24:
are examining the group differences of sometimes multiple independent variables on a singular outcome variable. In the provided example, the levels of the IV might include high school, college, and graduate school. The results of a MANOVA can tell us whether an individual who completed graduate school showed higher life AND job satisfaction than an individual who completed only high school or college. Results of an ANOVA can only tell us this information for life satisfaction. Analyzing group differences across multiple outcome variables often provides more accurate information as a pure relationship between only X and only Y rarely exists in nature.
2026:
5082:
4594:
20:
4580:
2017:
4618:
4606:
2021:
be multiple, are different combinations of the outcome variables. The analysis then determines which combination shows the greatest group differences for the independent variable. A descriptive discriminant analysis is then used as a post hoc test to determine what the makeup of that composite variable is that creates the greatest group differences.
406:
2020:
This is a graphical depiction of the required relationship amongst outcome variables in a multivariate analysis of variance. Part of the analysis involves creating a composite variable, which the group differences of the independent variable are analyzed against. The composite variables, as there can
23:
The image above depicts a visual comparison between multivariate analysis of variance (MANOVA) and univariate analysis of variance (ANOVA). In MANOVA, researchers are examining the group differences of a singular independent variable across multiple outcome variables, whereas in an ANOVA, researchers
1526:
51:
Without relation to the image, the dependent variables may be k life satisfactions scores measured at sequential time points and p job satisfaction scores measured at sequential time points. In this case there are k+p dependent variables whose linear combination follows a multivariate normal
2034:
MANOVA's power is affected by the correlations of the dependent variables and by the effect sizes associated with those variables. For example, when there are two groups and two dependent variables, MANOVA's power is lowest when the correlation equals the ratio of the smaller to the larger
2029:
This is a simple visual representation of the effect of two highly correlated dependent variables within a MANOVA. If two (or more) dependent variables are highly correlated, the chances of a Type I error occurring is reduced, but the trade-off is that the power of the MANOVA test is also
1848:
Discussion continues over the merits of each, although the greatest root leads only to a bound on significance which is not generally of practical interest. A further complication is that, except for the Roy's greatest root, the distribution of these statistics under the
1682:
263:
1778:
1353:
1118:
877:
529:
1843:
1203:
561:
appear. The diagonal entries are the same kinds of sums of squares that appear in univariate ANOVA. The off-diagonal entries are corresponding sums of products. Under normality assumptions about
1549:
1342:
1012:
254:
1209:. Note that alternatively one could also speak about covariances when the abovementioned matrices are scaled by 1/(n-1) since the subsequent test statistics do not change by multiplying
197:
1976:
1234:
2003:
1261:
401:{\displaystyle y_{i}=\mu ^{(g(i))}+\varepsilon _{i}\quad \varepsilon _{i}{\overset {\text{i.i.d.}}{\sim }}{\mathcal {N}}_{q}(0,\Sigma )\quad {\text{ for }}i=1,\dots ,n,}
1291:
1949:
1916:
910:
706:
604:
1782:
1697:
426:
1853:
is not straightforward and can only be approximated except in a few low-dimensional cases. An algorithm for the distribution of the Roy's largest root under the
1687:
674:
144:
784:
755:
954:
930:
726:
647:
627:
117:
97:
78:
1521:{\displaystyle \Lambda _{\text{Wilks}}=\prod _{1,\ldots ,p}(1/(1+\lambda _{p}))=\det(I+A)^{-1}=\det(S_{\text{res}})/\det(S_{\text{res}}+S_{\text{model}})}
2184:
439:
1020:
789:
3715:
52:
distribution, multivariate variance-covariance matrix homogeneity, and linear relationship, no multicollinearity, and each without outliers.
4656:
4220:
4370:
3994:
2635:
4981:
3768:
1792:
1123:
4207:
1889:
One can also test if there is a group effect after adjusting for covariates. For this, follow the procedure above but substitute
2060:
1677:{\displaystyle \Lambda _{\text{Pillai}}=\sum _{1,\ldots ,p}(\lambda _{p}/(1+\lambda _{p}))=\operatorname {tr} (A(I+A)^{-1})}
2630:
2330:
5005:
3234:
2382:
1884:
1296:
2209:
Chiani, M. (2016), "Distribution of the largest root of a matrix for Roy's test in multivariate analysis of variance",
2044:
562:
5056:
4803:
4649:
2264:
Frane, Andrew (2015). "Power and Type I Error
Control for Univariate Comparisons in Multivariate Two-Group Designs".
2254:
I.M. Johnstone, B. Nadler "Roy's largest root test under rank-one alternatives" arXiv preprint arXiv:1310.6581 (2013)
959:
4622:
4195:
4069:
2211:
257:
202:
5069:
4777:
4763:
4253:
3914:
3659:
3030:
2620:
5122:
5074:
4304:
3516:
3323:
3212:
3170:
2055:
2050:
3244:
5117:
4547:
3506:
2409:
1529:
4975:
4940:
4872:
4728:
4642:
4098:
4047:
4032:
4022:
3891:
3763:
3730:
3556:
3511:
3341:
554:
41:
5096:
5045:
4957:
4610:
4442:
4243:
4167:
3468:
3222:
2891:
2355:
1951:
with the predictions of the general linear model containing only the covariates (and an intercept). Then
149:
4853:
4327:
4299:
4294:
4042:
3801:
3707:
3687:
3595:
3306:
3124:
2607:
2479:
933:
4059:
3827:
3548:
3473:
3402:
3331:
3251:
3239:
3109:
3097:
3090:
2798:
2519:
2025:
5031:
5026:
4991:
4875:
4793:
4748:
4743:
4542:
4309:
4172:
3857:
3822:
3786:
3571:
3013:
2922:
2881:
2793:
2484:
2323:
2066:
558:
48:, and is often followed by significance tests involving individual dependent variables separately.
1954:
1212:
4999:
4451:
4064:
4004:
3941:
3579:
3563:
3301:
3163:
3153:
3003:
2917:
1872:
1536:
1206:
1981:
1239:
4986:
4962:
4906:
4848:
4489:
4419:
4212:
4149:
3904:
3791:
2788:
2685:
2592:
2471:
2370:
1269:
5091:
4935:
4835:
4809:
4788:
4768:
4705:
4688:
4665:
4514:
4456:
4399:
4225:
4118:
4027:
3753:
3637:
3496:
3488:
3378:
3370:
3185:
3081:
3059:
3018:
2983:
2950:
2896:
2871:
2826:
2765:
2725:
2527:
2350:
2162:
1773:{\displaystyle \Lambda _{\text{LH}}=\sum _{1,\ldots ,p}(\lambda _{p})=\operatorname {tr} (A)}
1925:
1892:
886:
682:
4951:
4889:
4883:
4437:
4012:
3961:
3937:
3899:
3817:
3796:
3748:
3627:
3605:
3574:
3483:
3360:
3311:
3229:
3202:
3158:
3114:
2876:
2652:
2532:
1919:
1347:
583:
566:
550:
between outcome variables in testing the statistical significance of the mean differences.
543:
539:
8:
5051:
5016:
4925:
4584:
4509:
4432:
4113:
3877:
3870:
3832:
3740:
3720:
3692:
3425:
3291:
3286:
3276:
3268:
3086:
3047:
2937:
2927:
2836:
2615:
2571:
2489:
2414:
2316:
411:
45:
2005:
is the residual sum of squares of the model containing the grouping and the covariates.
557:
appear in univariate analysis of variance, in multivariate analysis of variance certain
5086:
4693:
4598:
4409:
4263:
4159:
4108:
3984:
3881:
3865:
3842:
3619:
3353:
3336:
3296:
3207:
3102:
3064:
3035:
2995:
2955:
2901:
2818:
2504:
2499:
2289:
2238:
2220:
652:
122:
760:
731:
5081:
4843:
4830:
4820:
4733:
4710:
4702:
4698:
4673:
4593:
4504:
4474:
4466:
4286:
4277:
4202:
4133:
3989:
3974:
3949:
3837:
3778:
3644:
3632:
3258:
3175:
3119:
3042:
2886:
2808:
2587:
2461:
2281:
2092:
1871:
In the case of two groups, all the statistics are equivalent and the test reduces to
1543:
429:
2242:
5021:
4715:
4529:
4484:
4248:
4235:
4128:
4103:
4037:
3969:
3847:
3455:
3348:
3281:
3194:
3141:
2960:
2831:
2625:
2509:
2424:
2391:
2293:
2273:
2230:
2164:
1978:
are the additional sum of squares explained by adding the grouping information and
1691:
939:
915:
711:
632:
612:
102:
82:
63:
2093:"A primer on multivariate analysis of variance (MANOVA) for behavioral scientists"
5037:
4967:
4920:
4446:
4190:
4052:
3979:
3654:
3528:
3501:
3478:
3447:
3074:
3069:
3023:
2753:
2404:
2277:
2008:
Note that in case of unbalanced data, the order of adding the covariates matter.
1854:
1850:
1113:{\textstyle S_{\text{model}}:=({\hat {Y}}-{\bar {Y}})^{T}({\hat {Y}}-{\bar {Y}})}
433:
44:
sample means. As a multivariate procedure, it is used when there are two or more
3936:
4723:
4395:
4390:
2853:
2783:
2429:
2234:
1540:
19:
5111:
4861:
4738:
4552:
4519:
4382:
4343:
4154:
4123:
3587:
3541:
3146:
2848:
2675:
2439:
2434:
1861:
1266:
The most common statistics are summaries based on the roots (or eigenvalues)
872:{\textstyle {\frac {1}{{\text{size of group }}g(i)}}\sum _{k:g(k)=g(i)}y_{k}}
1857:
was derived in while the distribution under the alternative is studied in.
5011:
4494:
4427:
4404:
4319:
3649:
2945:
2843:
2778:
2720:
2705:
2642:
2597:
2285:
4867:
4798:
4783:
4753:
4537:
4499:
4182:
4083:
3945:
3758:
3725:
3217:
3134:
3129:
2773:
2730:
2710:
2690:
2680:
2449:
4634:
565:
distributions, the counterpart of the sum of squares due to error has a
4683:
3383:
2863:
2563:
2494:
2444:
2419:
2339:
547:
29:
1120:
is a generalization of the sum of squares explained by the group, and
4815:
3536:
3388:
3008:
2803:
2715:
2700:
2695:
2660:
1865:
2225:
2016:
3052:
2670:
2547:
2542:
2537:
2163:
UCLA: Academic
Technology Services, Statistical Consulting Group.
524:{\displaystyle H_{0}\!:\;\mu ^{(1)}=\mu ^{(2)}=\dots =\mu ^{(m)}.}
4557:
4258:
932:-th row is the best prediction given no information. That is the
4479:
3460:
3434:
3414:
2665:
2456:
2308:
1838:{\displaystyle \Lambda _{\text{Roy}}=\max _{p}(\lambda _{p})}
1198:{\textstyle S_{\text{res}}:=(Y-{\hat {Y}})^{T}(Y-{\hat {Y}})}
2399:
1922:, containing the group and the covariates, and substitute
728:-th row is the best prediction given the group membership
2150:
2115:
Applied multivariate statistics for the social sciences.
1984:
1957:
1928:
1895:
1299:
1272:
1242:
1215:
1126:
1023:
962:
942:
918:
889:
792:
763:
734:
714:
685:
655:
635:
615:
586:
414:
205:
152:
125:
105:
85:
66:
2185:"MANOVA Basic Concepts â Real Statistics Using Excel"
2011:
1795:
1700:
1552:
1356:
442:
266:
4221:
Autoregressive conditional heteroskedasticity (ARCH)
2132:
1878:
1337:{\textstyle A:=S_{\text{model}}S_{\text{res}}^{-1}}
3683:
1997:
1970:
1943:
1910:
1837:
1772:
1676:
1520:
1336:
1285:
1255:
1228:
1197:
1112:
1006:
948:
924:
904:
871:
778:
749:
720:
700:
668:
641:
621:
598:
523:
420:
400:
248:
191:
138:
111:
91:
72:
757:. That is the mean over all observation in group
453:
16:Procedure for comparing multivariate sample means
5109:
2143:
2141:
1810:
1486:
1462:
1431:
3769:Multivariate adaptive regression splines (MARS)
2097:Practical Assessment, Research & Evaluation
1007:{\textstyle {\frac {1}{n}}\sum _{k=1}^{n}y_{k}}
2125:
2123:
249:{\textstyle \mu ^{(g(i))}\in \mathbb {R} ^{q}}
4650:
2324:
2138:
186:
168:
2120:
2086:
2084:
2082:
538:MANOVA is a generalized form of univariate
199:and is distributed around the group center
4657:
4643:
2369:
2331:
2317:
2147:
533:
457:
4664:
2982:
2224:
236:
2129:
2079:
2024:
2015:
18:
5110:
4295:KaplanâMeier estimator (product limit)
2208:
4638:
4368:
3935:
3682:
2981:
2751:
2368:
2312:
2263:
2090:
575:
99:-dimensional observations, where the
4605:
4305:Accelerated failure time (AFT) model
5006:Generalized randomized block design
4617:
3900:Analysis of variance (ANOVA, anova)
2752:
1885:Multivariate analysis of covariance
192:{\textstyle g(i)\in \{1,\dots ,m\}}
13:
3995:CochranâMantelâHaenszel statistics
2621:Pearson product-moment correlation
2045:Permutational analysis of variance
2012:Correlation of dependent variables
1797:
1702:
1554:
1358:
415:
362:
342:
14:
5134:
5057:Sequential probability ratio test
2304:
2165:"Stata Annotated Output â MANOVA"
2061:Multivariate analysis of variance
1864:for Wilks' lambda was derived by
34:multivariate analysis of variance
5080:
4982:Polynomial and rational modeling
4616:
4604:
4592:
4579:
4578:
4369:
2266:Multivariate Behavioral Research
2212:Journal of Multivariate Analysis
2047:for a non-parametric alternative
1879:Introducing covariates (MANCOVA)
4254:Least-squares spectral analysis
1263:by the same non-zero constant.
368:
318:
40:) is a procedure for comparing
4749:Replication versus subsampling
3235:Mean-unbiased minimum-variance
2338:
2257:
2248:
2202:
2177:
2156:
2107:
2056:Canonical correlation analysis
2051:Discriminant function analysis
1935:
1902:
1832:
1819:
1767:
1761:
1749:
1736:
1671:
1659:
1646:
1640:
1628:
1625:
1606:
1588:
1515:
1489:
1478:
1465:
1447:
1434:
1425:
1422:
1403:
1392:
1192:
1186:
1171:
1162:
1155:
1140:
1107:
1101:
1086:
1077:
1068:
1061:
1046:
1037:
896:
854:
848:
839:
833:
813:
807:
773:
767:
744:
738:
692:
513:
507:
488:
482:
469:
463:
365:
353:
300:
297:
291:
285:
226:
223:
217:
211:
162:
156:
1:
4548:Geographic information system
3764:Simultaneous equations models
2117:Mahwah, NJ: Lawrence Erblaum.
2072:
1971:{\textstyle S_{\text{model}}}
1229:{\textstyle S_{\text{model}}}
4976:Response surface methodology
4884:Analysis of variance (Anova)
3731:Coefficient of determination
3342:Uniformly most powerful test
2278:10.1080/00273171.2014.968836
1918:with the predictions of the
580:First, define the following
7:
5046:Randomized controlled trial
4300:Proportional hazards models
4244:Spectral density estimation
4226:Vector autoregression (VAR)
3660:Maximum posterior estimator
2892:Randomized controlled trial
2038:
1998:{\textstyle S_{\text{res}}}
1256:{\textstyle S_{\text{res}}}
1205:is a generalization of the
10:
5139:
4060:Multivariate distributions
2480:Average absolute deviation
2235:10.1016/j.jmva.2015.10.007
2152:. Oxford University Press.
2148:Krzanowski, W. J. (1988).
2035:standardized effect size.
1882:
559:positive-definite matrices
542:(ANOVA), although, unlike
5065:
4934:
4829:
4762:
4672:
4574:
4528:
4465:
4418:
4381:
4377:
4364:
4336:
4318:
4285:
4276:
4234:
4181:
4142:
4091:
4082:
4048:Structural equation model
4003:
3960:
3956:
3931:
3890:
3856:
3810:
3777:
3739:
3706:
3702:
3678:
3618:
3527:
3446:
3410:
3401:
3384:Score/Lagrange multiplier
3369:
3322:
3267:
3193:
3184:
2994:
2990:
2977:
2936:
2910:
2862:
2817:
2799:Sample size determination
2764:
2760:
2747:
2651:
2606:
2580:
2562:
2518:
2470:
2390:
2381:
2377:
2364:
2346:
1286:{\textstyle \lambda _{p}}
146:is assigned to the group
5032:Repeated measures design
4744:Restricted randomization
4543:Environmental statistics
4065:Elliptical distributions
3858:Generalized linear model
3787:Simple linear regression
3557:HodgesâLehmann estimator
3014:Probability distribution
2923:Stochastic approximation
2485:Coefficient of variation
2130:Anderson, T. W. (1994).
2067:Repeated measures design
432:. Then we formulate our
55:
4203:Cross-correlation (XCF)
3811:Non-standard predictors
3245:LehmannâScheffĂ© theorem
2918:Adaptive clinical trial
2189:www.real-statistics.com
2113:Stevens, J. P. (2002).
1944:{\textstyle {\bar {Y}}}
1911:{\textstyle {\hat {Y}}}
1537:K. C. Sreedharan Pillai
1207:residual sum of squares
905:{\textstyle {\bar {Y}}}
701:{\textstyle {\hat {Y}}}
534:Relationship with ANOVA
5087:Mathematics portal
4849:Ordinary least squares
4599:Mathematics portal
4420:Engineering statistics
4328:NelsonâAalen estimator
3905:Analysis of covariance
3792:Ordinary least squares
3716:Pearson product-moment
3120:Statistical functional
3031:Empirical distribution
2864:Controlled experiments
2593:Frequency distribution
2371:Descriptive statistics
2031:
2022:
1999:
1972:
1945:
1912:
1839:
1774:
1678:
1522:
1338:
1287:
1257:
1230:
1199:
1114:
1008:
993:
950:
926:
906:
873:
780:
751:
722:
702:
670:
643:
623:
600:
599:{\textstyle n\times q}
525:
422:
402:
250:
193:
140:
113:
93:
74:
25:
5123:Design of experiments
4684:Scientific experiment
4666:Design of experiments
4515:Population statistics
4457:System identification
4191:Autocorrelation (ACF)
4119:Exponential smoothing
4033:Discriminant analysis
4028:Canonical correlation
3892:Partition of variance
3754:Regression validation
3598:(JonckheereâTerpstra)
3497:Likelihood-ratio test
3186:Frequentist inference
3098:Locationâscale family
3019:Sampling distribution
2984:Statistical inference
2951:Cross-sectional study
2938:Observational studies
2897:Randomized experiment
2726:Stem-and-leaf display
2528:Central limit theorem
2091:Warne, R. T. (2014).
2028:
2019:
2000:
1973:
1946:
1913:
1840:
1775:
1679:
1523:
1339:
1288:
1258:
1231:
1200:
1115:
1009:
973:
951:
927:
907:
874:
781:
752:
723:
703:
671:
644:
624:
601:
526:
423:
403:
258:multivariate Gaussian
251:
194:
141:
114:
94:
75:
22:
5118:Analysis of variance
4958:Fractional factorial
4438:Probabilistic design
4023:Principal components
3866:Exponential families
3818:Nonlinear regression
3797:General linear model
3759:Mixed effects models
3749:Errors and residuals
3726:Confounding variable
3628:Bayesian probability
3606:Van der Waerden test
3596:Ordered alternative
3361:Multiple comparisons
3240:RaoâBlackwellization
3203:Estimating equations
3159:Statistical distance
2877:Factorial experiment
2410:Arithmetic-Geometric
1982:
1955:
1926:
1920:general linear model
1893:
1873:Hotelling's T-square
1793:
1698:
1550:
1354:
1348:Samuel Stanley Wilks
1297:
1270:
1240:
1213:
1124:
1021:
960:
940:
916:
887:
790:
761:
732:
712:
683:
653:
649:-th row is equal to
633:
613:
584:
567:Wishart distribution
540:analysis of variance
440:
421:{\textstyle \Sigma }
412:
264:
203:
150:
123:
103:
83:
64:
5092:Statistical outline
5052:Sequential analysis
5017:Graeco-Latin square
4926:Multiple comparison
4873:Hierarchical model:
4510:Official statistics
4433:Methods engineering
4114:Seasonal adjustment
3882:Poisson regressions
3802:Bayesian regression
3741:Regression analysis
3721:Partial correlation
3693:Regression analysis
3292:Prediction interval
3287:Likelihood interval
3277:Confidence interval
3269:Interval estimation
3230:Unbiased estimators
3048:Model specification
2928:Up-and-down designs
2616:Partial correlation
2572:Index of dispersion
2490:Interquartile range
1783:Roy's greatest root
1333:
801:size of group
46:dependent variables
5097:Statistical topics
4689:Statistical design
4530:Spatial statistics
4410:Medical statistics
4310:First hitting time
4264:Whittle likelihood
3915:Degrees of freedom
3910:Multivariate ANOVA
3843:Heteroscedasticity
3655:Bayesian estimator
3620:Bayesian inference
3469:KolmogorovâSmirnov
3354:Randomization test
3324:Testing hypotheses
3297:Tolerance interval
3208:Maximum likelihood
3103:Exponential family
3036:Density estimation
2996:Statistical theory
2956:Natural experiment
2902:Scientific control
2819:Survey methodology
2505:Standard deviation
2032:
2023:
1995:
1968:
1941:
1908:
1835:
1818:
1787:Roy's largest root
1770:
1735:
1674:
1587:
1518:
1391:
1334:
1316:
1283:
1253:
1226:
1195:
1110:
1004:
946:
922:
902:
869:
858:
776:
747:
718:
698:
669:{\textstyle y_{i}}
666:
639:
619:
596:
576:Hypothesis Testing
521:
418:
398:
246:
189:
139:{\textstyle y_{i}}
136:
109:
89:
70:
26:
5105:
5104:
4992:Central composite
4890:Cochran's theorem
4844:Linear regression
4821:Nuisance variable
4734:Random assignment
4711:Experimental unit
4632:
4631:
4570:
4569:
4566:
4565:
4505:National accounts
4475:Actuarial science
4467:Social statistics
4360:
4359:
4356:
4355:
4352:
4351:
4287:Survival function
4272:
4271:
4134:Granger causality
3975:Contingency table
3950:Survival analysis
3927:
3926:
3923:
3922:
3779:Linear regression
3674:
3673:
3670:
3669:
3645:Credible interval
3614:
3613:
3397:
3396:
3213:Method of moments
3082:Parametric family
3043:Statistical model
2973:
2972:
2969:
2968:
2887:Random assignment
2809:Statistical power
2743:
2742:
2739:
2738:
2588:Contingency table
2558:
2557:
2425:Generalized/power
1992:
1965:
1938:
1905:
1809:
1803:
1714:
1708:
1566:
1560:
1512:
1499:
1475:
1370:
1364:
1323:
1313:
1250:
1223:
1189:
1158:
1134:
1104:
1089:
1064:
1049:
1031:
971:
899:
819:
817:
802:
779:{\textstyle g(i)}
750:{\textstyle g(i)}
695:
430:covariance matrix
372:
337:
336:
5130:
5085:
5084:
5022:Orthogonal array
4659:
4652:
4645:
4636:
4635:
4620:
4619:
4608:
4607:
4597:
4596:
4582:
4581:
4485:Crime statistics
4379:
4378:
4366:
4365:
4283:
4282:
4249:Fourier analysis
4236:Frequency domain
4216:
4163:
4129:Structural break
4089:
4088:
4038:Cluster analysis
3985:Log-linear model
3958:
3957:
3933:
3932:
3874:
3848:Homoscedasticity
3704:
3703:
3680:
3679:
3599:
3591:
3583:
3582:(KruskalâWallis)
3567:
3552:
3507:Cross validation
3492:
3474:AndersonâDarling
3421:
3408:
3407:
3379:Likelihood-ratio
3371:Parametric tests
3349:Permutation test
3332:1- & 2-tails
3223:Minimum distance
3195:Point estimation
3191:
3190:
3142:Optimal decision
3093:
2992:
2991:
2979:
2978:
2961:Quasi-experiment
2911:Adaptive designs
2762:
2761:
2749:
2748:
2626:Rank correlation
2388:
2387:
2379:
2378:
2366:
2365:
2333:
2326:
2319:
2310:
2309:
2298:
2297:
2261:
2255:
2252:
2246:
2245:
2228:
2206:
2200:
2199:
2197:
2195:
2181:
2175:
2174:
2172:
2171:
2160:
2154:
2153:
2145:
2136:
2135:
2127:
2118:
2111:
2105:
2104:
2088:
2004:
2002:
2001:
1996:
1994:
1993:
1990:
1977:
1975:
1974:
1969:
1967:
1966:
1963:
1950:
1948:
1947:
1942:
1940:
1939:
1931:
1917:
1915:
1914:
1909:
1907:
1906:
1898:
1844:
1842:
1841:
1836:
1831:
1830:
1817:
1805:
1804:
1801:
1779:
1777:
1776:
1771:
1748:
1747:
1734:
1710:
1709:
1706:
1683:
1681:
1680:
1675:
1670:
1669:
1624:
1623:
1605:
1600:
1599:
1586:
1562:
1561:
1558:
1527:
1525:
1524:
1519:
1514:
1513:
1510:
1501:
1500:
1497:
1485:
1477:
1476:
1473:
1458:
1457:
1421:
1420:
1402:
1390:
1366:
1365:
1362:
1343:
1341:
1340:
1335:
1332:
1324:
1321:
1315:
1314:
1311:
1292:
1290:
1289:
1284:
1282:
1281:
1262:
1260:
1259:
1254:
1252:
1251:
1248:
1235:
1233:
1232:
1227:
1225:
1224:
1221:
1204:
1202:
1201:
1196:
1191:
1190:
1182:
1170:
1169:
1160:
1159:
1151:
1136:
1135:
1132:
1119:
1117:
1116:
1111:
1106:
1105:
1097:
1091:
1090:
1082:
1076:
1075:
1066:
1065:
1057:
1051:
1050:
1042:
1033:
1032:
1029:
1017:Then the matrix
1013:
1011:
1010:
1005:
1003:
1002:
992:
987:
972:
964:
955:
953:
952:
947:
931:
929:
928:
923:
911:
909:
908:
903:
901:
900:
892:
878:
876:
875:
870:
868:
867:
857:
818:
816:
803:
800:
794:
785:
783:
782:
777:
756:
754:
753:
748:
727:
725:
724:
719:
707:
705:
704:
699:
697:
696:
688:
675:
673:
672:
667:
665:
664:
648:
646:
645:
640:
628:
626:
625:
620:
605:
603:
602:
597:
544:univariate ANOVA
530:
528:
527:
522:
517:
516:
492:
491:
473:
472:
452:
451:
427:
425:
424:
419:
407:
405:
404:
399:
373:
370:
352:
351:
346:
345:
338:
334:
330:
328:
327:
317:
316:
304:
303:
276:
275:
255:
253:
252:
247:
245:
244:
239:
230:
229:
198:
196:
195:
190:
145:
143:
142:
137:
135:
134:
119:âth observation
118:
116:
115:
110:
98:
96:
95:
90:
79:
77:
76:
71:
5138:
5137:
5133:
5132:
5131:
5129:
5128:
5127:
5108:
5107:
5106:
5101:
5079:
5061:
5038:Crossover study
5029:
5027:Latin hypercube
4963:PlackettâBurman
4942:
4939:
4938:
4930:
4833:
4825:
4766:
4758:
4675:
4668:
4663:
4633:
4628:
4591:
4562:
4524:
4461:
4447:quality control
4414:
4396:Clinical trials
4373:
4348:
4332:
4320:Hazard function
4314:
4268:
4230:
4214:
4177:
4173:BreuschâGodfrey
4161:
4138:
4078:
4053:Factor analysis
3999:
3980:Graphical model
3952:
3919:
3886:
3872:
3852:
3806:
3773:
3735:
3698:
3697:
3666:
3610:
3597:
3589:
3581:
3565:
3550:
3529:Rank statistics
3523:
3502:Model selection
3490:
3448:Goodness of fit
3442:
3419:
3393:
3365:
3318:
3263:
3252:Median unbiased
3180:
3091:
3024:Order statistic
2986:
2965:
2932:
2906:
2858:
2813:
2756:
2754:Data collection
2735:
2647:
2602:
2576:
2554:
2514:
2466:
2383:Continuous data
2373:
2360:
2342:
2337:
2307:
2302:
2301:
2262:
2258:
2253:
2249:
2207:
2203:
2193:
2191:
2183:
2182:
2178:
2169:
2167:
2161:
2157:
2146:
2139:
2128:
2121:
2112:
2108:
2089:
2080:
2075:
2041:
2014:
1989:
1985:
1983:
1980:
1979:
1962:
1958:
1956:
1953:
1952:
1930:
1929:
1927:
1924:
1923:
1897:
1896:
1894:
1891:
1890:
1887:
1881:
1860:The best-known
1855:null hypothesis
1851:null hypothesis
1826:
1822:
1813:
1800:
1796:
1794:
1791:
1790:
1743:
1739:
1718:
1705:
1701:
1699:
1696:
1695:
1662:
1658:
1619:
1615:
1601:
1595:
1591:
1570:
1557:
1553:
1551:
1548:
1547:
1528:distributed as
1509:
1505:
1496:
1492:
1481:
1472:
1468:
1450:
1446:
1416:
1412:
1398:
1374:
1361:
1357:
1355:
1352:
1351:
1325:
1320:
1310:
1306:
1298:
1295:
1294:
1277:
1273:
1271:
1268:
1267:
1247:
1243:
1241:
1238:
1237:
1220:
1216:
1214:
1211:
1210:
1181:
1180:
1165:
1161:
1150:
1149:
1131:
1127:
1125:
1122:
1121:
1096:
1095:
1081:
1080:
1071:
1067:
1056:
1055:
1041:
1040:
1028:
1024:
1022:
1019:
1018:
998:
994:
988:
977:
963:
961:
958:
957:
941:
938:
937:
917:
914:
913:
891:
890:
888:
885:
884:
863:
859:
823:
799:
798:
793:
791:
788:
787:
762:
759:
758:
733:
730:
729:
713:
710:
709:
687:
686:
684:
681:
680:
660:
656:
654:
651:
650:
634:
631:
630:
614:
611:
610:
585:
582:
581:
578:
572:
555:sums of squares
536:
506:
502:
481:
477:
462:
458:
447:
443:
441:
438:
437:
434:null hypothesis
413:
410:
409:
371: for
369:
347:
341:
340:
339:
329:
323:
319:
312:
308:
284:
280:
271:
267:
265:
262:
261:
240:
235:
234:
210:
206:
204:
201:
200:
151:
148:
147:
130:
126:
124:
121:
120:
104:
101:
100:
84:
81:
80:
65:
62:
61:
58:
17:
12:
11:
5:
5136:
5126:
5125:
5120:
5103:
5102:
5100:
5099:
5094:
5089:
5077:
5072:
5066:
5063:
5062:
5060:
5059:
5054:
5049:
5041:
5040:
5035:
5024:
5019:
5014:
5009:
5003:
4995:
4994:
4989:
4984:
4979:
4971:
4970:
4965:
4960:
4955:
4947:
4945:
4932:
4931:
4929:
4928:
4923:
4917:
4916:
4904:
4892:
4887:
4879:
4878:
4870:
4865:
4857:
4856:
4851:
4846:
4840:
4838:
4827:
4826:
4824:
4823:
4818:
4813:
4806:
4801:
4796:
4791:
4786:
4781:
4773:
4771:
4760:
4759:
4757:
4756:
4751:
4746:
4741:
4736:
4731:
4724:Optimal design
4719:
4718:
4713:
4708:
4696:
4691:
4686:
4680:
4678:
4670:
4669:
4662:
4661:
4654:
4647:
4639:
4630:
4629:
4627:
4626:
4614:
4602:
4588:
4575:
4572:
4571:
4568:
4567:
4564:
4563:
4561:
4560:
4555:
4550:
4545:
4540:
4534:
4532:
4526:
4525:
4523:
4522:
4517:
4512:
4507:
4502:
4497:
4492:
4487:
4482:
4477:
4471:
4469:
4463:
4462:
4460:
4459:
4454:
4449:
4440:
4435:
4430:
4424:
4422:
4416:
4415:
4413:
4412:
4407:
4402:
4393:
4391:Bioinformatics
4387:
4385:
4375:
4374:
4362:
4361:
4358:
4357:
4354:
4353:
4350:
4349:
4347:
4346:
4340:
4338:
4334:
4333:
4331:
4330:
4324:
4322:
4316:
4315:
4313:
4312:
4307:
4302:
4297:
4291:
4289:
4280:
4274:
4273:
4270:
4269:
4267:
4266:
4261:
4256:
4251:
4246:
4240:
4238:
4232:
4231:
4229:
4228:
4223:
4218:
4210:
4205:
4200:
4199:
4198:
4196:partial (PACF)
4187:
4185:
4179:
4178:
4176:
4175:
4170:
4165:
4157:
4152:
4146:
4144:
4143:Specific tests
4140:
4139:
4137:
4136:
4131:
4126:
4121:
4116:
4111:
4106:
4101:
4095:
4093:
4086:
4080:
4079:
4077:
4076:
4075:
4074:
4073:
4072:
4057:
4056:
4055:
4045:
4043:Classification
4040:
4035:
4030:
4025:
4020:
4015:
4009:
4007:
4001:
4000:
3998:
3997:
3992:
3990:McNemar's test
3987:
3982:
3977:
3972:
3966:
3964:
3954:
3953:
3929:
3928:
3925:
3924:
3921:
3920:
3918:
3917:
3912:
3907:
3902:
3896:
3894:
3888:
3887:
3885:
3884:
3868:
3862:
3860:
3854:
3853:
3851:
3850:
3845:
3840:
3835:
3830:
3828:Semiparametric
3825:
3820:
3814:
3812:
3808:
3807:
3805:
3804:
3799:
3794:
3789:
3783:
3781:
3775:
3774:
3772:
3771:
3766:
3761:
3756:
3751:
3745:
3743:
3737:
3736:
3734:
3733:
3728:
3723:
3718:
3712:
3710:
3700:
3699:
3696:
3695:
3690:
3684:
3676:
3675:
3672:
3671:
3668:
3667:
3665:
3664:
3663:
3662:
3652:
3647:
3642:
3641:
3640:
3635:
3624:
3622:
3616:
3615:
3612:
3611:
3609:
3608:
3603:
3602:
3601:
3593:
3585:
3569:
3566:(MannâWhitney)
3561:
3560:
3559:
3546:
3545:
3544:
3533:
3531:
3525:
3524:
3522:
3521:
3520:
3519:
3514:
3509:
3499:
3494:
3491:(ShapiroâWilk)
3486:
3481:
3476:
3471:
3466:
3458:
3452:
3450:
3444:
3443:
3441:
3440:
3432:
3423:
3411:
3405:
3403:Specific tests
3399:
3398:
3395:
3394:
3392:
3391:
3386:
3381:
3375:
3373:
3367:
3366:
3364:
3363:
3358:
3357:
3356:
3346:
3345:
3344:
3334:
3328:
3326:
3320:
3319:
3317:
3316:
3315:
3314:
3309:
3299:
3294:
3289:
3284:
3279:
3273:
3271:
3265:
3264:
3262:
3261:
3256:
3255:
3254:
3249:
3248:
3247:
3242:
3227:
3226:
3225:
3220:
3215:
3210:
3199:
3197:
3188:
3182:
3181:
3179:
3178:
3173:
3168:
3167:
3166:
3156:
3151:
3150:
3149:
3139:
3138:
3137:
3132:
3127:
3117:
3112:
3107:
3106:
3105:
3100:
3095:
3079:
3078:
3077:
3072:
3067:
3057:
3056:
3055:
3050:
3040:
3039:
3038:
3028:
3027:
3026:
3016:
3011:
3006:
3000:
2998:
2988:
2987:
2975:
2974:
2971:
2970:
2967:
2966:
2964:
2963:
2958:
2953:
2948:
2942:
2940:
2934:
2933:
2931:
2930:
2925:
2920:
2914:
2912:
2908:
2907:
2905:
2904:
2899:
2894:
2889:
2884:
2879:
2874:
2868:
2866:
2860:
2859:
2857:
2856:
2854:Standard error
2851:
2846:
2841:
2840:
2839:
2834:
2823:
2821:
2815:
2814:
2812:
2811:
2806:
2801:
2796:
2791:
2786:
2784:Optimal design
2781:
2776:
2770:
2768:
2758:
2757:
2745:
2744:
2741:
2740:
2737:
2736:
2734:
2733:
2728:
2723:
2718:
2713:
2708:
2703:
2698:
2693:
2688:
2683:
2678:
2673:
2668:
2663:
2657:
2655:
2649:
2648:
2646:
2645:
2640:
2639:
2638:
2633:
2623:
2618:
2612:
2610:
2604:
2603:
2601:
2600:
2595:
2590:
2584:
2582:
2581:Summary tables
2578:
2577:
2575:
2574:
2568:
2566:
2560:
2559:
2556:
2555:
2553:
2552:
2551:
2550:
2545:
2540:
2530:
2524:
2522:
2516:
2515:
2513:
2512:
2507:
2502:
2497:
2492:
2487:
2482:
2476:
2474:
2468:
2467:
2465:
2464:
2459:
2454:
2453:
2452:
2447:
2442:
2437:
2432:
2427:
2422:
2417:
2415:Contraharmonic
2412:
2407:
2396:
2394:
2385:
2375:
2374:
2362:
2361:
2359:
2358:
2353:
2347:
2344:
2343:
2336:
2335:
2328:
2321:
2313:
2306:
2305:External links
2303:
2300:
2299:
2272:(2): 233â247.
2256:
2247:
2201:
2176:
2155:
2137:
2119:
2106:
2077:
2076:
2074:
2071:
2070:
2069:
2064:
2058:
2053:
2048:
2040:
2037:
2013:
2010:
1988:
1961:
1937:
1934:
1904:
1901:
1883:Main article:
1880:
1877:
1846:
1845:
1834:
1829:
1825:
1821:
1816:
1812:
1808:
1799:
1780:
1769:
1766:
1763:
1760:
1757:
1754:
1751:
1746:
1742:
1738:
1733:
1730:
1727:
1724:
1721:
1717:
1713:
1704:
1684:
1673:
1668:
1665:
1661:
1657:
1654:
1651:
1648:
1645:
1642:
1639:
1636:
1633:
1630:
1627:
1622:
1618:
1614:
1611:
1608:
1604:
1598:
1594:
1590:
1585:
1582:
1579:
1576:
1573:
1569:
1565:
1556:
1541:M. S. Bartlett
1533:
1517:
1508:
1504:
1495:
1491:
1488:
1484:
1480:
1471:
1467:
1464:
1461:
1456:
1453:
1449:
1445:
1442:
1439:
1436:
1433:
1430:
1427:
1424:
1419:
1415:
1411:
1408:
1405:
1401:
1397:
1394:
1389:
1386:
1383:
1380:
1377:
1373:
1369:
1360:
1331:
1328:
1319:
1309:
1305:
1302:
1293:of the matrix
1280:
1276:
1246:
1219:
1194:
1188:
1185:
1179:
1176:
1173:
1168:
1164:
1157:
1154:
1148:
1145:
1142:
1139:
1130:
1109:
1103:
1100:
1094:
1088:
1085:
1079:
1074:
1070:
1063:
1060:
1054:
1048:
1045:
1039:
1036:
1027:
1015:
1014:
1001:
997:
991:
986:
983:
980:
976:
970:
967:
949:{\textstyle n}
945:
934:empirical mean
925:{\textstyle i}
921:
898:
895:
881:
880:
866:
862:
856:
853:
850:
847:
844:
841:
838:
835:
832:
829:
826:
822:
815:
812:
809:
806:
797:
775:
772:
769:
766:
746:
743:
740:
737:
721:{\textstyle i}
717:
694:
691:
677:
676:
663:
659:
642:{\textstyle i}
638:
622:{\textstyle Y}
618:
595:
592:
589:
577:
574:
546:, it uses the
535:
532:
520:
515:
512:
509:
505:
501:
498:
495:
490:
487:
484:
480:
476:
471:
468:
465:
461:
456:
450:
446:
417:
397:
394:
391:
388:
385:
382:
379:
376:
367:
364:
361:
358:
355:
350:
344:
333:
326:
322:
315:
311:
307:
302:
299:
296:
293:
290:
287:
283:
279:
274:
270:
243:
238:
233:
228:
225:
222:
219:
216:
213:
209:
188:
185:
182:
179:
176:
173:
170:
167:
164:
161:
158:
155:
133:
129:
112:{\textstyle i}
108:
92:{\textstyle q}
88:
73:{\textstyle n}
69:
57:
54:
15:
9:
6:
4:
3:
2:
5135:
5124:
5121:
5119:
5116:
5115:
5113:
5098:
5095:
5093:
5090:
5088:
5083:
5078:
5076:
5073:
5071:
5068:
5067:
5064:
5058:
5055:
5053:
5050:
5048:
5047:
5043:
5042:
5039:
5036:
5034:
5033:
5028:
5025:
5023:
5020:
5018:
5015:
5013:
5010:
5007:
5004:
5002:
5001:
4997:
4996:
4993:
4990:
4988:
4985:
4983:
4980:
4978:
4977:
4973:
4972:
4969:
4966:
4964:
4961:
4959:
4956:
4954:
4953:
4949:
4948:
4946:
4944:
4937:
4933:
4927:
4924:
4922:
4921:Compare means
4919:
4918:
4915:
4913:
4909:
4905:
4903:
4901:
4897:
4893:
4891:
4888:
4886:
4885:
4881:
4880:
4877:
4874:
4871:
4869:
4866:
4864:
4863:
4862:Random effect
4859:
4858:
4855:
4852:
4850:
4847:
4845:
4842:
4841:
4839:
4837:
4832:
4828:
4822:
4819:
4817:
4814:
4812:
4811:
4807:
4805:
4804:Orthogonality
4802:
4800:
4797:
4795:
4792:
4790:
4787:
4785:
4782:
4780:
4779:
4775:
4774:
4772:
4770:
4765:
4761:
4755:
4752:
4750:
4747:
4745:
4742:
4740:
4739:Randomization
4737:
4735:
4732:
4730:
4726:
4725:
4721:
4720:
4717:
4714:
4712:
4709:
4707:
4704:
4700:
4697:
4695:
4692:
4690:
4687:
4685:
4682:
4681:
4679:
4677:
4671:
4667:
4660:
4655:
4653:
4648:
4646:
4641:
4640:
4637:
4625:
4624:
4615:
4613:
4612:
4603:
4601:
4600:
4595:
4589:
4587:
4586:
4577:
4576:
4573:
4559:
4556:
4554:
4553:Geostatistics
4551:
4549:
4546:
4544:
4541:
4539:
4536:
4535:
4533:
4531:
4527:
4521:
4520:Psychometrics
4518:
4516:
4513:
4511:
4508:
4506:
4503:
4501:
4498:
4496:
4493:
4491:
4488:
4486:
4483:
4481:
4478:
4476:
4473:
4472:
4470:
4468:
4464:
4458:
4455:
4453:
4450:
4448:
4444:
4441:
4439:
4436:
4434:
4431:
4429:
4426:
4425:
4423:
4421:
4417:
4411:
4408:
4406:
4403:
4401:
4397:
4394:
4392:
4389:
4388:
4386:
4384:
4383:Biostatistics
4380:
4376:
4372:
4367:
4363:
4345:
4344:Log-rank test
4342:
4341:
4339:
4335:
4329:
4326:
4325:
4323:
4321:
4317:
4311:
4308:
4306:
4303:
4301:
4298:
4296:
4293:
4292:
4290:
4288:
4284:
4281:
4279:
4275:
4265:
4262:
4260:
4257:
4255:
4252:
4250:
4247:
4245:
4242:
4241:
4239:
4237:
4233:
4227:
4224:
4222:
4219:
4217:
4215:(BoxâJenkins)
4211:
4209:
4206:
4204:
4201:
4197:
4194:
4193:
4192:
4189:
4188:
4186:
4184:
4180:
4174:
4171:
4169:
4168:DurbinâWatson
4166:
4164:
4158:
4156:
4153:
4151:
4150:DickeyâFuller
4148:
4147:
4145:
4141:
4135:
4132:
4130:
4127:
4125:
4124:Cointegration
4122:
4120:
4117:
4115:
4112:
4110:
4107:
4105:
4102:
4100:
4099:Decomposition
4097:
4096:
4094:
4090:
4087:
4085:
4081:
4071:
4068:
4067:
4066:
4063:
4062:
4061:
4058:
4054:
4051:
4050:
4049:
4046:
4044:
4041:
4039:
4036:
4034:
4031:
4029:
4026:
4024:
4021:
4019:
4016:
4014:
4011:
4010:
4008:
4006:
4002:
3996:
3993:
3991:
3988:
3986:
3983:
3981:
3978:
3976:
3973:
3971:
3970:Cohen's kappa
3968:
3967:
3965:
3963:
3959:
3955:
3951:
3947:
3943:
3939:
3934:
3930:
3916:
3913:
3911:
3908:
3906:
3903:
3901:
3898:
3897:
3895:
3893:
3889:
3883:
3879:
3875:
3869:
3867:
3864:
3863:
3861:
3859:
3855:
3849:
3846:
3844:
3841:
3839:
3836:
3834:
3831:
3829:
3826:
3824:
3823:Nonparametric
3821:
3819:
3816:
3815:
3813:
3809:
3803:
3800:
3798:
3795:
3793:
3790:
3788:
3785:
3784:
3782:
3780:
3776:
3770:
3767:
3765:
3762:
3760:
3757:
3755:
3752:
3750:
3747:
3746:
3744:
3742:
3738:
3732:
3729:
3727:
3724:
3722:
3719:
3717:
3714:
3713:
3711:
3709:
3705:
3701:
3694:
3691:
3689:
3686:
3685:
3681:
3677:
3661:
3658:
3657:
3656:
3653:
3651:
3648:
3646:
3643:
3639:
3636:
3634:
3631:
3630:
3629:
3626:
3625:
3623:
3621:
3617:
3607:
3604:
3600:
3594:
3592:
3586:
3584:
3578:
3577:
3576:
3573:
3572:Nonparametric
3570:
3568:
3562:
3558:
3555:
3554:
3553:
3547:
3543:
3542:Sample median
3540:
3539:
3538:
3535:
3534:
3532:
3530:
3526:
3518:
3515:
3513:
3510:
3508:
3505:
3504:
3503:
3500:
3498:
3495:
3493:
3487:
3485:
3482:
3480:
3477:
3475:
3472:
3470:
3467:
3465:
3463:
3459:
3457:
3454:
3453:
3451:
3449:
3445:
3439:
3437:
3433:
3431:
3429:
3424:
3422:
3417:
3413:
3412:
3409:
3406:
3404:
3400:
3390:
3387:
3385:
3382:
3380:
3377:
3376:
3374:
3372:
3368:
3362:
3359:
3355:
3352:
3351:
3350:
3347:
3343:
3340:
3339:
3338:
3335:
3333:
3330:
3329:
3327:
3325:
3321:
3313:
3310:
3308:
3305:
3304:
3303:
3300:
3298:
3295:
3293:
3290:
3288:
3285:
3283:
3280:
3278:
3275:
3274:
3272:
3270:
3266:
3260:
3257:
3253:
3250:
3246:
3243:
3241:
3238:
3237:
3236:
3233:
3232:
3231:
3228:
3224:
3221:
3219:
3216:
3214:
3211:
3209:
3206:
3205:
3204:
3201:
3200:
3198:
3196:
3192:
3189:
3187:
3183:
3177:
3174:
3172:
3169:
3165:
3162:
3161:
3160:
3157:
3155:
3152:
3148:
3147:loss function
3145:
3144:
3143:
3140:
3136:
3133:
3131:
3128:
3126:
3123:
3122:
3121:
3118:
3116:
3113:
3111:
3108:
3104:
3101:
3099:
3096:
3094:
3088:
3085:
3084:
3083:
3080:
3076:
3073:
3071:
3068:
3066:
3063:
3062:
3061:
3058:
3054:
3051:
3049:
3046:
3045:
3044:
3041:
3037:
3034:
3033:
3032:
3029:
3025:
3022:
3021:
3020:
3017:
3015:
3012:
3010:
3007:
3005:
3002:
3001:
2999:
2997:
2993:
2989:
2985:
2980:
2976:
2962:
2959:
2957:
2954:
2952:
2949:
2947:
2944:
2943:
2941:
2939:
2935:
2929:
2926:
2924:
2921:
2919:
2916:
2915:
2913:
2909:
2903:
2900:
2898:
2895:
2893:
2890:
2888:
2885:
2883:
2880:
2878:
2875:
2873:
2870:
2869:
2867:
2865:
2861:
2855:
2852:
2850:
2849:Questionnaire
2847:
2845:
2842:
2838:
2835:
2833:
2830:
2829:
2828:
2825:
2824:
2822:
2820:
2816:
2810:
2807:
2805:
2802:
2800:
2797:
2795:
2792:
2790:
2787:
2785:
2782:
2780:
2777:
2775:
2772:
2771:
2769:
2767:
2763:
2759:
2755:
2750:
2746:
2732:
2729:
2727:
2724:
2722:
2719:
2717:
2714:
2712:
2709:
2707:
2704:
2702:
2699:
2697:
2694:
2692:
2689:
2687:
2684:
2682:
2679:
2677:
2676:Control chart
2674:
2672:
2669:
2667:
2664:
2662:
2659:
2658:
2656:
2654:
2650:
2644:
2641:
2637:
2634:
2632:
2629:
2628:
2627:
2624:
2622:
2619:
2617:
2614:
2613:
2611:
2609:
2605:
2599:
2596:
2594:
2591:
2589:
2586:
2585:
2583:
2579:
2573:
2570:
2569:
2567:
2565:
2561:
2549:
2546:
2544:
2541:
2539:
2536:
2535:
2534:
2531:
2529:
2526:
2525:
2523:
2521:
2517:
2511:
2508:
2506:
2503:
2501:
2498:
2496:
2493:
2491:
2488:
2486:
2483:
2481:
2478:
2477:
2475:
2473:
2469:
2463:
2460:
2458:
2455:
2451:
2448:
2446:
2443:
2441:
2438:
2436:
2433:
2431:
2428:
2426:
2423:
2421:
2418:
2416:
2413:
2411:
2408:
2406:
2403:
2402:
2401:
2398:
2397:
2395:
2393:
2389:
2386:
2384:
2380:
2376:
2372:
2367:
2363:
2357:
2354:
2352:
2349:
2348:
2345:
2341:
2334:
2329:
2327:
2322:
2320:
2315:
2314:
2311:
2295:
2291:
2287:
2283:
2279:
2275:
2271:
2267:
2260:
2251:
2244:
2240:
2236:
2232:
2227:
2222:
2218:
2214:
2213:
2205:
2190:
2186:
2180:
2166:
2159:
2151:
2144:
2142:
2133:
2126:
2124:
2116:
2110:
2102:
2098:
2094:
2087:
2085:
2083:
2078:
2068:
2065:
2063:(Wikiversity)
2062:
2059:
2057:
2054:
2052:
2049:
2046:
2043:
2042:
2036:
2027:
2018:
2009:
2006:
1986:
1959:
1932:
1921:
1899:
1886:
1876:
1874:
1869:
1867:
1863:
1862:approximation
1858:
1856:
1852:
1827:
1823:
1814:
1806:
1788:
1785:(also called
1784:
1781:
1764:
1758:
1755:
1752:
1744:
1740:
1731:
1728:
1725:
1722:
1719:
1715:
1711:
1693:
1689:
1685:
1666:
1663:
1655:
1652:
1649:
1643:
1637:
1634:
1631:
1620:
1616:
1612:
1609:
1602:
1596:
1592:
1583:
1580:
1577:
1574:
1571:
1567:
1563:
1545:
1542:
1538:
1534:
1531:
1506:
1502:
1493:
1482:
1469:
1459:
1454:
1451:
1443:
1440:
1437:
1428:
1417:
1413:
1409:
1406:
1399:
1395:
1387:
1384:
1381:
1378:
1375:
1371:
1367:
1349:
1346:
1345:
1344:
1329:
1326:
1317:
1307:
1303:
1300:
1278:
1274:
1264:
1244:
1217:
1208:
1183:
1177:
1174:
1166:
1152:
1146:
1143:
1137:
1128:
1098:
1092:
1083:
1072:
1058:
1052:
1043:
1034:
1025:
999:
995:
989:
984:
981:
978:
974:
968:
965:
956:observations
943:
935:
919:
893:
883:
882:
864:
860:
851:
845:
842:
836:
830:
827:
824:
820:
810:
804:
795:
770:
764:
741:
735:
715:
689:
679:
678:
661:
657:
636:
616:
609:
608:
607:
593:
590:
587:
573:
570:
568:
564:
560:
556:
551:
549:
545:
541:
531:
518:
510:
503:
499:
496:
493:
485:
478:
474:
466:
459:
454:
448:
444:
435:
431:
395:
392:
389:
386:
383:
380:
377:
374:
359:
356:
348:
331:
324:
320:
313:
309:
305:
294:
288:
281:
277:
272:
268:
259:
241:
231:
220:
214:
207:
183:
180:
177:
174:
171:
165:
159:
153:
131:
127:
106:
86:
67:
53:
49:
47:
43:
39:
35:
31:
21:
5044:
5030:
5012:Latin square
4998:
4974:
4950:
4911:
4907:
4900:multivariate
4899:
4895:
4894:
4882:
4860:
4808:
4776:
4722:
4621:
4609:
4590:
4583:
4495:Econometrics
4445: /
4428:Chemometrics
4405:Epidemiology
4398: /
4371:Applications
4213:ARIMA model
4160:Q-statistic
4109:Stationarity
4017:
4005:Multivariate
3948: /
3944: /
3942:Multivariate
3940: /
3909:
3880: /
3876: /
3650:Bayes factor
3549:Signed rank
3461:
3435:
3427:
3415:
3110:Completeness
2946:Cohort study
2844:Opinion poll
2779:Missing data
2766:Study design
2721:Scatter plot
2643:Scatter plot
2636:Spearman's Ï
2598:Grouped data
2269:
2265:
2259:
2250:
2216:
2210:
2204:
2192:. Retrieved
2188:
2179:
2168:. Retrieved
2158:
2149:
2131:
2114:
2109:
2100:
2096:
2033:
2007:
1888:
1870:
1859:
1847:
1786:
1265:
1016:
912:: where the
708:: where the
629:: where the
579:
571:
552:
537:
59:
50:
42:multivariate
37:
33:
27:
4987:BoxâBehnken
4868:Mixed model
4799:Confounding
4794:Interaction
4784:Effect size
4754:Sample size
4623:WikiProject
4538:Cartography
4500:Jurimetrics
4452:Reliability
4183:Time domain
4162:(LjungâBox)
4084:Time-series
3962:Categorical
3946:Time-series
3938:Categorical
3873:(Bernoulli)
3708:Correlation
3688:Correlation
3484:JarqueâBera
3456:Chi-squared
3218:M-estimator
3171:Asymptotics
3115:Sufficiency
2882:Interaction
2794:Replication
2774:Effect size
2731:Violin plot
2711:Radar chart
2691:Forest plot
2681:Correlogram
2631:Kendall's Ï
2226:1401.3987v3
2219:: 467â471,
2103:(17): 1â10.
5112:Categories
4943:randomized
4941:Completely
4912:covariance
4674:Scientific
4490:Demography
4208:ARMA model
4013:Regression
3590:(Friedman)
3551:(Wilcoxon)
3489:Normality
3479:Lilliefors
3426:Student's
3302:Resampling
3176:Robustness
3164:divergence
3154:Efficiency
3092:(monotone)
3087:Likelihood
3004:Population
2837:Stratified
2789:Population
2608:Dependence
2564:Count data
2495:Percentile
2472:Dispersion
2405:Arithmetic
2340:Statistics
2170:2024-02-10
2073:References
606:matrices:
548:covariance
30:statistics
4952:Factorial
4836:inference
4816:Covariate
4778:Treatment
4764:Treatment
3871:Logistic
3638:posterior
3564:Rank sum
3312:Jackknife
3307:Bootstrap
3125:Bootstrap
3060:Parameter
3009:Statistic
2804:Statistic
2716:Run chart
2701:Pie chart
2696:Histogram
2686:Fan chart
2661:Bar chart
2543:L-moments
2430:Geometric
1936:¯
1903:^
1866:C. R. Rao
1824:λ
1798:Λ
1759:
1741:λ
1726:…
1716:∑
1703:Λ
1692:Hotelling
1664:−
1638:
1617:λ
1593:λ
1578:…
1568:∑
1555:Λ
1452:−
1414:λ
1382:…
1372:∏
1359:Λ
1327:−
1275:λ
1187:^
1178:−
1156:^
1147:−
1102:¯
1093:−
1087:^
1062:¯
1053:−
1047:^
975:∑
936:over all
897:¯
821:∑
693:^
591:×
504:μ
497:⋯
479:μ
460:μ
416:Σ
387:…
363:Σ
332:∼
321:ε
310:ε
282:μ
232:∈
208:μ
178:…
166:∈
5075:Category
5070:Glossary
4876:Bayesian
4854:Bayesian
4810:Blocking
4789:Contrast
4769:blocking
4729:Bayesian
4716:Blinding
4706:validity
4703:external
4699:Internal
4585:Category
4278:Survival
4155:Johansen
3878:Binomial
3833:Isotonic
3420:(normal)
3065:location
2872:Blocking
2827:Sampling
2706:QâQ plot
2671:Box plot
2653:Graphics
2548:Skewness
2538:Kurtosis
2510:Variance
2440:Heronian
2435:Harmonic
2286:26609880
2243:37620291
2134:. Wiley.
2039:See also
2030:reduced.
4968:Taguchi
4936:Designs
4694:Control
4611:Commons
4558:Kriging
4443:Process
4400:studies
4259:Wavelet
4092:General
3259:Plug-in
3053:L space
2832:Cluster
2533:Moments
2351:Outline
2294:1532673
2194:5 April
1694:trace,
428:is the
260:noise:
60:Assume
5008:(GRBD)
4908:Ancova
4896:Manova
4831:Models
4676:method
4480:Census
4070:Normal
4018:Manova
3838:Robust
3588:2-way
3580:1-way
3418:-test
3089:
2666:Biplot
2457:Median
2450:Lehmer
2392:Center
2292:
2284:
2241:
1688:Lawley
1559:Pillai
1530:lambda
553:Where
408:where
335:i.i.d.
38:MANOVA
5000:Block
4104:Trend
3633:prior
3575:anova
3464:-test
3438:-test
3430:-test
3337:Power
3282:Pivot
3075:shape
3070:scale
2520:Shape
2500:Range
2445:Heinz
2420:Cubic
2356:Index
2290:S2CID
2239:S2CID
2221:arXiv
1964:model
1544:trace
1511:model
1363:Wilks
1312:model
1222:model
1030:model
563:error
256:with
56:Model
4834:and
4767:and
4701:and
4337:Test
3537:Sign
3389:Wald
2462:Mode
2400:Mean
2282:PMID
2196:2018
1686:the
1535:the
1236:and
436:as
3517:BIC
3512:AIC
2274:doi
2231:doi
2217:143
1991:res
1811:max
1802:Roy
1789:),
1532:(Î)
1498:res
1487:det
1474:res
1463:det
1432:det
1322:res
1249:res
1133:res
28:In
5114::
4727::
2288:.
2280:.
2270:50
2268:.
2237:,
2229:,
2215:,
2187:.
2140:^
2122:^
2101:19
2099:.
2095:.
2081:^
1875:.
1868:.
1756:tr
1707:LH
1635:tr
1546:,
1350:'
1304::=
1138::=
1035::=
786::
569:.
32:,
4914:)
4910:(
4902:)
4898:(
4658:e
4651:t
4644:v
3462:G
3436:F
3428:t
3416:Z
3135:V
3130:U
2332:e
2325:t
2318:v
2296:.
2276::
2233::
2223::
2198:.
2173:.
1987:S
1960:S
1933:Y
1900:Y
1833:)
1828:p
1820:(
1815:p
1807:=
1768:)
1765:A
1762:(
1753:=
1750:)
1745:p
1737:(
1732:p
1729:,
1723:,
1720:1
1712:=
1690:â
1672:)
1667:1
1660:)
1656:A
1653:+
1650:I
1647:(
1644:A
1641:(
1632:=
1629:)
1626:)
1621:p
1613:+
1610:1
1607:(
1603:/
1597:p
1589:(
1584:p
1581:,
1575:,
1572:1
1564:=
1539:â
1516:)
1507:S
1503:+
1494:S
1490:(
1483:/
1479:)
1470:S
1466:(
1460:=
1455:1
1448:)
1444:A
1441:+
1438:I
1435:(
1429:=
1426:)
1423:)
1418:p
1410:+
1407:1
1404:(
1400:/
1396:1
1393:(
1388:p
1385:,
1379:,
1376:1
1368:=
1330:1
1318:S
1308:S
1301:A
1279:p
1245:S
1218:S
1193:)
1184:Y
1175:Y
1172:(
1167:T
1163:)
1153:Y
1144:Y
1141:(
1129:S
1108:)
1099:Y
1084:Y
1078:(
1073:T
1069:)
1059:Y
1044:Y
1038:(
1026:S
1000:k
996:y
990:n
985:1
982:=
979:k
969:n
966:1
944:n
920:i
894:Y
879:.
865:k
861:y
855:)
852:i
849:(
846:g
843:=
840:)
837:k
834:(
831:g
828::
825:k
814:)
811:i
808:(
805:g
796:1
774:)
771:i
768:(
765:g
745:)
742:i
739:(
736:g
716:i
690:Y
662:i
658:y
637:i
617:Y
594:q
588:n
519:.
514:)
511:m
508:(
500:=
494:=
489:)
486:2
483:(
475:=
470:)
467:1
464:(
455::
449:0
445:H
396:,
393:n
390:,
384:,
381:1
378:=
375:i
366:)
360:,
357:0
354:(
349:q
343:N
325:i
314:i
306:+
301:)
298:)
295:i
292:(
289:g
286:(
278:=
273:i
269:y
242:q
237:R
227:)
224:)
221:i
218:(
215:g
212:(
187:}
184:m
181:,
175:,
172:1
169:{
163:)
160:i
157:(
154:g
132:i
128:y
107:i
87:q
68:n
36:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
