3651:
3637:
3675:
3663:
85:
We consider a binary outcome variable such as case status (e.g. lung cancer) and a binary predictor such as treatment status (e.g. smoking). The observations are grouped in strata. The stratified data are summarized in a series of 2 × 2 contingency tables, one for each stratum. The
1250:
710:
366:
1093:
for homogeneous association. The CMH test supposes that the effect of the treatment is homogeneous in all strata. The
Breslow-Day test allows to test this assumption. This is not a concern if the strata are small e.g.
53:. It allows an investigator to test the association between a binary predictor or treatment and a binary outcome such as case or control status while taking into account the stratification. Unlike the
455:
811:
223:
943:
447:
3721:
1079:
is more general than the CMH test as it can handle continuous variable and perform multivariate analysis. When the CMH test can be applied, the CMH test statistic and the
1046:
1010:
3701:
856:
One generally expects the risk of an event unconditional on the stratification to be bounded between the highest and lowest risk within the strata (or identically with
740:
408:
905:
2772:
3277:
974:
878:
851:
831:
3427:
69:. Extensions of this test to a categorical response and/or to several groups are commonly called Cochran–Mantel–Haenszel statistics. It is often used in
1692:
2825:
1314:
Day N.E., Byar D.P. (September 1979). "Testing hypotheses in case-control studies-equivalence of Mantel–Haenszel statistics and logit score tests".
3264:
1687:
1387:
833:
is the number of strata. If the stratification were removed, there would be one aggregate risk ratio of the collapsed table; let this be
2291:
1439:
3679:
1056:
and not dependent on the order of the strata. Then the CMH statistic is the unique well-behaved statistic satisfying subset stability.
1175:
Nathan Mantel and
William Haenszel (April 1959). "Statistical aspects of the analysis of data from retrospective studies of disease".
3074:
2966:
1298:
1124:
1360:
371:
The null hypothesis is that there is no association between the treatment and the outcome. More precisely, the null hypothesis is
3252:
3126:
43:
3310:
2971:
2716:
2087:
1677:
1084:
1076:
2301:
3361:
2573:
2380:
2269:
2227:
1466:
1210:
Nathan Mantel (September 1963). "Chi-Square Tests with One Degree of
Freedom, Extensions of the Mantel–Haenszel Procedure".
3604:
2563:
705:{\displaystyle \xi _{\text{CMH}}={\frac {\left^{2}}{\sum _{i=1}^{K}{N_{1i}N_{2i}M_{1i}M_{2i} \over T_{i}^{2}(T_{i}-1)}}}.}
2613:
3716:
3155:
3104:
3089:
3079:
2948:
2820:
2787:
2568:
2398:
3224:
2525:
3711:
3499:
3300:
2279:
1948:
1412:
3384:
3351:
3356:
3099:
2858:
2764:
2744:
2652:
2363:
2181:
1664:
1536:
2530:
2296:
2154:
3116:
2884:
2605:
2459:
2388:
2308:
2166:
2147:
1855:
1576:
361:{\displaystyle R={{\sum _{i=1}^{K}{\frac {A_{i}D_{i}}{T_{i}}}} \over {\sum _{i=1}^{K}{B_{i}C_{i} \over T_{i}}}},}
3229:
3599:
3366:
2914:
2879:
2843:
2628:
2070:
1979:
1938:
1850:
1541:
1380:
2636:
2620:
757:
949:, and as with Simpson's paradox, it is difficult to interpret the statistic and decide policy based upon it.
3508:
3121:
3061:
2998:
2358:
2220:
2210:
2060:
1974:
3269:
3206:
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1845:
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1649:
1528:
1427:
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3706:
3571:
3513:
3456:
3282:
3175:
3084:
2810:
2694:
2553:
2435:
2427:
2242:
2138:
2116:
2075:
2040:
2007:
1953:
1928:
1883:
1822:
1782:
1584:
1407:
70:
47:
3650:
2540:
1090:
3494:
3069:
3018:
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2874:
2853:
2805:
2684:
2662:
2631:
2417:
2368:
2286:
2259:
2215:
2171:
1933:
1709:
1589:
946:
910:
3641:
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3489:
3170:
2934:
2927:
2889:
2797:
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2482:
2348:
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2333:
2325:
2143:
2104:
1994:
1984:
1893:
1672:
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1546:
1471:
1373:
413:
3216:
3655:
3466:
3320:
3165:
3041:
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2899:
2676:
2410:
2393:
2353:
2264:
2159:
2121:
2092:
2052:
2012:
1958:
1875:
1561:
1556:
1331:
1271:
1227:
1157:
1015:
979:
58:
718:
374:
3561:
3531:
3523:
3343:
3334:
3259:
3190:
3046:
3031:
3006:
2894:
2835:
2701:
2689:
2315:
2232:
2176:
2099:
1943:
1865:
1644:
1518:
1339:
1294:
1192:
1120:
57:, which can only handle pairs, the CMH test handles arbitrary strata sizes. It is named after
3586:
3541:
3305:
3292:
3185:
3160:
3094:
3026:
2904:
2512:
2405:
2338:
2251:
2198:
2017:
1888:
1682:
1481:
1448:
1323:
1263:
1219:
1184:
1149:
66:
50:
17:
883:
3503:
3247:
3109:
3036:
2711:
2585:
2558:
2535:
2504:
2131:
2126:
2080:
1810:
1461:
1251:"An Analysis of U.S. Domestic Migration via Subset-stable Measures of Administrative Data"
1140:
William G. Cochran (December 1954). "Some
Methods for Strengthening the Common χ2 Tests".
1053:
73:
in which random assignment of subjects to different treatments cannot be controlled but
3452:
3447:
1910:
1840:
1486:
959:
863:
836:
816:
3695:
3609:
3576:
3439:
3400:
3211:
3180:
2644:
2598:
2203:
1905:
1732:
1496:
1491:
1275:
62:
1762:
3551:
3484:
3461:
3376:
2706:
2002:
1900:
1835:
1777:
1699:
1654:
1223:
1070:
1066:
54:
3594:
3556:
3239:
3140:
3002:
2815:
2782:
2274:
2191:
2186:
1830:
1787:
1767:
1747:
1737:
1506:
1245:
74:
1267:
2440:
1920:
1620:
1551:
1501:
1476:
1396:
1080:
857:
751:
210:
31:
2593:
2445:
2065:
1860:
1772:
1757:
1752:
1717:
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2109:
1727:
1604:
1599:
1594:
1566:
1343:
3614:
3315:
1335:
1231:
1161:
1073:
as their test statistics are identical when each stratum shows a pair.
3536:
2517:
2491:
2471:
1722:
1513:
1119:. Hoboken, New Jersey: John Wiley & Sons, Inc. pp. 231–232.
1327:
1153:
860:). It is easy to construct examples where this is not the case, and
27:
Test used in the analysis of stratified or matched categorical data
742:
distribution asymptotically with 1 df under the null hypothesis.
1456:
1293:. Hoboken, New Jersey: John Wiley & Sons, Inc. p. 413.
3425:
2992:
2739:
2038:
1808:
1425:
1369:
1069:
can only handle pairs. The CMH test is a generalization of the
1365:
754:
of all strata could be calculated, giving risk ratios
1018:
982:
962:
913:
886:
866:
839:
819:
760:
721:
458:
416:
377:
226:
3278:
Autoregressive conditional heteroskedasticity (ARCH)
3585:
3522:
3475:
3438:
3393:
3375:
3342:
3333:
3291:
3238:
3199:
3148:
3139:
3060:
3017:
2947:
2913:
2867:
2834:
2796:
2763:
2675:
2584:
2503:
2458:
2426:
2379:
2324:
2250:
2241:
2051:
1993:
1967:
1919:
1874:
1821:
1708:
1663:
1637:
1619:
1575:
1527:
1447:
1438:
1249:
1040:
1004:
968:
937:
899:
872:
845:
825:
805:
734:
704:
441:
402:
360:
1361:Introduction to the Cochran-Mantel-Haenszel Test
1019:
983:
2826:Multivariate adaptive regression splines (MARS)
1212:Journal of the American Statistical Association
1381:
8:
3435:
3422:
3339:
3145:
3014:
2989:
2760:
2736:
2464:
2247:
2048:
2035:
1818:
1805:
1444:
1435:
1422:
1388:
1374:
1366:
945:. This is comparable but not identical to
3722:Summary statistics for contingency tables
1110:
1108:
1029:
1017:
993:
981:
961:
912:
891:
885:
865:
838:
818:
797:
778:
765:
759:
726:
720:
678:
665:
660:
645:
632:
619:
606:
599:
593:
582:
571:
553:
539:
526:
519:
510:
495:
484:
472:
463:
457:
421:
415:
382:
376:
344:
333:
323:
316:
310:
299:
294:
285:
274:
264:
257:
251:
240:
235:
233:
225:
3702:Statistical tests for contingency tables
1177:Journal of the National Cancer Institute
806:{\displaystyle r_{1},r_{2},\dots ,r_{n}}
92:
1256:Journal of Computational Social Science
1104:
3352:Kaplan–Meier estimator (product limit)
7:
3662:
3362:Accelerated failure time (AFT) model
42:) is a test used in the analysis of
3674:
2957:Analysis of variance (ANOVA, anova)
3052:Cochran–Mantel–Haenszel statistics
1678:Pearson product-moment correlation
952:Klemens defines a statistic to be
410:and the alternative hypothesis is
217:contingency tables is defined as:
25:
880:is larger or smaller than all of
3673:
3661:
3649:
3636:
3635:
3311:Least-squares spectral analysis
1085:conditional logistic regression
1077:Conditional logistic regression
938:{\displaystyle i\in 1,\dots ,n}
90:-th such contingency table is:
2292:Mean-unbiased minimum-variance
1224:10.1080/01621459.1963.10500879
1035:
1022:
999:
986:
690:
671:
1:
3605:Geographic information system
2821:Simultaneous equations models
442:{\displaystyle H_{1}:R\neq 1}
2788:Coefficient of determination
2399:Uniformly most powerful test
77:covariates can be measured.
36:Cochran–Mantel–Haenszel test
18:Cochran-Mantel-Haenszel test
3357:Proportional hazards models
3301:Spectral density estimation
3283:Vector autoregression (VAR)
2717:Maximum posterior estimator
1949:Randomized controlled trial
1041:{\displaystyle \max(r_{i})}
1005:{\displaystyle \min(r_{i})}
3738:
3117:Multivariate distributions
1537:Average absolute deviation
1268:10.1007/s42001-021-00124-w
3631:
3434:
3421:
3105:Structural equation model
3013:
2988:
2759:
2735:
2467:
2441:Score/Lagrange multiplier
2047:
2034:
1856:Sample size determination
1817:
1804:
1434:
1421:
1403:
1291:Categorical Data Analysis
1117:Categorical Data Analysis
1054:infinitely differentiable
735:{\displaystyle \chi ^{2}}
449:. The test statistic is:
403:{\displaystyle H_{0}:R=1}
3600:Environmental statistics
3122:Elliptical distributions
2915:Generalized linear model
2844:Simple linear regression
2614:Hodges–Lehmann estimator
2071:Probability distribution
1980:Stochastic approximation
1542:Coefficient of variation
3260:Cross-correlation (XCF)
2868:Non-standard predictors
2302:Lehmann–Scheffé theorem
1975:Adaptive clinical trial
3656:Mathematics portal
3477:Engineering statistics
3385:Nelson–Aalen estimator
2962:Analysis of covariance
2849:Ordinary least squares
2773:Pearson product-moment
2177:Statistical functional
2088:Empirical distribution
1921:Controlled experiments
1650:Frequency distribution
1428:Descriptive statistics
1289:Agresti, Alan (2002).
1115:Agresti, Alan (2002).
1042:
1006:
970:
939:
901:
874:
847:
827:
807:
750:The standard odds- or
736:
706:
598:
500:
443:
404:
362:
315:
256:
3572:Population statistics
3514:System identification
3248:Autocorrelation (ACF)
3176:Exponential smoothing
3090:Discriminant analysis
3085:Canonical correlation
2949:Partition of variance
2811:Regression validation
2655:(Jonckheere–Terpstra)
2554:Likelihood-ratio test
2243:Frequentist inference
2155:Location–scale family
2076:Sampling distribution
2041:Statistical inference
2008:Cross-sectional study
1995:Observational studies
1954:Randomized experiment
1783:Stem-and-leaf display
1585:Central limit theorem
1189:10.1093/jnci/22.4.719
1043:
1007:
971:
940:
902:
900:{\displaystyle r_{i}}
875:
848:
828:
808:
737:
707:
578:
480:
444:
405:
363:
295:
236:
71:observational studies
3495:Probabilistic design
3080:Principal components
2923:Exponential families
2875:Nonlinear regression
2854:General linear model
2816:Mixed effects models
2806:Errors and residuals
2783:Confounding variable
2685:Bayesian probability
2663:Van der Waerden test
2653:Ordered alternative
2418:Multiple comparisons
2297:Rao–Blackwellization
2260:Estimating equations
2216:Statistical distance
1934:Factorial experiment
1467:Arithmetic-Geometric
1016:
980:
960:
911:
884:
864:
837:
817:
758:
719:
456:
414:
375:
224:
3717:Bayesian statistics
3567:Official statistics
3490:Methods engineering
3171:Seasonal adjustment
2939:Poisson regressions
2859:Bayesian regression
2798:Regression analysis
2778:Partial correlation
2750:Regression analysis
2349:Prediction interval
2344:Likelihood interval
2334:Confidence interval
2326:Interval estimation
2287:Unbiased estimators
2105:Model specification
1985:Up-and-down designs
1673:Partial correlation
1629:Index of dispersion
1547:Interquartile range
1052:statistic as being
976:is bounded between
670:
3712:Medical statistics
3587:Spatial statistics
3467:Medical statistics
3367:First hitting time
3321:Whittle likelihood
2972:Degrees of freedom
2967:Multivariate ANOVA
2900:Heteroscedasticity
2712:Bayesian estimator
2677:Bayesian inference
2526:Kolmogorov–Smirnov
2411:Randomization test
2381:Testing hypotheses
2354:Tolerance interval
2265:Maximum likelihood
2160:Exponential family
2093:Density estimation
2053:Statistical theory
2013:Natural experiment
1959:Scientific control
1876:Survey methodology
1562:Standard deviation
1038:
1002:
966:
935:
897:
870:
843:
823:
803:
732:
702:
656:
439:
400:
358:
59:William G. Cochran
3689:
3688:
3627:
3626:
3623:
3622:
3562:National accounts
3532:Actuarial science
3524:Social statistics
3417:
3416:
3413:
3412:
3409:
3408:
3344:Survival function
3329:
3328:
3191:Granger causality
3032:Contingency table
3007:Survival analysis
2984:
2983:
2980:
2979:
2836:Linear regression
2731:
2730:
2727:
2726:
2702:Credible interval
2671:
2670:
2454:
2453:
2270:Method of moments
2139:Parametric family
2100:Statistical model
2030:
2029:
2026:
2025:
1944:Random assignment
1866:Statistical power
1800:
1799:
1796:
1795:
1645:Contingency table
1615:
1614:
1482:Generalized/power
1083:statistic of the
969:{\displaystyle R}
947:Simpson's paradox
873:{\displaystyle R}
846:{\displaystyle R}
826:{\displaystyle n}
697:
694:
559:
466:
353:
350:
291:
207:
206:
16:(Redirected from
3729:
3677:
3676:
3665:
3664:
3654:
3653:
3639:
3638:
3542:Crime statistics
3436:
3423:
3340:
3306:Fourier analysis
3293:Frequency domain
3273:
3220:
3186:Structural break
3146:
3095:Cluster analysis
3042:Log-linear model
3015:
2990:
2931:
2905:Homoscedasticity
2761:
2737:
2656:
2648:
2640:
2639:(Kruskal–Wallis)
2624:
2609:
2564:Cross validation
2549:
2531:Anderson–Darling
2478:
2465:
2436:Likelihood-ratio
2428:Parametric tests
2406:Permutation test
2389:1- & 2-tails
2280:Minimum distance
2252:Point estimation
2248:
2199:Optimal decision
2150:
2049:
2036:
2018:Quasi-experiment
1968:Adaptive designs
1819:
1806:
1683:Rank correlation
1445:
1436:
1423:
1390:
1383:
1376:
1367:
1348:
1347:
1311:
1305:
1304:
1286:
1280:
1279:
1253:
1242:
1236:
1235:
1218:(303): 690–700.
1207:
1201:
1200:
1172:
1166:
1165:
1137:
1131:
1130:
1112:
1091:Breslow–Day test
1047:
1045:
1044:
1039:
1034:
1033:
1011:
1009:
1008:
1003:
998:
997:
975:
973:
972:
967:
944:
942:
941:
936:
906:
904:
903:
898:
896:
895:
879:
877:
876:
871:
852:
850:
849:
844:
832:
830:
829:
824:
812:
810:
809:
804:
802:
801:
783:
782:
770:
769:
746:Subset stability
741:
739:
738:
733:
731:
730:
711:
709:
708:
703:
698:
696:
695:
693:
683:
682:
669:
664:
654:
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640:
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520:
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499:
494:
473:
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448:
446:
445:
440:
426:
425:
409:
407:
406:
401:
387:
386:
367:
365:
364:
359:
354:
352:
351:
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348:
339:
338:
337:
328:
327:
317:
314:
309:
293:
292:
290:
289:
280:
279:
278:
269:
268:
258:
255:
250:
234:
93:
67:William Haenszel
51:categorical data
21:
3737:
3736:
3732:
3731:
3730:
3728:
3727:
3726:
3692:
3691:
3690:
3685:
3648:
3619:
3581:
3518:
3504:quality control
3471:
3453:Clinical trials
3430:
3405:
3389:
3377:Hazard function
3371:
3325:
3287:
3271:
3234:
3230:Breusch–Godfrey
3218:
3195:
3135:
3110:Factor analysis
3056:
3037:Graphical model
3009:
2976:
2943:
2929:
2909:
2863:
2830:
2792:
2755:
2754:
2723:
2667:
2654:
2646:
2638:
2622:
2607:
2586:Rank statistics
2580:
2559:Model selection
2547:
2505:Goodness of fit
2499:
2476:
2450:
2422:
2375:
2320:
2309:Median unbiased
2237:
2148:
2081:Order statistic
2043:
2022:
1989:
1963:
1915:
1870:
1813:
1811:Data collection
1792:
1704:
1659:
1633:
1611:
1571:
1523:
1440:Continuous data
1430:
1417:
1399:
1394:
1357:
1352:
1351:
1328:10.2307/2530253
1313:
1312:
1308:
1301:
1288:
1287:
1283:
1244:
1243:
1239:
1209:
1208:
1204:
1174:
1173:
1169:
1154:10.2307/3001616
1139:
1138:
1134:
1127:
1114:
1113:
1106:
1101:
1062:
1025:
1014:
1013:
989:
978:
977:
958:
957:
909:
908:
887:
882:
881:
862:
861:
835:
834:
815:
814:
793:
774:
761:
756:
755:
748:
722:
717:
716:
674:
655:
641:
628:
615:
602:
601:
577:
549:
535:
522:
521:
506:
505:
501:
479:
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459:
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453:
417:
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411:
378:
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340:
329:
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184:
168:
156:
148:
136:
124:
116:
83:
28:
23:
22:
15:
12:
11:
5:
3735:
3733:
3725:
3724:
3719:
3714:
3709:
3704:
3694:
3693:
3687:
3686:
3684:
3683:
3671:
3659:
3645:
3632:
3629:
3628:
3625:
3624:
3621:
3620:
3618:
3617:
3612:
3607:
3602:
3597:
3591:
3589:
3583:
3582:
3580:
3579:
3574:
3569:
3564:
3559:
3554:
3549:
3544:
3539:
3534:
3528:
3526:
3520:
3519:
3517:
3516:
3511:
3506:
3497:
3492:
3487:
3481:
3479:
3473:
3472:
3470:
3469:
3464:
3459:
3450:
3448:Bioinformatics
3444:
3442:
3432:
3431:
3426:
3419:
3418:
3415:
3414:
3411:
3410:
3407:
3406:
3404:
3403:
3397:
3395:
3391:
3390:
3388:
3387:
3381:
3379:
3373:
3372:
3370:
3369:
3364:
3359:
3354:
3348:
3346:
3337:
3331:
3330:
3327:
3326:
3324:
3323:
3318:
3313:
3308:
3303:
3297:
3295:
3289:
3288:
3286:
3285:
3280:
3275:
3267:
3262:
3257:
3256:
3255:
3253:partial (PACF)
3244:
3242:
3236:
3235:
3233:
3232:
3227:
3222:
3214:
3209:
3203:
3201:
3200:Specific tests
3197:
3196:
3194:
3193:
3188:
3183:
3178:
3173:
3168:
3163:
3158:
3152:
3150:
3143:
3137:
3136:
3134:
3133:
3132:
3131:
3130:
3129:
3114:
3113:
3112:
3102:
3100:Classification
3097:
3092:
3087:
3082:
3077:
3072:
3066:
3064:
3058:
3057:
3055:
3054:
3049:
3047:McNemar's test
3044:
3039:
3034:
3029:
3023:
3021:
3011:
3010:
2993:
2986:
2985:
2982:
2981:
2978:
2977:
2975:
2974:
2969:
2964:
2959:
2953:
2951:
2945:
2944:
2942:
2941:
2925:
2919:
2917:
2911:
2910:
2908:
2907:
2902:
2897:
2892:
2887:
2885:Semiparametric
2882:
2877:
2871:
2869:
2865:
2864:
2862:
2861:
2856:
2851:
2846:
2840:
2838:
2832:
2831:
2829:
2828:
2823:
2818:
2813:
2808:
2802:
2800:
2794:
2793:
2791:
2790:
2785:
2780:
2775:
2769:
2767:
2757:
2756:
2753:
2752:
2747:
2741:
2740:
2733:
2732:
2729:
2728:
2725:
2724:
2722:
2721:
2720:
2719:
2709:
2704:
2699:
2698:
2697:
2692:
2681:
2679:
2673:
2672:
2669:
2668:
2666:
2665:
2660:
2659:
2658:
2650:
2642:
2626:
2623:(Mann–Whitney)
2618:
2617:
2616:
2603:
2602:
2601:
2590:
2588:
2582:
2581:
2579:
2578:
2577:
2576:
2571:
2566:
2556:
2551:
2548:(Shapiro–Wilk)
2543:
2538:
2533:
2528:
2523:
2515:
2509:
2507:
2501:
2500:
2498:
2497:
2489:
2480:
2468:
2462:
2460:Specific tests
2456:
2455:
2452:
2451:
2449:
2448:
2443:
2438:
2432:
2430:
2424:
2423:
2421:
2420:
2415:
2414:
2413:
2403:
2402:
2401:
2391:
2385:
2383:
2377:
2376:
2374:
2373:
2372:
2371:
2366:
2356:
2351:
2346:
2341:
2336:
2330:
2328:
2322:
2321:
2319:
2318:
2313:
2312:
2311:
2306:
2305:
2304:
2299:
2284:
2283:
2282:
2277:
2272:
2267:
2256:
2254:
2245:
2239:
2238:
2236:
2235:
2230:
2225:
2224:
2223:
2213:
2208:
2207:
2206:
2196:
2195:
2194:
2189:
2184:
2174:
2169:
2164:
2163:
2162:
2157:
2152:
2136:
2135:
2134:
2129:
2124:
2114:
2113:
2112:
2107:
2097:
2096:
2095:
2085:
2084:
2083:
2073:
2068:
2063:
2057:
2055:
2045:
2044:
2039:
2032:
2031:
2028:
2027:
2024:
2023:
2021:
2020:
2015:
2010:
2005:
1999:
1997:
1991:
1990:
1988:
1987:
1982:
1977:
1971:
1969:
1965:
1964:
1962:
1961:
1956:
1951:
1946:
1941:
1936:
1931:
1925:
1923:
1917:
1916:
1914:
1913:
1911:Standard error
1908:
1903:
1898:
1897:
1896:
1891:
1880:
1878:
1872:
1871:
1869:
1868:
1863:
1858:
1853:
1848:
1843:
1841:Optimal design
1838:
1833:
1827:
1825:
1815:
1814:
1809:
1802:
1801:
1798:
1797:
1794:
1793:
1791:
1790:
1785:
1780:
1775:
1770:
1765:
1760:
1755:
1750:
1745:
1740:
1735:
1730:
1725:
1720:
1714:
1712:
1706:
1705:
1703:
1702:
1697:
1696:
1695:
1690:
1680:
1675:
1669:
1667:
1661:
1660:
1658:
1657:
1652:
1647:
1641:
1639:
1638:Summary tables
1635:
1634:
1632:
1631:
1625:
1623:
1617:
1616:
1613:
1612:
1610:
1609:
1608:
1607:
1602:
1597:
1587:
1581:
1579:
1573:
1572:
1570:
1569:
1564:
1559:
1554:
1549:
1544:
1539:
1533:
1531:
1525:
1524:
1522:
1521:
1516:
1511:
1510:
1509:
1504:
1499:
1494:
1489:
1484:
1479:
1474:
1472:Contraharmonic
1469:
1464:
1453:
1451:
1442:
1432:
1431:
1426:
1419:
1418:
1416:
1415:
1410:
1404:
1401:
1400:
1395:
1393:
1392:
1385:
1378:
1370:
1364:
1363:
1356:
1355:External links
1353:
1350:
1349:
1322:(3): 623–630.
1306:
1299:
1281:
1237:
1202:
1183:(4): 719–748.
1167:
1148:(4): 417–451.
1132:
1125:
1103:
1102:
1100:
1097:
1096:
1095:
1088:
1087:are identical.
1074:
1061:
1058:
1037:
1032:
1028:
1024:
1021:
1001:
996:
992:
988:
985:
965:
934:
931:
928:
925:
922:
919:
916:
894:
890:
869:
842:
822:
800:
796:
792:
789:
786:
781:
777:
773:
768:
764:
747:
744:
729:
725:
713:
712:
701:
692:
689:
686:
681:
677:
673:
668:
663:
659:
651:
648:
644:
638:
635:
631:
625:
622:
618:
612:
609:
605:
596:
591:
588:
585:
581:
574:
569:
564:
556:
552:
545:
542:
538:
532:
529:
525:
518:
513:
509:
504:
498:
493:
490:
487:
483:
478:
471:
462:
438:
435:
432:
429:
424:
420:
399:
396:
393:
390:
385:
381:
369:
368:
357:
347:
343:
336:
332:
326:
322:
313:
308:
305:
302:
298:
288:
284:
277:
273:
267:
263:
254:
249:
246:
243:
239:
232:
229:
205:
204:
200:
196:
190:
185:
179:
174:
170:
169:
163:
158:
154:
150:
146:
142:
138:
137:
131:
126:
122:
118:
114:
110:
106:
105:
102:
99:
96:
82:
79:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3734:
3723:
3720:
3718:
3715:
3713:
3710:
3708:
3705:
3703:
3700:
3699:
3697:
3682:
3681:
3672:
3670:
3669:
3660:
3658:
3657:
3652:
3646:
3644:
3643:
3634:
3633:
3630:
3616:
3613:
3611:
3610:Geostatistics
3608:
3606:
3603:
3601:
3598:
3596:
3593:
3592:
3590:
3588:
3584:
3578:
3577:Psychometrics
3575:
3573:
3570:
3568:
3565:
3563:
3560:
3558:
3555:
3553:
3550:
3548:
3545:
3543:
3540:
3538:
3535:
3533:
3530:
3529:
3527:
3525:
3521:
3515:
3512:
3510:
3507:
3505:
3501:
3498:
3496:
3493:
3491:
3488:
3486:
3483:
3482:
3480:
3478:
3474:
3468:
3465:
3463:
3460:
3458:
3454:
3451:
3449:
3446:
3445:
3443:
3441:
3440:Biostatistics
3437:
3433:
3429:
3424:
3420:
3402:
3401:Log-rank test
3399:
3398:
3396:
3392:
3386:
3383:
3382:
3380:
3378:
3374:
3368:
3365:
3363:
3360:
3358:
3355:
3353:
3350:
3349:
3347:
3345:
3341:
3338:
3336:
3332:
3322:
3319:
3317:
3314:
3312:
3309:
3307:
3304:
3302:
3299:
3298:
3296:
3294:
3290:
3284:
3281:
3279:
3276:
3274:
3272:(Box–Jenkins)
3268:
3266:
3263:
3261:
3258:
3254:
3251:
3250:
3249:
3246:
3245:
3243:
3241:
3237:
3231:
3228:
3226:
3225:Durbin–Watson
3223:
3221:
3215:
3213:
3210:
3208:
3207:Dickey–Fuller
3205:
3204:
3202:
3198:
3192:
3189:
3187:
3184:
3182:
3181:Cointegration
3179:
3177:
3174:
3172:
3169:
3167:
3164:
3162:
3159:
3157:
3156:Decomposition
3154:
3153:
3151:
3147:
3144:
3142:
3138:
3128:
3125:
3124:
3123:
3120:
3119:
3118:
3115:
3111:
3108:
3107:
3106:
3103:
3101:
3098:
3096:
3093:
3091:
3088:
3086:
3083:
3081:
3078:
3076:
3073:
3071:
3068:
3067:
3065:
3063:
3059:
3053:
3050:
3048:
3045:
3043:
3040:
3038:
3035:
3033:
3030:
3028:
3027:Cohen's kappa
3025:
3024:
3022:
3020:
3016:
3012:
3008:
3004:
3000:
2996:
2991:
2987:
2973:
2970:
2968:
2965:
2963:
2960:
2958:
2955:
2954:
2952:
2950:
2946:
2940:
2936:
2932:
2926:
2924:
2921:
2920:
2918:
2916:
2912:
2906:
2903:
2901:
2898:
2896:
2893:
2891:
2888:
2886:
2883:
2881:
2880:Nonparametric
2878:
2876:
2873:
2872:
2870:
2866:
2860:
2857:
2855:
2852:
2850:
2847:
2845:
2842:
2841:
2839:
2837:
2833:
2827:
2824:
2822:
2819:
2817:
2814:
2812:
2809:
2807:
2804:
2803:
2801:
2799:
2795:
2789:
2786:
2784:
2781:
2779:
2776:
2774:
2771:
2770:
2768:
2766:
2762:
2758:
2751:
2748:
2746:
2743:
2742:
2738:
2734:
2718:
2715:
2714:
2713:
2710:
2708:
2705:
2703:
2700:
2696:
2693:
2691:
2688:
2687:
2686:
2683:
2682:
2680:
2678:
2674:
2664:
2661:
2657:
2651:
2649:
2643:
2641:
2635:
2634:
2633:
2630:
2629:Nonparametric
2627:
2625:
2619:
2615:
2612:
2611:
2610:
2604:
2600:
2599:Sample median
2597:
2596:
2595:
2592:
2591:
2589:
2587:
2583:
2575:
2572:
2570:
2567:
2565:
2562:
2561:
2560:
2557:
2555:
2552:
2550:
2544:
2542:
2539:
2537:
2534:
2532:
2529:
2527:
2524:
2522:
2520:
2516:
2514:
2511:
2510:
2508:
2506:
2502:
2496:
2494:
2490:
2488:
2486:
2481:
2479:
2474:
2470:
2469:
2466:
2463:
2461:
2457:
2447:
2444:
2442:
2439:
2437:
2434:
2433:
2431:
2429:
2425:
2419:
2416:
2412:
2409:
2408:
2407:
2404:
2400:
2397:
2396:
2395:
2392:
2390:
2387:
2386:
2384:
2382:
2378:
2370:
2367:
2365:
2362:
2361:
2360:
2357:
2355:
2352:
2350:
2347:
2345:
2342:
2340:
2337:
2335:
2332:
2331:
2329:
2327:
2323:
2317:
2314:
2310:
2307:
2303:
2300:
2298:
2295:
2294:
2293:
2290:
2289:
2288:
2285:
2281:
2278:
2276:
2273:
2271:
2268:
2266:
2263:
2262:
2261:
2258:
2257:
2255:
2253:
2249:
2246:
2244:
2240:
2234:
2231:
2229:
2226:
2222:
2219:
2218:
2217:
2214:
2212:
2209:
2205:
2204:loss function
2202:
2201:
2200:
2197:
2193:
2190:
2188:
2185:
2183:
2180:
2179:
2178:
2175:
2173:
2170:
2168:
2165:
2161:
2158:
2156:
2153:
2151:
2145:
2142:
2141:
2140:
2137:
2133:
2130:
2128:
2125:
2123:
2120:
2119:
2118:
2115:
2111:
2108:
2106:
2103:
2102:
2101:
2098:
2094:
2091:
2090:
2089:
2086:
2082:
2079:
2078:
2077:
2074:
2072:
2069:
2067:
2064:
2062:
2059:
2058:
2056:
2054:
2050:
2046:
2042:
2037:
2033:
2019:
2016:
2014:
2011:
2009:
2006:
2004:
2001:
2000:
1998:
1996:
1992:
1986:
1983:
1981:
1978:
1976:
1973:
1972:
1970:
1966:
1960:
1957:
1955:
1952:
1950:
1947:
1945:
1942:
1940:
1937:
1935:
1932:
1930:
1927:
1926:
1924:
1922:
1918:
1912:
1909:
1907:
1906:Questionnaire
1904:
1902:
1899:
1895:
1892:
1890:
1887:
1886:
1885:
1882:
1881:
1879:
1877:
1873:
1867:
1864:
1862:
1859:
1857:
1854:
1852:
1849:
1847:
1844:
1842:
1839:
1837:
1834:
1832:
1829:
1828:
1826:
1824:
1820:
1816:
1812:
1807:
1803:
1789:
1786:
1784:
1781:
1779:
1776:
1774:
1771:
1769:
1766:
1764:
1761:
1759:
1756:
1754:
1751:
1749:
1746:
1744:
1741:
1739:
1736:
1734:
1733:Control chart
1731:
1729:
1726:
1724:
1721:
1719:
1716:
1715:
1713:
1711:
1707:
1701:
1698:
1694:
1691:
1689:
1686:
1685:
1684:
1681:
1679:
1676:
1674:
1671:
1670:
1668:
1666:
1662:
1656:
1653:
1651:
1648:
1646:
1643:
1642:
1640:
1636:
1630:
1627:
1626:
1624:
1622:
1618:
1606:
1603:
1601:
1598:
1596:
1593:
1592:
1591:
1588:
1586:
1583:
1582:
1580:
1578:
1574:
1568:
1565:
1563:
1560:
1558:
1555:
1553:
1550:
1548:
1545:
1543:
1540:
1538:
1535:
1534:
1532:
1530:
1526:
1520:
1517:
1515:
1512:
1508:
1505:
1503:
1500:
1498:
1495:
1493:
1490:
1488:
1485:
1483:
1480:
1478:
1475:
1473:
1470:
1468:
1465:
1463:
1460:
1459:
1458:
1455:
1454:
1452:
1450:
1446:
1443:
1441:
1437:
1433:
1429:
1424:
1420:
1414:
1411:
1409:
1406:
1405:
1402:
1398:
1391:
1386:
1384:
1379:
1377:
1372:
1371:
1368:
1362:
1359:
1358:
1354:
1345:
1341:
1337:
1333:
1329:
1325:
1321:
1317:
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3707:Epidemiology
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3647:
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3552:Econometrics
3502: /
3485:Chemometrics
3462:Epidemiology
3455: /
3428:Applications
3270:ARIMA model
3217:Q-statistic
3166:Stationarity
3062:Multivariate
3051:
3005: /
3001: /
2999:Multivariate
2997: /
2937: /
2933: /
2707:Bayes factor
2606:Signed rank
2518:
2492:
2484:
2472:
2167:Completeness
2003:Cohort study
1901:Opinion poll
1836:Missing data
1823:Study design
1778:Scatter plot
1700:Scatter plot
1693:Spearman's ρ
1655:Grouped data
1319:
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1071:McNemar test
1067:McNemar test
1050:well-behaved
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101:No treatment
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55:McNemar test
39:
35:
29:
3680:WikiProject
3595:Cartography
3557:Jurimetrics
3509:Reliability
3240:Time domain
3219:(Ljung–Box)
3141:Time-series
3019:Categorical
3003:Time-series
2995:Categorical
2930:(Bernoulli)
2765:Correlation
2745:Correlation
2541:Jarque–Bera
2513:Chi-squared
2275:M-estimator
2228:Asymptotics
2172:Sufficiency
1939:Interaction
1851:Replication
1831:Effect size
1788:Violin plot
1768:Radar chart
1748:Forest plot
1738:Correlogram
1688:Kendall's τ
1262:: 351–382.
1246:Ben Klemens
858:odds ratios
209:The common
75:confounding
3696:Categories
3547:Demography
3265:ARMA model
3070:Regression
2647:(Friedman)
2608:(Wilcoxon)
2546:Normality
2536:Lilliefors
2483:Student's
2359:Resampling
2233:Robustness
2221:divergence
2211:Efficiency
2149:(monotone)
2144:Likelihood
2061:Population
1894:Stratified
1846:Population
1665:Dependence
1621:Count data
1552:Percentile
1529:Dispersion
1462:Arithmetic
1397:Statistics
1316:Biometrics
1142:Biometrics
1081:score test
752:risk ratio
211:odds-ratio
104:Row total
81:Definition
44:stratified
32:statistics
2928:Logistic
2695:posterior
2621:Rank sum
2369:Jackknife
2364:Bootstrap
2182:Bootstrap
2117:Parameter
2066:Statistic
1861:Statistic
1773:Run chart
1758:Pie chart
1753:Histogram
1743:Fan chart
1718:Bar chart
1600:L-moments
1487:Geometric
1276:236308711
927:…
918:∈
788:…
724:χ
685:−
580:∑
517:−
482:∑
461:ξ
434:≠
297:∑
238:∑
98:Treatment
3642:Category
3335:Survival
3212:Johansen
2935:Binomial
2890:Isotonic
2477:(normal)
2122:location
1929:Blocking
1884:Sampling
1763:Q–Q plot
1728:Box plot
1710:Graphics
1605:Skewness
1595:Kurtosis
1567:Variance
1497:Heronian
1492:Harmonic
1197:13655060
1048:, and a
813:, where
141:Controls
3668:Commons
3615:Kriging
3500:Process
3457:studies
3316:Wavelet
3149:General
2316:Plug-in
2110:L space
1889:Cluster
1590:Moments
1408:Outline
1336:2530253
1232:2282717
1162:3001616
213:of the
48:matched
3537:Census
3127:Normal
3075:Manova
2895:Robust
2645:2-way
2637:1-way
2475:-test
2146:
1723:Biplot
1514:Median
1507:Lehmer
1449:Center
1344:497345
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1094:pairs.
34:, the
3161:Trend
2690:prior
2632:anova
2521:-test
2495:-test
2487:-test
2394:Power
2339:Pivot
2132:shape
2127:scale
1577:Shape
1557:Range
1502:Heinz
1477:Cubic
1413:Index
1332:JSTOR
1272:S2CID
1228:JSTOR
1158:JSTOR
1099:Notes
3394:Test
2594:Sign
2446:Wald
1519:Mode
1457:Mean
1340:PMID
1295:ISBN
1193:PMID
1121:ISBN
1065:The
1012:and
956:iff
907:for
109:Case
65:and
2574:BIC
2569:AIC
1324:doi
1264:doi
1220:doi
1185:doi
1150:doi
1020:max
984:min
465:CMH
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40:CMH
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