
341:b
337:l
333:(
89:,
83:,
77:,
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