902:
through assigning the same coefficient to the French and
Italian categories and a different one to the Germans. The signs assigned indicate the direction of the relationship (hence giving Germans a negative sign is indicative of their lower hypothesized optimism scores). Hypothesis 2: French and Italians are expected to differ on their optimism scores (French = +0.50, Italian = â0.50, German = 0). Here, assigning a zero value to Germans demonstrates their non-inclusion in the analysis of this hypothesis. Again, the signs assigned are indicative of the proposed relationship.
1035:
but may also be employed when the independent variable is categorical. We cannot simply choose values to probe the interaction as we would in the continuous variable case because of the nominal nature of the data (i.e., in the continuous case, one could analyze the data at high, moderate, and low levels assigning 1 standard deviation above the mean, at the mean, and at one standard deviation below the mean respectively). In our categorical case we would use a simple regression equation for each group to investigate the simple slopes. It is common practice to
22:
3583:
3569:
455:. In such a case, it is logically assumed that an infinite number of categories exist, but at any one time most of them (in fact, all but a finite number) have never been seen. All formulas are phrased in terms of the number of categories actually seen so far rather than the (infinite) total number of potential categories in existence, and methods are created for incremental updating of statistical distributions, including adding "new" categories.
3607:
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counting (how many people have a given last name), or finding the mode (which name occurs most often). However, we cannot meaningfully compute the "sum" of Smith + Johnson, or ask whether Smith is "less than" or "greater than" Johnson. As a result, we cannot meaningfully ask what the "average name" (the mean) or the "middle-most name" (the median) is in a set of names.
845:
specific research question. This tailored hypothesis is generally based on previous theory and/or research. The hypotheses proposed are generally as follows: first, there is the central hypothesis which postulates a large difference between two sets of groups; the second hypothesis suggests that within each set, the differences among the groups are small. Through its
356:, we cannot meaningfully evaluate "Smith < Johnson" at all, because no consistent ordering is defined for such characters. However, if we do consider the names as written, e.g., in the Latin alphabet, and define an ordering corresponding to standard alphabetical order, then we have effectively converted them into
1008:
may arise when considering the relationship among three or more variables, and describes a situation in which the simultaneous influence of two variables on a third is not additive. Interactions may arise with categorical variables in two ways: either categorical by categorical variable interactions,
844:
The contrast coding system allows a researcher to directly ask specific questions. Rather than having the coding system dictate the comparison being made (i.e., against a control group as in dummy coding, or against all groups as in effects coding) one can design a unique comparison catering to one's
964:
Nonsense coding occurs when one uses arbitrary values in place of the designated "0"s "1"s and "-1"s seen in the previous coding systems. Although it produces correct mean values for the variables, the use of nonsense coding is not recommended as it will lead to uninterpretable statistical results.
1034:
used in regression which is similar to the simple effects analysis in ANOVA, used to analyze interactions. In this test, we are examining the simple slopes of one independent variable at specific values of the other independent variable. Such a test is not limited to use with continuous variables,
571:
and the mean of the control group. It is suggested that three criteria be met for specifying a suitable control group: the group should be a well-established group (e.g. should not be an "other" category), there should be a logical reason for selecting this group as a comparison (e.g. the group is
901:
To illustrate the construction of contrast codes consider the following table. Coefficients were chosen to illustrate our a priori hypotheses: Hypothesis 1: French and
Italian persons will score higher on optimism than Germans (French = +0.33, Italian = +0.33, German = â0.66). This is illustrated
713:
Effects coding can either be weighted or unweighted. Weighted effects coding is simply calculating a weighted grand mean, thus taking into account the sample size in each variable. This is most appropriate in situations where the sample is representative of the population in question. Unweighted
336:
can be defined. As an example, given a set of people, we can consider the set of categorical variables corresponding to their last names. We can consider operations such as equivalence (whether two people have the same last name), set membership (whether a person has a name in a given list),
438:
It is also possible to consider categorical variables where the number of categories is not fixed in advance. As an example, for a categorical variable describing a particular word, we might not know in advance the size of the vocabulary, and we would like to allow for the possibility of
1017:
This type of interaction arises when we have two categorical variables. In order to probe this type of interaction, one would code using the system that addresses the researcher's hypothesis most appropriately. The product of the codes yields the interaction. One may then calculate the
575:
In dummy coding, the reference group is assigned a value of 0 for each code variable, the group of interest for comparison to the reference group is assigned a value of 1 for its specified code variable, while all other groups are assigned 0 for that particular code variable.
868:
or non-orthogonal, in regression, it is essential that the coefficient values assigned in contrast coding be orthogonal. Furthermore, in regression, coefficient values must be either in fractional or decimal form. They cannot take on interval values.
742:
value would entail the coded group as having scored less than the mean of all groups on the dependent variable. Using our previous example of optimism scores among nationalities, if the group of interest is
Italians, observing a negative
588:. To illustrate this, suppose that we are measuring optimism among several nationalities and we have decided that French people would serve as a useful control. If we are comparing them against Italians, and we observe a negative
583:
values should be interpreted such that the experimental group is being compared against the control group. Therefore, yielding a negative b value would entail the experimental group have scored less than the control group on the
984:) vector spaces, usually in such a way that âsimilarâ values are assigned âsimilarâ vectors, or with respect to some other kind of criterion making the vectors useful for the respective application. A common special case are
300:
possible values). In general, however, the numbers are arbitrary, and have no significance beyond simply providing a convenient label for a particular value. In other words, the values in a categorical variable exist on a
159:. However, particularly when considering data analysis, it is common to use the term "categorical data" to apply to data sets that, while containing some categorical variables, may also contain non-categorical variables.
701:
In the effects coding system, data are analyzed through comparing one group to all other groups. Unlike dummy coding, there is no control group. Rather, the comparison is being made at the mean of all groups combined
737:
values should be interpreted such that the experimental group is being compared against the mean of all groups combined (or weighted grand mean in the case of weighted effects coding). Therefore, yielding a negative
725:
In effects coding, we code the group of interest with a 1, just as we would for dummy coding. The principal difference is that we code â1 for the group we are least interested in. Since we continue to use a
1039:
or center variables to make the data more interpretable in simple slopes analysis; however, categorical variables should never be standardized or centered. This test can be used with all coding systems.
506:
There are three main coding systems typically used in the analysis of categorical variables in regression: dummy coding, effects coding, and contrast coding. The regression equation takes the form of
447:, assume that the number of categories is known in advance, and changing the number of categories on the fly is tricky. In such cases, more advanced techniques must be used. An example is the
722:
is the difference between the mean of the experimental group and the grand mean, whereas in the weighted situation it is the mean of the experimental group minus the weighted grand mean.
730:- 1 coding scheme, it is in fact the â1 coded group that will not produce data, hence the fact that we are least interested in that group. A code of 0 is assigned to all other groups.
495:
being the number of groups) are coded. This minimizes redundancy while still representing the complete data set as no additional information would be gained from coding the total
503:= 2: male and female), if we only code females everyone left over would necessarily be males. In general, the group that one does not code for is the group of least interest.
4050:
97:
that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or
572:
anticipated to score highest on the dependent variable), and finally, the group's sample size should be substantive and not small compared to the other groups.
348:
and consider the
Cyrillic ordering of letters, we might get a different result of evaluating "Smith < Johnson" than if we write the names in the standard
894:
values, indicating that we would reach the same conclusions about whether or not there is a significant difference; however, we can no longer interpret the
4111:
4070:
344:, which is a property that is not inherent in the names themselves, but in the way we construct the labels. For example, if we write the names in
4065:
2704:
538:
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effects coding is most appropriate in situations where differences in sample size are the result of incidental factors. The interpretation of
4131:
3209:
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and regression. Unlike when used in ANOVA, where it is at the researcher's discretion whether they choose coefficient values that are either
4080:
3359:
2983:
1624:
710:). Therefore, one is not looking for data in relation to another group but rather, one is seeking data in relation to the grand mean.
3645:
2757:
4090:
3196:
4075:
4022:
531:, and these values take on different meanings based on the coding system used. The choice of coding system does not affect the
431:, etc.). As a result, the term "categorical variable" is often reserved for cases with 3 or more outcomes, sometimes termed a
487:
in order to be able to analyze the data. One does so through the use of coding systems. Analyses are conducted such that only
4055:
1215:
1104:
419:). Because of their importance, these variables are often considered a separate category, with a separate distribution (the
1619:
1319:
1054:
411:
Categorical variables that have only two possible outcomes (e.g., "yes" vs. "no" or "success" vs. "failure") are known as
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2223:
1371:
4012:
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65:
43:
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The difference between the sum of the positive coefficients and the sum of the negative coefficients should equal 1.
36:
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or comparison group in mind. One is therefore analyzing the data of one group in relation to the comparison group:
113:. Commonly (though not in this article), each of the possible values of a categorical variable is referred to as a
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4167:
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2903:
2648:
2019:
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statistics. However, one chooses a coding system based on the comparison of interest since the interpretation of
444:
397:
4157:
4152:
3293:
2505:
2312:
2201:
2159:
1090:
392:, which counts the frequency of each possible combination of numbers of occurrences of the various categories.
2233:
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encountering words that we have not already seen. Standard statistical models, such as those involving the
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3638:
3087:
3036:
3021:
3011:
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2719:
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2500:
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For ease in statistical processing, categorical variables may be assigned numeric indices, e.g. 1 through
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205:
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consisting of categorical variables or of data that has been converted into that form, for example as
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2002:
1911:
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30:
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method of scoring data (i.e. represents categories or group membership). These can be included as
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3053:
2993:
2930:
2568:
2552:
2290:
2152:
2142:
1992:
1906:
846:
105:. In computer science and some branches of mathematics, categorical variables are referred to as
384:-way categorical variable to be expressed with separate probabilities specified for each of the
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4017:
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3478:
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1777:
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1237:. Springer Texts in Statistics (Second ed.). New York: Springer-Verlag. pp. xvi+483.
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grouped within given intervals. Often, purely categorical data are summarised in the form of a
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possible outcomes. Such multiple-category categorical variables are often analyzed using a
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8:
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309:, and cannot be otherwise manipulated as numbers could be. Instead, valid operations are
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2196:
2091:
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2024:
1984:
1944:
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1807:
1493:
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1156:
Applied multiple regression/correlation analysis for the behavioural sciences (3rd ed.)
850:
585:
568:
401:
353:
341:
305:: they each represent a logically separate concept, cannot necessarily be meaningfully
188:; categorical variables are often assumed to be polytomous unless otherwise specified.
181:
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is treating continuous data or polytomous variables as if they were binary variables.
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2012:
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1285:(updated electronic version of the (University of Aalborg) 3rd (1989) ed.).
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Certain differences emerge when we compare our a priori coefficients between
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302:
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The sum of the contrast coefficients per each code variable must equal zero.
592:
value, this would suggest
Italians obtain lower optimism scores on average.
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3783:
3483:
3416:
3393:
3308:
2638:
1934:
1832:
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1709:
1694:
1631:
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977:
160:
143:. More specifically, categorical data may derive from observations made of
140:
106:
3623:
3526:
3488:
3171:
3072:
2934:
2747:
2714:
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2123:
2118:
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1699:
1679:
1669:
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as the control group and C1, C2, and C3 respectively being the codes for
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is the slope and gives the weight empirically assigned to an explanator,
257:
220:
The roll of a six-sided dice: possible outcomes are 1, 2, 3, 4, 5, or 6.
216:
Examples of values that might be represented in a categorical variable:
3971:
2372:
1852:
1552:
1483:
1433:
1408:
1328:
707:
227:
170:
A categorical variable that can take on exactly two values is termed a
82:
184:. Categorical variables with more than two possible values are called
2525:
2377:
1997:
1792:
1704:
1689:
1684:
1649:
1110:
996:
and words with similar meanings are to be assigned similar vectors.
296:-way categorical variable (i.e. a variable that can express exactly
2041:
1659:
1536:
1531:
1526:
1012:
993:
345:
1025:
3546:
3247:
872:
The construction of contrast codes is restricted by three rules:
253:
78:
Variable capable of taking on a limited number of possible values
988:, where the possible values of the categorical variable are the
223:
Demographic information of a population: gender, disease status.
4116:
3721:
3468:
2449:
2423:
2403:
1654:
1445:
204:
often treats category membership with one or more quantitative
857:
when compared with the less directed previous coding systems.
1297:
1089:
Yates, Daniel S.; Moore, David S.; Starnes, Daren S. (2003).
861:
849:
focused hypotheses, contrast coding may yield an increase in
1189:
Discrete
Statistical Models with Social Science Applications
1022:
value and determine whether the interaction is significant.
1388:
989:
4051:
Household, Income and Labour
Dynamics in Australia Survey
750:
The following table is an example of effects coding with
976:
are codings of categorical values into low-dimensional
595:
The following table is an example of dummy coding with
458:
1194:
3210:
Autoregressive conditional heteroskedasticity (ARCH)
1009:
or categorical by continuous variable interactions.
718:
is different for each: in unweighted effects coding
211:
4117:
European
Society for Opinion and Marketing Research
1206:
2672:
1203:
747:value suggest they obtain a lower optimism score.
324:of a set of categorical variables is given by its
1088:
4187:
4112:American Association for Public Opinion Research
4071:National Health and Nutrition Examination Survey
1013:Categorical by categorical variable interactions
396:on categorical outcomes is accomplished through
2758:Multivariate adaptive regression splines (MARS)
1026:Categorical by continuous variable interactions
499:groups: for example, when coding gender (where
4066:List of household surveys in the United States
267:The identity of a particular word (e.g., in a
4132:World Association for Public Opinion Research
3639:
1313:
563:represents the mean of the control group and
435:variable in opposition to a binary variable.
4081:Suffolk University Political Research Center
367:
1232:
275:possible choices, for a vocabulary of size
3653:
3646:
3632:
1358:
1320:
1306:
567:is the difference between the mean of the
376:are normally described statistically by a
1971:
1272:
1235:Log-linear models and logistic regression
611:(neither French nor Italian nor German):
237:that a voter might vote for, e. g.
66:Learn how and when to remove this message
29:This article includes a list of general
4091:Quinnipiac University Polling Institute
1145:
1143:
1141:
1139:
1137:
1135:
1133:
1131:
1129:
1127:
4188:
4076:New Zealand Attitudes and Values Study
4023:Comparative Study of Electoral Systems
3284:KaplanâMeier estimator (product limit)
3627:
3357:
2924:
2671:
1970:
1740:
1357:
1301:
1168:
882:Coded variables should be orthogonal.
555:Dummy coding is used when there is a
3594:
3294:Accelerated failure time (AFT) model
1124:
1082:
1055:List of analyses of categorical data
459:Categorical variables and regression
317:, and other set-related operations.
15:
4122:International Statistical Institute
3606:
2889:Analysis of variance (ANOVA, anova)
1741:
1150:Cohen, J.; Cohen, P.; West, S. G.;
1030:Simple slopes analysis is a common
886:Violating rule 2 produces accurate
180:; an important special case is the
13:
4013:American National Election Studies
4003:List of comparative social surveys
2984:CochranâMantelâHaenszel statistics
1610:Pearson product-moment correlation
1181:
959:
839:
463:Categorical variables represent a
423:) and separate regression models (
163:have a meaningful ordering, while
35:it lacks sufficient corresponding
14:
4212:
696:
520:is the explanatory variable, and
212:Examples of categorical variables
147:that are summarised as counts or
125:categorical variable is called a
3605:
3593:
3581:
3568:
3567:
3358:
754:as the group of least interest.
20:
3243:Least-squares spectral analysis
1292:Handbook of Statistical Methods
1171:Regression with dummy variables
999:
550:
445:multinomial logistic regression
398:multinomial logistic regression
352:; and if we write the names in
2224:Mean-unbiased minimum-variance
1327:
1279:Lectures on Contingency Tables
1162:
451:, which falls in the realm of
1:
3537:Geographic information system
2753:Simultaneous equations models
1075:
968:
898:values as a mean difference.
475:or as dependent variables in
167:have no meaningful ordering.
2720:Coefficient of determination
2331:Uniformly most powerful test
1265:Visualizing categorical data
1233:Christensen, Ronald (1997).
380:, which allows an arbitrary
340:This ignores the concept of
7:
4056:International Social Survey
3289:Proportional hazards models
3233:Spectral density estimation
3215:Vector autoregression (VAR)
2649:Maximum posterior estimator
1881:Randomized controlled trial
1043:
483:, but must be converted to
283:
230:of a person: A, B, AB or O.
196:as if it were categorical.
10:
4217:
3049:Multivariate distributions
1469:Average absolute deviation
1187:Andersen, Erling B. 1980.
1158:. New York, NY: Routledge.
1095:(2nd ed.). New York:
1092:The Practice of Statistics
151:, or from observations of
4140:
4104:
4086:The Phillips Academy Poll
3995:
3959:
3914:Exploratory data analysis
3884:
3804:
3767:Sample size determination
3712:
3662:
3563:
3517:
3454:
3407:
3370:
3366:
3353:
3325:
3307:
3274:
3265:
3223:
3170:
3131:
3080:
3071:
3037:Structural equation model
2992:
2949:
2945:
2920:
2879:
2845:
2799:
2766:
2728:
2695:
2691:
2667:
2607:
2516:
2435:
2399:
2390:
2373:Score/Lagrange multiplier
2358:
2311:
2256:
2182:
2173:
1983:
1979:
1966:
1925:
1899:
1851:
1806:
1788:Sample size determination
1753:
1749:
1736:
1640:
1595:
1569:
1551:
1507:
1459:
1379:
1370:
1366:
1353:
1335:
1202:; Holland, P. W. (1975).
1173:. Newbury Park, CA: Sage.
368:Number of possible values
3532:Environmental statistics
3054:Elliptical distributions
2847:Generalized linear model
2776:Simple linear regression
2546:HodgesâLehmann estimator
2003:Probability distribution
1912:Stochastic approximation
1474:Coefficient of variation
453:nonparametric statistics
441:categorical distribution
390:multinomial distribution
378:categorical distribution
127:categorical distribution
119:probability distribution
4027:Emerson College Polling
3919:Multivariate statistics
3762:Nonprobability sampling
3192:Cross-correlation (XCF)
2800:Non-standard predictors
2234:LehmannâScheffĂ© theorem
1907:Adaptive clinical trial
1169:Hardy, Melissa (1993).
50:more precise citations.
4196:Statistical data types
4036:European Social Survey
4018:Asian Barometer Survey
3909:Descriptive statistics
3794:Cross-sequential study
3747:Simple random sampling
3588:Mathematics portal
3409:Engineering statistics
3317:NelsonâAalen estimator
2894:Analysis of covariance
2781:Ordinary least squares
2705:Pearson product-moment
2109:Statistical functional
2020:Empirical distribution
1853:Controlled experiments
1582:Frequency distribution
1360:Descriptive statistics
1191:. North Holland, 1980.
421:Bernoulli distribution
4046:General Social Survey
3929:Statistical inference
3789:Cross-sectional study
3504:Population statistics
3446:System identification
3180:Autocorrelation (ACF)
3108:Exponential smoothing
3022:Discriminant analysis
3017:Canonical correlation
2881:Partition of variance
2743:Regression validation
2587:(JonckheereâTerpstra)
2486:Likelihood-ratio test
2175:Frequentist inference
2087:Locationâscale family
2008:Sampling distribution
1973:Statistical inference
1940:Cross-sectional study
1927:Observational studies
1886:Randomized experiment
1715:Stem-and-leaf display
1517:Central limit theorem
1274:Lauritzen, Steffen L.
1065:Statistical data type
469:independent variables
404:or a related type of
137:statistical data type
101:on the basis of some
3967:Audience measurement
3904:Level of measurement
3737:Sampling for surveys
3427:Probabilistic design
3012:Principal components
2855:Exponential families
2807:Nonlinear regression
2786:General linear model
2748:Mixed effects models
2738:Errors and residuals
2715:Confounding variable
2617:Bayesian probability
2595:Van der Waerden test
2585:Ordered alternative
2350:Multiple comparisons
2229:RaoâBlackwellization
2192:Estimating equations
2148:Statistical distance
1866:Factorial experiment
1399:Arithmetic-Geometric
1289:NIST/SEMATEK (2008)
1269:SAS Institute, 2000.
1050:Level of measurement
252:The type of a rock:
186:polytomous variables
178:dichotomous variable
103:qualitative property
91:qualitative variable
87:categorical variable
4127:Pew Research Center
4096:World Values Survey
3839:Specification error
3757:Stratified sampling
3499:Official statistics
3422:Methods engineering
3103:Seasonal adjustment
2871:Poisson regressions
2791:Bayesian regression
2730:Regression analysis
2710:Partial correlation
2682:Regression analysis
2281:Prediction interval
2276:Likelihood interval
2266:Confidence interval
2258:Interval estimation
2219:Unbiased estimators
2037:Model specification
1917:Up-and-down designs
1605:Partial correlation
1561:Index of dispersion
1479:Interquartile range
477:logistic regression
473:regression analysis
425:logistic regression
417:Bernoulli variables
394:Regression analysis
202:Regression analysis
3934:Statistical models
3834:Non-sampling error
3732:Statistical sample
3672:Collection methods
3519:Spatial statistics
3399:Medical statistics
3299:First hitting time
3253:Whittle likelihood
2904:Degrees of freedom
2899:Multivariate ANOVA
2832:Heteroscedasticity
2644:Bayesian estimator
2609:Bayesian inference
2458:KolmogorovâSmirnov
2343:Randomization test
2313:Testing hypotheses
2286:Tolerance interval
2197:Maximum likelihood
2092:Exponential family
2025:Density estimation
1985:Statistical theory
1945:Natural experiment
1891:Scientific control
1808:Survey methodology
1494:Standard deviation
586:dependent variable
569:experimental group
547:values will vary.
402:multinomial probit
354:Chinese characters
342:alphabetical order
243:Christian Democrat
182:Bernoulli variable
121:associated with a
4183:
4182:
3899:Contingency table
3874:Processing errors
3859:Non-response bias
3849:Measurement error
3829:Systematic errors
3621:
3620:
3559:
3558:
3555:
3554:
3494:National accounts
3464:Actuarial science
3456:Social statistics
3349:
3348:
3345:
3344:
3341:
3340:
3276:Survival function
3261:
3260:
3123:Granger causality
2964:Contingency table
2939:Survival analysis
2916:
2915:
2912:
2911:
2768:Linear regression
2663:
2662:
2659:
2658:
2634:Credible interval
2603:
2602:
2386:
2385:
2202:Method of moments
2071:Parametric family
2032:Statistical model
1962:
1961:
1958:
1957:
1876:Random assignment
1798:Statistical power
1732:
1731:
1728:
1727:
1577:Contingency table
1547:
1546:
1414:Generalized/power
1260:Friendly, Michael
1217:978-0-262-02113-5
1106:978-0-7167-4773-4
957:
956:
837:
836:
694:
693:
485:quantitative data
481:probit regression
449:Dirichlet process
429:probit regression
358:ordinal variables
320:As a result, the
165:nominal variables
161:Ordinal variables
157:contingency table
153:quantitative data
149:cross tabulations
76:
75:
68:
4208:
4201:Categorical data
3894:Categorical data
3648:
3641:
3634:
3625:
3624:
3609:
3608:
3597:
3596:
3586:
3585:
3571:
3570:
3474:Crime statistics
3368:
3367:
3355:
3354:
3272:
3271:
3238:Fourier analysis
3225:Frequency domain
3205:
3152:
3118:Structural break
3078:
3077:
3027:Cluster analysis
2974:Log-linear model
2947:
2946:
2922:
2921:
2863:
2837:Homoscedasticity
2693:
2692:
2669:
2668:
2588:
2580:
2572:
2571:(KruskalâWallis)
2556:
2541:
2496:Cross validation
2481:
2463:AndersonâDarling
2410:
2397:
2396:
2368:Likelihood-ratio
2360:Parametric tests
2338:Permutation test
2321:1- & 2-tails
2212:Minimum distance
2184:Point estimation
2180:
2179:
2131:Optimal decision
2082:
1981:
1980:
1968:
1967:
1950:Quasi-experiment
1900:Adaptive designs
1751:
1750:
1738:
1737:
1615:Rank correlation
1377:
1376:
1368:
1367:
1355:
1354:
1322:
1315:
1308:
1299:
1298:
1286:
1284:
1256:
1229:
1209:
1196:Bishop, Y. M. M.
1175:
1174:
1166:
1160:
1159:
1147:
1122:
1121:
1119:
1118:
1109:. Archived from
1086:
1070:One hot encoding
1060:Qualitative data
905:
904:
855:statistical test
757:
756:
614:
613:
413:binary variables
374:random variables
322:central tendency
145:qualitative data
133:Categorical data
111:enumerated types
99:nominal category
71:
64:
60:
57:
51:
46:this article by
37:inline citations
24:
23:
16:
4216:
4215:
4211:
4210:
4209:
4207:
4206:
4205:
4186:
4185:
4184:
4179:
4136:
4100:
4061:LatinobarĂłmetro
3991:
3977:Market research
3955:
3880:
3854:Response errors
3800:
3774:Research design
3742:Random sampling
3708:
3692:Semi-structured
3664:Data collection
3658:
3656:survey research
3652:
3622:
3617:
3580:
3551:
3513:
3450:
3436:quality control
3403:
3385:Clinical trials
3362:
3337:
3321:
3309:Hazard function
3303:
3257:
3219:
3203:
3166:
3162:BreuschâGodfrey
3150:
3127:
3067:
3042:Factor analysis
2988:
2969:Graphical model
2941:
2908:
2875:
2861:
2841:
2795:
2762:
2724:
2687:
2686:
2655:
2599:
2586:
2578:
2570:
2554:
2539:
2518:Rank statistics
2512:
2491:Model selection
2479:
2437:Goodness of fit
2431:
2408:
2382:
2354:
2307:
2252:
2241:Median unbiased
2169:
2080:
2013:Order statistic
1975:
1954:
1921:
1895:
1847:
1802:
1745:
1743:Data collection
1724:
1636:
1591:
1565:
1543:
1503:
1455:
1372:Continuous data
1362:
1349:
1331:
1326:
1282:
1245:
1218:
1200:Fienberg, S. E.
1184:
1182:Further reading
1179:
1178:
1167:
1163:
1148:
1125:
1116:
1114:
1107:
1087:
1083:
1078:
1046:
1028:
1015:
1002:
986:word embeddings
971:
962:
960:Nonsense coding
842:
840:Contrast coding
699:
553:
461:
406:discrete choice
370:
286:
247:Social Democrat
235:political party
214:
206:dummy variables
198:Dichotomization
194:continuous data
173:binary variable
79:
72:
61:
55:
52:
42:Please help to
41:
25:
21:
12:
11:
5:
4214:
4204:
4203:
4198:
4181:
4180:
4178:
4177:
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4170:
4165:
4160:
4155:
4147:
4141:
4138:
4137:
4135:
4134:
4129:
4124:
4119:
4114:
4108:
4106:
4102:
4101:
4099:
4098:
4093:
4088:
4083:
4078:
4073:
4068:
4063:
4058:
4053:
4048:
4043:
4038:
4033:
4028:
4025:
4020:
4015:
4010:
4005:
3999:
3997:
3993:
3992:
3990:
3989:
3987:Public opinion
3984:
3979:
3974:
3969:
3963:
3961:
3957:
3956:
3954:
3953:
3952:
3951:
3946:
3941:
3931:
3926:
3921:
3916:
3911:
3906:
3901:
3896:
3890:
3888:
3882:
3881:
3879:
3878:
3877:
3876:
3871:
3869:Pseudo-opinion
3866:
3864:Coverage error
3861:
3856:
3851:
3846:
3841:
3831:
3826:
3821:
3819:Standard error
3816:
3814:Sampling error
3810:
3808:
3802:
3801:
3799:
3798:
3797:
3796:
3791:
3786:
3781:
3771:
3770:
3769:
3764:
3759:
3754:
3752:Quota sampling
3749:
3744:
3734:
3729:
3727:Sampling frame
3724:
3718:
3716:
3710:
3709:
3707:
3706:
3705:
3704:
3699:
3694:
3689:
3679:
3674:
3668:
3666:
3660:
3659:
3651:
3650:
3643:
3636:
3628:
3619:
3618:
3616:
3615:
3603:
3591:
3577:
3564:
3561:
3560:
3557:
3556:
3553:
3552:
3550:
3549:
3544:
3539:
3534:
3529:
3523:
3521:
3515:
3514:
3512:
3511:
3506:
3501:
3496:
3491:
3486:
3481:
3476:
3471:
3466:
3460:
3458:
3452:
3451:
3449:
3448:
3443:
3438:
3429:
3424:
3419:
3413:
3411:
3405:
3404:
3402:
3401:
3396:
3391:
3382:
3380:Bioinformatics
3376:
3374:
3364:
3363:
3351:
3350:
3347:
3346:
3343:
3342:
3339:
3338:
3336:
3335:
3329:
3327:
3323:
3322:
3320:
3319:
3313:
3311:
3305:
3304:
3302:
3301:
3296:
3291:
3286:
3280:
3278:
3269:
3263:
3262:
3259:
3258:
3256:
3255:
3250:
3245:
3240:
3235:
3229:
3227:
3221:
3220:
3218:
3217:
3212:
3207:
3199:
3194:
3189:
3188:
3187:
3185:partial (PACF)
3176:
3174:
3168:
3167:
3165:
3164:
3159:
3154:
3146:
3141:
3135:
3133:
3132:Specific tests
3129:
3128:
3126:
3125:
3120:
3115:
3110:
3105:
3100:
3095:
3090:
3084:
3082:
3075:
3069:
3068:
3066:
3065:
3064:
3063:
3062:
3061:
3046:
3045:
3044:
3034:
3032:Classification
3029:
3024:
3019:
3014:
3009:
3004:
2998:
2996:
2990:
2989:
2987:
2986:
2981:
2979:McNemar's test
2976:
2971:
2966:
2961:
2955:
2953:
2943:
2942:
2918:
2917:
2914:
2913:
2910:
2909:
2907:
2906:
2901:
2896:
2891:
2885:
2883:
2877:
2876:
2874:
2873:
2857:
2851:
2849:
2843:
2842:
2840:
2839:
2834:
2829:
2824:
2819:
2817:Semiparametric
2814:
2809:
2803:
2801:
2797:
2796:
2794:
2793:
2788:
2783:
2778:
2772:
2770:
2764:
2763:
2761:
2760:
2755:
2750:
2745:
2740:
2734:
2732:
2726:
2725:
2723:
2722:
2717:
2712:
2707:
2701:
2699:
2689:
2688:
2685:
2684:
2679:
2673:
2665:
2664:
2661:
2660:
2657:
2656:
2654:
2653:
2652:
2651:
2641:
2636:
2631:
2630:
2629:
2624:
2613:
2611:
2605:
2604:
2601:
2600:
2598:
2597:
2592:
2591:
2590:
2582:
2574:
2558:
2555:(MannâWhitney)
2550:
2549:
2548:
2535:
2534:
2533:
2522:
2520:
2514:
2513:
2511:
2510:
2509:
2508:
2503:
2498:
2488:
2483:
2480:(ShapiroâWilk)
2475:
2470:
2465:
2460:
2455:
2447:
2441:
2439:
2433:
2432:
2430:
2429:
2421:
2412:
2400:
2394:
2392:Specific tests
2388:
2387:
2384:
2383:
2381:
2380:
2375:
2370:
2364:
2362:
2356:
2355:
2353:
2352:
2347:
2346:
2345:
2335:
2334:
2333:
2323:
2317:
2315:
2309:
2308:
2306:
2305:
2304:
2303:
2298:
2288:
2283:
2278:
2273:
2268:
2262:
2260:
2254:
2253:
2251:
2250:
2245:
2244:
2243:
2238:
2237:
2236:
2231:
2216:
2215:
2214:
2209:
2204:
2199:
2188:
2186:
2177:
2171:
2170:
2168:
2167:
2162:
2157:
2156:
2155:
2145:
2140:
2139:
2138:
2128:
2127:
2126:
2121:
2116:
2106:
2101:
2096:
2095:
2094:
2089:
2084:
2068:
2067:
2066:
2061:
2056:
2046:
2045:
2044:
2039:
2029:
2028:
2027:
2017:
2016:
2015:
2005:
2000:
1995:
1989:
1987:
1977:
1976:
1964:
1963:
1960:
1959:
1956:
1955:
1953:
1952:
1947:
1942:
1937:
1931:
1929:
1923:
1922:
1920:
1919:
1914:
1909:
1903:
1901:
1897:
1896:
1894:
1893:
1888:
1883:
1878:
1873:
1868:
1863:
1857:
1855:
1849:
1848:
1846:
1845:
1843:Standard error
1840:
1835:
1830:
1829:
1828:
1823:
1812:
1810:
1804:
1803:
1801:
1800:
1795:
1790:
1785:
1780:
1775:
1773:Optimal design
1770:
1765:
1759:
1757:
1747:
1746:
1734:
1733:
1730:
1729:
1726:
1725:
1723:
1722:
1717:
1712:
1707:
1702:
1697:
1692:
1687:
1682:
1677:
1672:
1667:
1662:
1657:
1652:
1646:
1644:
1638:
1637:
1635:
1634:
1629:
1628:
1627:
1622:
1612:
1607:
1601:
1599:
1593:
1592:
1590:
1589:
1584:
1579:
1573:
1571:
1570:Summary tables
1567:
1566:
1564:
1563:
1557:
1555:
1549:
1548:
1545:
1544:
1542:
1541:
1540:
1539:
1534:
1529:
1519:
1513:
1511:
1505:
1504:
1502:
1501:
1496:
1491:
1486:
1481:
1476:
1471:
1465:
1463:
1457:
1456:
1454:
1453:
1448:
1443:
1442:
1441:
1436:
1431:
1426:
1421:
1416:
1411:
1406:
1404:Contraharmonic
1401:
1396:
1385:
1383:
1374:
1364:
1363:
1351:
1350:
1348:
1347:
1342:
1336:
1333:
1332:
1325:
1324:
1317:
1310:
1302:
1296:
1295:
1287:
1270:
1257:
1243:
1230:
1216:
1192:
1183:
1180:
1177:
1176:
1161:
1123:
1105:
1080:
1079:
1077:
1074:
1073:
1072:
1067:
1062:
1057:
1052:
1045:
1042:
1027:
1024:
1014:
1011:
1001:
998:
982:complex-valued
970:
967:
961:
958:
955:
954:
951:
948:
944:
943:
940:
937:
933:
932:
929:
926:
922:
921:
916:
911:
884:
883:
880:
877:
841:
838:
835:
834:
831:
828:
825:
821:
820:
817:
814:
811:
807:
806:
803:
800:
797:
793:
792:
789:
786:
783:
779:
778:
773:
768:
763:
698:
697:Effects coding
695:
692:
691:
688:
685:
682:
678:
677:
674:
671:
668:
664:
663:
660:
657:
654:
650:
649:
646:
643:
640:
636:
635:
630:
625:
620:
552:
549:
460:
457:
369:
366:
360:defined on an
350:Latin alphabet
328:; neither the
315:set membership
285:
282:
281:
280:
269:language model
265:
250:
231:
224:
221:
213:
210:
190:Discretization
77:
74:
73:
28:
26:
19:
9:
6:
4:
3:
2:
4213:
4202:
4199:
4197:
4194:
4193:
4191:
4174:
4171:
4169:
4166:
4164:
4161:
4159:
4156:
4154:
4151:
4150:
4148:
4146:
4143:
4142:
4139:
4133:
4130:
4128:
4125:
4123:
4120:
4118:
4115:
4113:
4110:
4109:
4107:
4103:
4097:
4094:
4092:
4089:
4087:
4084:
4082:
4079:
4077:
4074:
4072:
4069:
4067:
4064:
4062:
4059:
4057:
4054:
4052:
4049:
4047:
4044:
4042:
4039:
4037:
4034:
4032:
4031:Eurobarometer
4029:
4026:
4024:
4021:
4019:
4016:
4014:
4011:
4009:
4008:Afrobarometer
4006:
4004:
4001:
4000:
3998:
3996:Major surveys
3994:
3988:
3985:
3983:
3980:
3978:
3975:
3973:
3970:
3968:
3965:
3964:
3962:
3958:
3950:
3947:
3945:
3942:
3940:
3937:
3936:
3935:
3932:
3930:
3927:
3925:
3924:Psychometrics
3922:
3920:
3917:
3915:
3912:
3910:
3907:
3905:
3902:
3900:
3897:
3895:
3892:
3891:
3889:
3887:
3886:Data analysis
3883:
3875:
3872:
3870:
3867:
3865:
3862:
3860:
3857:
3855:
3852:
3850:
3847:
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3842:
3840:
3837:
3836:
3835:
3832:
3830:
3827:
3825:
3824:Sampling bias
3822:
3820:
3817:
3815:
3812:
3811:
3809:
3807:
3806:Survey errors
3803:
3795:
3792:
3790:
3787:
3785:
3782:
3780:
3777:
3776:
3775:
3772:
3768:
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3680:
3678:
3677:Questionnaire
3675:
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3589:
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3578:
3576:
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3566:
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3562:
3548:
3545:
3543:
3542:Geostatistics
3540:
3538:
3535:
3533:
3530:
3528:
3525:
3524:
3522:
3520:
3516:
3510:
3509:Psychometrics
3507:
3505:
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3497:
3495:
3492:
3490:
3487:
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3397:
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3392:
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3386:
3383:
3381:
3378:
3377:
3375:
3373:
3372:Biostatistics
3369:
3365:
3361:
3356:
3352:
3334:
3333:Log-rank test
3331:
3330:
3328:
3324:
3318:
3315:
3314:
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3306:
3300:
3297:
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3234:
3231:
3230:
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3216:
3213:
3211:
3208:
3206:
3204:(BoxâJenkins)
3200:
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3190:
3186:
3183:
3182:
3181:
3178:
3177:
3175:
3173:
3169:
3163:
3160:
3158:
3157:DurbinâWatson
3155:
3153:
3147:
3145:
3142:
3140:
3139:DickeyâFuller
3137:
3136:
3134:
3130:
3124:
3121:
3119:
3116:
3114:
3113:Cointegration
3111:
3109:
3106:
3104:
3101:
3099:
3096:
3094:
3091:
3089:
3088:Decomposition
3086:
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3008:
3005:
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3000:
2999:
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2985:
2982:
2980:
2977:
2975:
2972:
2970:
2967:
2965:
2962:
2960:
2959:Cohen's kappa
2957:
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2838:
2835:
2833:
2830:
2828:
2825:
2823:
2820:
2818:
2815:
2813:
2812:Nonparametric
2810:
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2805:
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2798:
2792:
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2596:
2593:
2589:
2583:
2581:
2575:
2573:
2567:
2566:
2565:
2562:
2561:Nonparametric
2559:
2557:
2551:
2547:
2544:
2543:
2542:
2536:
2532:
2531:Sample median
2529:
2528:
2527:
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2178:
2176:
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2166:
2163:
2161:
2158:
2154:
2151:
2150:
2149:
2146:
2144:
2141:
2137:
2136:loss function
2134:
2133:
2132:
2129:
2125:
2122:
2120:
2117:
2115:
2112:
2111:
2110:
2107:
2105:
2102:
2100:
2097:
2093:
2090:
2088:
2085:
2083:
2077:
2074:
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2026:
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2018:
2014:
2011:
2010:
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2006:
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1867:
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1844:
1841:
1839:
1838:Questionnaire
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1668:
1666:
1665:Control chart
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1246:
1244:0-387-98247-7
1240:
1236:
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1223:
1219:
1213:
1210:. MIT Press.
1208:
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1128:
1113:on 2005-02-09
1112:
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1066:
1063:
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1041:
1038:
1033:
1032:post hoc test
1023:
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1007:
997:
995:
991:
987:
983:
979:
975:
966:
952:
949:
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422:
418:
414:
409:
407:
403:
399:
395:
391:
387:
383:
379:
375:
365:
363:
362:ordinal scale
359:
355:
351:
347:
343:
338:
335:
331:
327:
323:
318:
316:
312:
308:
304:
303:nominal scale
299:
295:
291:
278:
274:
270:
266:
263:
259:
255:
251:
248:
244:
240:
236:
232:
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138:
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128:
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120:
116:
112:
108:
104:
100:
96:
92:
89:(also called
88:
84:
70:
67:
59:
49:
45:
39:
38:
32:
27:
18:
17:
4105:Associations
3982:Opinion poll
3960:Applications
3893:
3784:Cohort study
3697:Unstructured
3610:
3598:
3579:
3572:
3484:Econometrics
3434: /
3417:Chemometrics
3394:Epidemiology
3387: /
3360:Applications
3202:ARIMA model
3149:Q-statistic
3098:Stationarity
2994:Multivariate
2950:
2937: /
2933: /
2931:Multivariate
2929: /
2926:
2869: /
2865: /
2639:Bayes factor
2538:Signed rank
2450:
2424:
2416:
2404:
2099:Completeness
1935:Cohort study
1833:Opinion poll
1768:Missing data
1755:Study design
1710:Scatter plot
1632:Scatter plot
1625:Spearman's Ï
1587:Grouped data
1291:
1278:
1263:
1234:
1205:
1188:
1170:
1164:
1155:
1152:Aiken, L. S.
1115:. Retrieved
1111:the original
1091:
1084:
1029:
1019:
1016:
1003:
1000:Interactions
973:
972:
963:
918:
913:
908:
900:
895:
891:
887:
885:
871:
859:
843:
775:
770:
765:
760:
751:
749:
744:
739:
734:
732:
727:
724:
719:
715:
712:
703:
700:
632:
627:
622:
617:
608:
604:
600:
596:
594:
589:
580:
578:
574:
564:
560:
554:
551:Dummy coding
544:
539:
532:
526:
521:
517:
513:
508:
507:
505:
500:
496:
492:
488:
462:
437:
432:
416:
412:
410:
385:
381:
372:Categorical
371:
339:
319:
297:
293:
289:
287:
276:
272:
246:
242:
238:
215:
192:is treating
185:
177:
171:
169:
141:grouped data
132:
131:
114:
107:enumerations
90:
86:
80:
62:
53:
34:
4041:Gallup Poll
3844:Frame error
3779:Panel study
3714:Methodology
3612:WikiProject
3527:Cartography
3489:Jurimetrics
3441:Reliability
3172:Time domain
3151:(LjungâBox)
3073:Time-series
2951:Categorical
2935:Time-series
2927:Categorical
2862:(Bernoulli)
2697:Correlation
2677:Correlation
2473:JarqueâBera
2445:Chi-squared
2207:M-estimator
2160:Asymptotics
2104:Sufficiency
1871:Interaction
1783:Replication
1763:Effect size
1720:Violin plot
1700:Radar chart
1680:Forest plot
1670:Correlogram
1620:Kendall's Ï
1037:standardize
1006:interaction
980:(sometimes
978:real-valued
909:Nationality
761:Nationality
706:is now the
618:Nationality
465:qualitative
311:equivalence
262:metamorphic
258:sedimentary
239:Green Party
48:introducing
4190:Categories
4173:Statistics
4163:Psychology
3972:Demography
3949:Structural
3944:Log-linear
3687:Structured
3479:Demography
3197:ARMA model
3002:Regression
2579:(Friedman)
2540:(Wilcoxon)
2478:Normality
2468:Lilliefors
2415:Student's
2291:Resampling
2165:Robustness
2153:divergence
2143:Efficiency
2081:(monotone)
2076:Likelihood
1993:Population
1826:Stratified
1778:Population
1597:Dependence
1553:Count data
1484:Percentile
1461:Dispersion
1394:Arithmetic
1329:Statistics
1117:2014-09-28
1076:References
974:Embeddings
969:Embeddings
866:orthogonal
708:grand mean
529:-intercept
509:Y = bX + a
271:): One of
228:blood type
83:statistics
31:references
4168:Sociology
4149:Projects
3939:Graphical
3682:Interview
2860:Logistic
2627:posterior
2553:Rank sum
2301:Jackknife
2296:Bootstrap
2114:Bootstrap
2049:Parameter
1998:Statistic
1793:Statistic
1705:Run chart
1690:Pie chart
1685:Histogram
1675:Fan chart
1650:Bar chart
1532:L-moments
1419:Geometric
1276:(2002) .
433:multi-way
56:July 2024
4158:Politics
4153:Business
4145:Category
3574:Category
3267:Survival
3144:Johansen
2867:Binomial
2822:Isotonic
2409:(normal)
2054:location
1861:Blocking
1816:Sampling
1695:QâQ plot
1660:Box plot
1642:Graphics
1537:Skewness
1527:Kurtosis
1499:Variance
1429:Heronian
1424:Harmonic
1154:(2003).
1044:See also
994:language
847:a priori
512:, where
346:Cyrillic
332:nor the
284:Notation
95:variable
3654:Social
3600:Commons
3547:Kriging
3432:Process
3389:studies
3248:Wavelet
3081:General
2248:Plug-in
2042:L space
1821:Cluster
1522:Moments
1340:Outline
1253:1633357
1226:0381130
1097:Freeman
936:Italian
853:of the
796:Italian
653:Italian
601:Italian
557:control
524:is the
408:model.
307:ordered
254:igneous
135:is the
93:) is a
44:improve
3722:Census
3702:Couple
3469:Census
3059:Normal
3007:Manova
2827:Robust
2577:2-way
2569:1-way
2407:-test
2078:
1655:Biplot
1446:Median
1439:Lehmer
1381:Center
1251:
1241:
1224:
1214:
1103:
947:German
942:â0.50
931:+0.50
925:French
810:German
782:French
667:German
639:French
607:, and
605:German
597:French
334:median
292:for a
249:, etc.
123:random
117:. The
33:, but
3093:Trend
2622:prior
2564:anova
2453:-test
2427:-test
2419:-test
2326:Power
2271:Pivot
2064:shape
2059:scale
1509:Shape
1489:Range
1434:Heinz
1409:Cubic
1345:Index
1283:(PDF)
992:in a
990:words
950:â0.66
939:+0.33
928:+0.33
862:ANOVA
851:power
824:Other
752:Other
681:Other
609:Other
471:in a
176:or a
115:level
3326:Test
2526:Sign
2378:Wald
1451:Mode
1389:Mean
1239:ISBN
1212:ISBN
1101:ISBN
890:and
733:The
579:The
491:-1 (
443:and
415:(or
330:mean
326:mode
233:The
226:The
85:, a
2506:BIC
2501:AIC
1004:An
833:â1
537:or
479:or
260:or
109:or
81:In
4192::
1262:.
1249:MR
1247:.
1222:MR
1220:.
1198:;
1126:^
1099:.
953:0
919:C2
914:C1
830:â1
827:â1
819:0
805:0
791:1
776:C3
771:C2
766:C1
690:1
676:0
662:0
648:0
633:C3
628:C2
623:C1
603:,
427:,
400:,
364:.
313:,
256:,
245:,
241:,
208:.
129:.
3647:e
3640:t
3633:v
2451:G
2425:F
2417:t
2405:Z
2124:V
2119:U
1321:e
1314:t
1307:v
1267:.
1255:.
1228:.
1120:.
1020:b
896:b
892:F
888:R
816:1
813:0
802:0
799:1
788:0
785:0
745:b
740:b
735:b
728:g
720:b
716:b
704:a
702:(
687:0
684:0
673:1
670:0
659:0
656:1
645:0
642:0
590:b
581:b
565:b
561:a
545:b
540:R
534:F
527:Y
522:a
518:X
514:b
501:g
497:g
493:g
489:g
386:K
382:K
298:K
294:K
290:K
279:.
277:V
273:V
264:.
69:)
63:(
58:)
54:(
40:.
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