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The parametric alternative to the
Scheirer–Ray–Hare test is multi-factorial ANOVA, which requires a normal distribution of data within the samples. The Kruskal–Wallis test, from which the Scheirer–Ray–Hare test is derived, serves in contrast to this to investigate the influence of exactly one factor
160:. the probability of actually finding a statistically significant result, is significantly lower than that of the parametric multi-factorial ANOVA, so that it is considered more conservative in comparison of both methods. For this reason, and because the method was described later than most other
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that the two factors examined in each case have no influence on the positional parameter of the samples and thus on the measure, and that there are no interactions between the two factors. A p-value less than 0.05 for one or more of these three hypotheses leads to their rejection. As with many
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The
Scheirer–Ray–Hare test is analogous to the parametric multi-factorial ANOVA of investigating the influence of two different factors on a measure for which different samples are available for the factors. As with the parametric analysis of variance, the test can be used to investigate the
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variance analysis tests, it has found little use in textbooks and statistical analysis software. With computer programs that contain a function for parametric multi-factorial ANOVA, however, with additional manual effort and a calculation of the
Scheirer Ray Hare test is possible.
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other non-parametric methods, the analysis in this method relies on the evaluation of the ranks of the samples in the samples rather than the actual observations. Modifications also allow extending the test to examine more than two factors.
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that can be used to examine whether a measure is affected by two or more factors. Since it does not require a normal distribution of the data, it is one of the non-parametric methods. It is an extension of the
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on the measured variable. A non-parametric test comparing exactly two unpaired samples is the
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analyses. The test is named after James
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The
Analysis of Ranked Data Derived from Completely Randomized Factorial Designs.
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Biometry: The
Principles And Practice of Statistics In Biological Research.
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test, the non-parametric equivalent for one-way analysis of variance (
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32(2)/1976. International
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Autoregressive conditional heteroskedasticity (ARCH)
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test that compares the individual samples in pairs.
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Choosing And Using
Statistics: A Biologist's Guide.
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265:Third edition. Freeman, New York 1995,
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2295:Accelerated failure time (AFT) model
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55:"Scheirer–Ray–Hare test"
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228:Scheirer–Ray–Hare test.
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3082:Statistical outline
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230:In: Calvin Dytham:
3087:Statistical topics
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1905:Degrees of freedom
1900:Multivariate ANOVA
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1614:
1612:
1606:
1605:
1602:
1601:
1599:
1598:
1593:
1592:
1591:
1583:
1575:
1559:
1556:(Mann–Whitney)
1551:
1550:
1549:
1536:
1535:
1534:
1523:
1521:
1515:
1514:
1512:
1511:
1510:
1509:
1504:
1499:
1489:
1484:
1481:(Shapiro–Wilk)
1476:
1471:
1466:
1461:
1456:
1448:
1442:
1440:
1434:
1433:
1431:
1430:
1422:
1413:
1401:
1395:
1393:Specific tests
1389:
1388:
1385:
1384:
1382:
1381:
1376:
1371:
1365:
1363:
1357:
1356:
1354:
1353:
1348:
1347:
1346:
1336:
1335:
1334:
1324:
1318:
1316:
1310:
1309:
1307:
1306:
1305:
1304:
1299:
1289:
1284:
1279:
1274:
1269:
1263:
1261:
1255:
1254:
1252:
1251:
1246:
1245:
1244:
1239:
1238:
1237:
1232:
1217:
1216:
1215:
1210:
1205:
1200:
1189:
1187:
1178:
1172:
1171:
1169:
1168:
1163:
1158:
1157:
1156:
1146:
1141:
1140:
1139:
1129:
1128:
1127:
1122:
1117:
1107:
1102:
1097:
1096:
1095:
1090:
1085:
1069:
1068:
1067:
1062:
1057:
1047:
1046:
1045:
1040:
1030:
1029:
1028:
1018:
1017:
1016:
1006:
1001:
996:
990:
988:
978:
977:
972:
965:
964:
961:
960:
957:
956:
954:
953:
948:
943:
938:
932:
930:
924:
923:
921:
920:
915:
910:
904:
902:
898:
897:
895:
894:
889:
884:
879:
874:
869:
864:
858:
856:
850:
849:
847:
846:
844:Standard error
841:
836:
831:
830:
829:
824:
813:
811:
805:
804:
802:
801:
796:
791:
786:
781:
776:
774:Optimal design
771:
766:
760:
758:
748:
747:
742:
735:
734:
731:
730:
727:
726:
724:
723:
718:
713:
708:
703:
698:
693:
688:
683:
678:
673:
668:
663:
658:
653:
647:
645:
639:
638:
636:
635:
630:
629:
628:
623:
613:
608:
602:
600:
594:
593:
591:
590:
585:
580:
574:
572:
571:Summary tables
568:
567:
565:
564:
558:
556:
550:
549:
546:
545:
543:
542:
541:
540:
535:
530:
520:
514:
512:
506:
505:
503:
502:
497:
492:
487:
482:
477:
472:
466:
464:
458:
457:
455:
454:
449:
444:
443:
442:
437:
432:
427:
422:
417:
412:
407:
405:Contraharmonic
402:
397:
386:
384:
375:
365:
364:
359:
352:
351:
349:
348:
343:
337:
334:
333:
328:
326:
325:
318:
311:
303:
296:
295:
275:
274:
259:F. James Rohlf
250:
247:
245:
244:
217:
192:
190:
187:
181:
178:
166:non-parametric
144:
141:
129:Kruskal–Wallis
114:
113:
28:
26:
19:
13:
10:
9:
6:
4:
3:
2:
3135:
3124:
3121:
3119:
3116:
3114:
3111:
3109:
3106:
3105:
3103:
3088:
3085:
3083:
3080:
3078:
3073:
3068:
3066:
3063:
3061:
3058:
3057:
3054:
3048:
3045:
3043:
3040:
3038:
3037:
3033:
3032:
3029:
3026:
3024:
3023:
3018:
3015:
3013:
3010:
3008:
3005:
3003:
3000:
2997:
2994:
2992:
2991:
2987:
2986:
2983:
2980:
2978:
2975:
2973:
2970:
2968:
2967:
2963:
2962:
2959:
2956:
2954:
2951:
2949:
2946:
2944:
2943:
2939:
2938:
2936:
2934:
2927:
2923:
2917:
2914:
2912:
2911:Compare means
2909:
2908:
2905:
2903:
2899:
2895:
2893:
2891:
2887:
2883:
2881:
2878:
2876:
2875:
2871:
2870:
2867:
2864:
2861:
2859:
2856:
2854:
2853:
2852:Random effect
2849:
2848:
2845:
2842:
2840:
2837:
2835:
2832:
2831:
2829:
2827:
2822:
2818:
2812:
2809:
2807:
2804:
2802:
2801:
2797:
2795:
2794:Orthogonality
2792:
2790:
2787:
2785:
2782:
2780:
2777:
2775:
2772:
2770:
2769:
2765:
2764:
2762:
2760:
2755:
2751:
2745:
2742:
2740:
2737:
2735:
2732:
2730:
2729:Randomization
2727:
2725:
2722:
2720:
2716:
2715:
2711:
2710:
2707:
2704:
2702:
2699:
2697:
2694:
2690:
2687:
2685:
2682:
2680:
2677:
2675:
2672:
2671:
2669:
2667:
2661:
2657:
2650:
2645:
2643:
2638:
2636:
2631:
2630:
2627:
2615:
2614:
2605:
2603:
2602:
2593:
2591:
2590:
2585:
2579:
2577:
2576:
2567:
2566:
2563:
2549:
2546:
2544:
2543:Geostatistics
2541:
2539:
2536:
2534:
2531:
2529:
2526:
2525:
2523:
2521:
2517:
2511:
2510:Psychometrics
2508:
2506:
2503:
2501:
2498:
2496:
2493:
2491:
2488:
2486:
2483:
2481:
2478:
2476:
2473:
2471:
2468:
2466:
2463:
2462:
2460:
2458:
2454:
2448:
2445:
2443:
2440:
2438:
2434:
2431:
2429:
2426:
2424:
2421:
2419:
2416:
2415:
2413:
2411:
2407:
2401:
2398:
2396:
2393:
2391:
2387:
2384:
2382:
2379:
2378:
2376:
2374:
2373:Biostatistics
2370:
2366:
2362:
2357:
2353:
2335:
2334:Log-rank test
2332:
2331:
2329:
2325:
2319:
2316:
2315:
2313:
2311:
2307:
2301:
2298:
2296:
2293:
2291:
2288:
2286:
2283:
2282:
2280:
2278:
2274:
2271:
2269:
2265:
2255:
2252:
2250:
2247:
2245:
2242:
2240:
2237:
2235:
2232:
2231:
2229:
2227:
2223:
2217:
2214:
2212:
2209:
2207:
2205:(Box–Jenkins)
2201:
2199:
2196:
2194:
2191:
2187:
2184:
2183:
2182:
2179:
2178:
2176:
2174:
2170:
2164:
2161:
2159:
2158:Durbin–Watson
2156:
2154:
2148:
2146:
2143:
2141:
2140:Dickey–Fuller
2138:
2137:
2135:
2131:
2125:
2122:
2120:
2117:
2115:
2114:Cointegration
2112:
2110:
2107:
2105:
2102:
2100:
2097:
2095:
2092:
2090:
2089:Decomposition
2087:
2086:
2084:
2080:
2077:
2075:
2071:
2061:
2058:
2057:
2056:
2053:
2052:
2051:
2048:
2044:
2041:
2040:
2039:
2036:
2034:
2031:
2029:
2026:
2024:
2021:
2019:
2016:
2014:
2011:
2009:
2006:
2004:
2001:
2000:
1998:
1996:
1992:
1986:
1983:
1981:
1978:
1976:
1973:
1971:
1968:
1966:
1963:
1961:
1960:Cohen's kappa
1958:
1957:
1955:
1953:
1949:
1945:
1941:
1937:
1933:
1929:
1924:
1920:
1906:
1903:
1901:
1898:
1896:
1893:
1891:
1888:
1887:
1885:
1883:
1879:
1873:
1869:
1865:
1859:
1857:
1854:
1853:
1851:
1849:
1845:
1839:
1836:
1834:
1831:
1829:
1826:
1824:
1821:
1819:
1816:
1814:
1813:Nonparametric
1811:
1809:
1806:
1805:
1803:
1799:
1793:
1790:
1788:
1785:
1783:
1780:
1778:
1775:
1774:
1772:
1770:
1766:
1760:
1757:
1755:
1752:
1750:
1747:
1745:
1742:
1740:
1737:
1736:
1734:
1732:
1728:
1722:
1719:
1717:
1714:
1712:
1709:
1707:
1704:
1703:
1701:
1699:
1695:
1691:
1684:
1681:
1679:
1676:
1675:
1671:
1667:
1651:
1648:
1647:
1646:
1643:
1641:
1638:
1636:
1633:
1629:
1626:
1624:
1621:
1620:
1619:
1616:
1615:
1613:
1611:
1607:
1597:
1594:
1590:
1584:
1582:
1576:
1574:
1568:
1567:
1566:
1563:
1562:Nonparametric
1560:
1558:
1552:
1548:
1545:
1544:
1543:
1537:
1533:
1532:Sample median
1530:
1529:
1528:
1525:
1524:
1522:
1520:
1516:
1508:
1505:
1503:
1500:
1498:
1495:
1494:
1493:
1490:
1488:
1485:
1483:
1477:
1475:
1472:
1470:
1467:
1465:
1462:
1460:
1457:
1455:
1453:
1449:
1447:
1444:
1443:
1441:
1439:
1435:
1429:
1427:
1423:
1421:
1419:
1414:
1412:
1407:
1403:
1402:
1399:
1396:
1394:
1390:
1380:
1377:
1375:
1372:
1370:
1367:
1366:
1364:
1362:
1358:
1352:
1349:
1345:
1342:
1341:
1340:
1337:
1333:
1330:
1329:
1328:
1325:
1323:
1320:
1319:
1317:
1315:
1311:
1303:
1300:
1298:
1295:
1294:
1293:
1290:
1288:
1285:
1283:
1280:
1278:
1275:
1273:
1270:
1268:
1265:
1264:
1262:
1260:
1256:
1250:
1247:
1243:
1240:
1236:
1233:
1231:
1228:
1227:
1226:
1223:
1222:
1221:
1218:
1214:
1211:
1209:
1206:
1204:
1201:
1199:
1196:
1195:
1194:
1191:
1190:
1188:
1186:
1182:
1179:
1177:
1173:
1167:
1164:
1162:
1159:
1155:
1152:
1151:
1150:
1147:
1145:
1142:
1138:
1137:loss function
1135:
1134:
1133:
1130:
1126:
1123:
1121:
1118:
1116:
1113:
1112:
1111:
1108:
1106:
1103:
1101:
1098:
1094:
1091:
1089:
1086:
1084:
1078:
1075:
1074:
1073:
1070:
1066:
1063:
1061:
1058:
1056:
1053:
1052:
1051:
1048:
1044:
1041:
1039:
1036:
1035:
1034:
1031:
1027:
1024:
1023:
1022:
1019:
1015:
1012:
1011:
1010:
1007:
1005:
1002:
1000:
997:
995:
992:
991:
989:
987:
983:
979:
975:
970:
966:
952:
949:
947:
944:
942:
939:
937:
934:
933:
931:
929:
925:
919:
916:
914:
911:
909:
906:
905:
903:
899:
893:
890:
888:
885:
883:
880:
878:
875:
873:
870:
868:
865:
863:
860:
859:
857:
855:
851:
845:
842:
840:
839:Questionnaire
837:
835:
832:
828:
825:
823:
820:
819:
818:
815:
814:
812:
810:
806:
800:
797:
795:
792:
790:
787:
785:
782:
780:
777:
775:
772:
770:
767:
765:
762:
761:
759:
757:
753:
749:
745:
740:
736:
722:
719:
717:
714:
712:
709:
707:
704:
702:
699:
697:
694:
692:
689:
687:
684:
682:
679:
677:
674:
672:
669:
667:
666:Control chart
664:
662:
659:
657:
654:
652:
649:
648:
646:
644:
640:
634:
631:
627:
624:
622:
619:
618:
617:
614:
612:
609:
607:
604:
603:
601:
599:
595:
589:
586:
584:
581:
579:
576:
575:
573:
569:
563:
560:
559:
557:
555:
551:
539:
536:
534:
531:
529:
526:
525:
524:
521:
519:
516:
515:
513:
511:
507:
501:
498:
496:
493:
491:
488:
486:
483:
481:
478:
476:
473:
471:
468:
467:
465:
463:
459:
453:
450:
448:
445:
441:
438:
436:
433:
431:
428:
426:
423:
421:
418:
416:
413:
411:
408:
406:
403:
401:
398:
396:
393:
392:
391:
388:
387:
385:
383:
379:
376:
374:
370:
366:
362:
357:
353:
347:
344:
342:
339:
338:
335:
331:
324:
319:
317:
312:
310:
305:
304:
301:
294:
289:
284:
280:
272:
271:0-71-672411-1
268:
264:
260:
256:
253:
252:
248:
241:
237:
233:
229:
224:
222:
218:
215:
211:
207:
203:
197:
194:
188:
186:
179:
177:
175:
170:
167:
163:
159:
154:
151:
142:
140:
138:
134:
130:
125:
121:
110:
107:
99:
96:February 2019
88:
85:
81:
78:
74:
71:
67:
64:
60:
57: –
56:
52:
51:Find sources:
45:
41:
35:
34:
29:This article
27:
23:
18:
17:
3034:
3020:
3002:Latin square
2988:
2964:
2940:
2901:
2897:
2890:multivariate
2889:
2885:
2872:
2850:
2798:
2766:
2712:
2611:
2599:
2580:
2573:
2485:Econometrics
2435: /
2418:Chemometrics
2395:Epidemiology
2388: /
2361:Applications
2203:ARIMA model
2150:Q-statistic
2099:Stationarity
1995:Multivariate
1938: /
1934: /
1932:Multivariate
1930: /
1870: /
1866: /
1640:Bayes factor
1539:Signed rank
1451:
1425:
1417:
1405:
1100:Completeness
936:Cohort study
834:Opinion poll
769:Missing data
756:Study design
711:Scatter plot
633:Scatter plot
626:Spearman's ρ
588:Grouped data
262:
231:
227:
205:
201:
196:
183:
171:
157:
155:
146:
119:
117:
102:
93:
83:
76:
69:
62:
50:
38:Please help
33:verification
30:
2977:Box–Behnken
2858:Mixed model
2789:Confounding
2784:Interaction
2774:Effect size
2744:Sample size
2613:WikiProject
2528:Cartography
2490:Jurimetrics
2442:Reliability
2173:Time domain
2152:(Ljung–Box)
2074:Time-series
1952:Categorical
1936:Time-series
1928:Categorical
1863:(Bernoulli)
1698:Correlation
1678:Correlation
1474:Jarque–Bera
1446:Chi-squared
1208:M-estimator
1161:Asymptotics
1105:Sufficiency
872:Interaction
784:Replication
764:Effect size
721:Violin plot
701:Radar chart
681:Forest plot
671:Correlogram
621:Kendall's τ
293:Mathematics
206:Biometrics.
3102:Categories
2933:randomized
2931:Completely
2902:covariance
2664:Scientific
2480:Demography
2198:ARMA model
2003:Regression
1580:(Friedman)
1541:(Wilcoxon)
1479:Normality
1469:Lilliefors
1416:Student's
1292:Resampling
1166:Robustness
1154:divergence
1144:Efficiency
1082:(monotone)
1077:Likelihood
994:Population
827:Stratified
779:Population
598:Dependence
554:Count data
485:Percentile
462:Dispersion
395:Arithmetic
330:Statistics
249:Literature
240:1405102438
189:References
162:parametric
66:newspapers
2942:Factorial
2826:inference
2806:Covariate
2768:Treatment
2754:Treatment
1861:Logistic
1628:posterior
1554:Rank sum
1302:Jackknife
1297:Bootstrap
1115:Bootstrap
1050:Parameter
999:Statistic
794:Statistic
706:Run chart
691:Pie chart
686:Histogram
676:Fan chart
651:Bar chart
533:L-moments
420:Geometric
3065:Category
3060:Glossary
2866:Bayesian
2844:Bayesian
2800:Blocking
2779:Contrast
2759:blocking
2719:Bayesian
2706:Blinding
2696:validity
2693:external
2689:Internal
2575:Category
2268:Survival
2145:Johansen
1868:Binomial
1823:Isotonic
1410:(normal)
1055:location
862:Blocking
817:Sampling
696:Q–Q plot
661:Box plot
643:Graphics
538:Skewness
528:Kurtosis
500:Variance
430:Heronian
425:Harmonic
174:post-hoc
2958:Taguchi
2926:Designs
2684:Control
2601:Commons
2548:Kriging
2433:Process
2390:studies
2249:Wavelet
2082:General
1249:Plug-in
1043:L space
822:Cluster
523:Moments
341:Outline
80:scholar
2998:(GRBD)
2898:Ancova
2886:Manova
2821:Models
2666:method
2470:Census
2060:Normal
2008:Manova
1828:Robust
1578:2-way
1570:1-way
1408:-test
1079:
656:Biplot
447:Median
440:Lehmer
382:Center
279:Portal
269:
238:
82:
75:
68:
61:
53:
2990:Block
2094:Trend
1623:prior
1565:anova
1454:-test
1428:-test
1420:-test
1327:Power
1272:Pivot
1065:shape
1060:scale
510:Shape
490:Range
435:Heinz
410:Cubic
346:Index
133:ANOVA
122:is a
87:JSTOR
73:books
2824:and
2757:and
2691:and
2327:Test
1527:Sign
1379:Wald
452:Mode
390:Mean
267:ISBN
236:ISBN
204:In:
164:and
118:The
59:news
1507:BIC
1502:AIC
210:doi
158:i.e
42:by
3104::
2717::
261::
257:,
220:^
2904:)
2900:(
2892:)
2888:(
2648:e
2641:t
2634:v
1452:G
1426:F
1418:t
1406:Z
1125:V
1120:U
322:e
315:t
308:v
281::
212::
109:)
103:(
98:)
94:(
84:·
77:·
70:·
63:·
36:.
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