481:
994:
Michel G. Soete. A new theory on the measurement of association between two binary variables in medical sciences: association can be expressed in a fraction (per unum, percentage, pro mille....) of perfect association (2013), e-article,
213:
301:
465:
618:. The transformed table has the same degree of association (the same OR) as the original not-crosswise symmetric table. Therefore, the association in asymmetric tables can be measured by Yule's
400:
549:(multiplied by 100 it represents this fraction in a more familiar percentage). Indeed, the formula transforms the original 2×2 table in a crosswise symmetric table wherein
1011:
502:
138:
593:
it is very easy to see that it can be split up in two tables. In such tables association can be measured in a perfectly clear way by dividing (
825:
The following asymmetric table can be transformed in a table with an equal degree of association (the odds ratios of both tables are equal).
649:
measures association in a substantial, intuitively understandable way and therefore it is the measure of preference to measure association.
314:, +1 reflects perfect positive association while 0 reflects no association at all. These correspond to the values for the more common
528:
243:
506:
406:
491:
510:
495:
346:
642:) give the same result in crosswise symmetric tables, presenting the association as a fraction in both cases.
546:
315:
977:
969:
31:
55:
30:, is a measure of association between two binary variables. The measure was developed by
1005:
622:, interpreting it in just the same way as with symmetric tables. Of course, Yule's
208:{\displaystyle Y={\frac {{\sqrt {ad}}-{\sqrt {bc}}}{{\sqrt {ad}}+{\sqrt {bc}}}}.}
480:
326:
311:
223:
939: = (3 − 1)/(3 + 1) = 0.5 (50%)
43:
39:
35:
822:
It is obvious that the degree of association equals 0.6 per unum (60%).
981:
973:
957:
958:"On the Methods of Measuring Association Between Two Attributes"
577:
For a crosswise symmetric table with frequencies or proportions
609:). In transformed tables b has to be substituted by 1 and a by
474:
310:
varies from −1 to +1. −1 reflects total negative
332:, which can also be expressed in terms of the odds ratio.
296:{\displaystyle Y={\frac {{\sqrt {OR}}-1}{{\sqrt {OR}}+1}}}
460:{\displaystyle Y={\frac {1-{\sqrt {1-Q^{2}}}}{Q}}\ .}
409:
349:
246:
141:
935:
The odds ratios of both tables are equal to 9.
16:
Measure of association between two binary variables
459:
394:
295:
207:
545:gives the fraction of perfect association in per
8:
509:. Unsourced material may be challenged and
395:{\displaystyle Q={\frac {2Y}{1+Y^{2}}}\ ,}
1012:Summary statistics for contingency tables
529:Learn how and when to remove this message
437:
425:
416:
408:
377:
356:
348:
274:
256:
253:
245:
189:
176:
164:
151:
148:
140:
34:in 1912, and should not be confused with
962:Journal of the Royal Statistical Society
884:
829:
771:
716:
661:
657:The following crosswise symmetric table
69:
948:
7:
880:Here follows the transformed table:
507:adding citations to reliable sources
237:) as is seen in following formula:
14:
712:can be split up into two tables:
479:
65:with frequencies or proportions
325:is also related to the similar
1:
1028:
222:is closely related to the
28:coefficient of colligation
956:Yule, G. Udny (1912).
461:
396:
297:
209:
462:
397:
298:
210:
503:improve this section
407:
347:
244:
139:
54:For a 2×2 table for
26:, also known as the
316:Pearson correlation
457:
392:
293:
205:
36:Yule's coefficient
931:
930:
876:
875:
818:
817:
763:
762:
708:
707:
539:
538:
531:
453:
449:
443:
388:
384:
291:
282:
264:
200:
197:
184:
172:
159:
124:
123:
1019:
996:
992:
986:
985:
953:
885:
830:
772:
717:
662:
617:
616:
573:
572:
534:
527:
523:
520:
514:
483:
475:
466:
464:
463:
458:
451:
450:
445:
444:
442:
441:
426:
417:
401:
399:
398:
393:
386:
385:
383:
382:
381:
365:
357:
340:are related by:
302:
300:
299:
294:
292:
290:
283:
275:
272:
265:
257:
254:
214:
212:
211:
206:
201:
199:
198:
190:
185:
177:
174:
173:
165:
160:
152:
149:
70:
56:binary variables
32:George Udny Yule
1027:
1026:
1022:
1021:
1020:
1018:
1017:
1016:
1002:
1001:
1000:
999:
993:
989:
974:10.2307/2340126
955:
954:
950:
945:
655:
612:
610:
568:
566:
535:
524:
518:
515:
500:
484:
473:
433:
418:
405:
404:
373:
366:
358:
345:
344:
273:
255:
242:
241:
175:
150:
137:
136:
52:
19:In statistics,
17:
12:
11:
5:
1025:
1023:
1015:
1014:
1004:
1003:
998:
997:
987:
968:(6): 579–652.
947:
946:
944:
941:
933:
932:
929:
928:
925:
922:
915:
914:
911:
908:
901:
900:
894:
888:
878:
877:
874:
873:
870:
867:
860:
859:
856:
853:
846:
845:
839:
833:
820:
819:
816:
815:
812:
809:
802:
801:
798:
795:
788:
787:
781:
775:
765:
764:
761:
760:
757:
754:
747:
746:
743:
740:
733:
732:
726:
720:
710:
709:
706:
705:
702:
699:
692:
691:
688:
685:
678:
677:
671:
665:
654:
651:
537:
536:
487:
485:
478:
472:
471:Interpretation
469:
468:
467:
456:
448:
440:
436:
432:
429:
424:
421:
415:
412:
402:
391:
380:
376:
372:
369:
364:
361:
355:
352:
304:
303:
289:
286:
281:
278:
271:
268:
263:
260:
252:
249:
216:
215:
204:
196:
193:
188:
183:
180:
171:
168:
163:
158:
155:
147:
144:
126:
125:
122:
121:
116:
111:
104:
103:
98:
93:
86:
85:
79:
73:
51:
48:
38:for measuring
15:
13:
10:
9:
6:
4:
3:
2:
1024:
1013:
1010:
1009:
1007:
991:
988:
983:
979:
975:
971:
967:
963:
959:
952:
949:
942:
940:
938:
926:
923:
920:
917:
916:
912:
909:
906:
903:
902:
898:
895:
892:
889:
887:
886:
883:
882:
881:
871:
868:
865:
862:
861:
857:
854:
851:
848:
847:
843:
840:
837:
834:
832:
831:
828:
827:
826:
823:
813:
810:
807:
804:
803:
799:
796:
793:
790:
789:
785:
782:
779:
776:
774:
773:
770:
769:
768:
758:
755:
752:
749:
748:
744:
741:
738:
735:
734:
730:
727:
724:
721:
719:
718:
715:
714:
713:
703:
700:
697:
694:
693:
689:
686:
683:
680:
679:
675:
672:
669:
666:
664:
663:
660:
659:
658:
652:
650:
648:
643:
641:
638: +
637:
633:
630: −
629:
625:
621:
615:
608:
604:
600:
596:
592:
588:
584:
580:
575:
571:
564:
560:
556:
552:
548:
544:
533:
530:
522:
519:February 2016
512:
508:
504:
498:
497:
493:
488:This section
486:
482:
477:
476:
470:
454:
446:
438:
434:
430:
427:
422:
419:
413:
410:
403:
389:
378:
374:
370:
367:
362:
359:
353:
350:
343:
342:
341:
339:
335:
331:
330:
324:
319:
317:
313:
309:
287:
284:
279:
276:
269:
266:
261:
258:
250:
247:
240:
239:
238:
236:
232:
229: =
228:
225:
221:
202:
194:
191:
186:
181:
178:
169:
166:
161:
156:
153:
145:
142:
135:
134:
133:
131:
120:
117:
115:
112:
109:
106:
105:
102:
99:
97:
94:
91:
88:
87:
83:
80:
77:
74:
72:
71:
68:
67:
66:
64:
60:
57:
49:
47:
45:
41:
37:
33:
29:
25:
24:
990:
965:
961:
951:
936:
934:
918:
904:
896:
890:
879:
863:
849:
841:
835:
824:
821:
805:
791:
783:
777:
766:
750:
736:
728:
722:
711:
695:
681:
673:
667:
656:
646:
644:
639:
635:
631:
627:
623:
619:
613:
606:
602:
598:
594:
590:
586:
582:
578:
576:
569:
562:
558:
554:
550:
542:
540:
525:
516:
501:Please help
489:
337:
333:
328:
322:
320:
307:
305:
234:
230:
226:
219:
217:
132:is given by
129:
127:
118:
113:
107:
100:
95:
89:
81:
75:
62:
58:
53:
27:
22:
20:
18:
995:BoekBoek.be
312:correlation
943:References
224:odds ratio
490:does not
431:−
423:−
267:−
162:−
44:quartiles
42:based on
1006:Category
653:Examples
557:= 1 and
40:skewness
982:2340126
645:Yule's
611:√
567:√
541:Yule's
511:removed
496:sources
327:Yule's
321:Yule's
306:Yule's
218:Yule's
128:Yule's
50:Formula
21:Yule's
980:
601:) by (
452:
387:
978:JSTOR
626:and (
899:= 1
844:= 1
786:= 1
767:and
731:= 1
676:= 1
585:and
547:unum
494:any
492:cite
336:and
84:= 1
61:and
970:doi
921:= 1
907:= 0
893:= 0
866:= 1
852:= 0
838:= 0
814:30
808:= 1
794:= 0
780:= 0
759:10
753:= 1
745:10
739:= 0
725:= 0
704:40
698:= 1
690:10
684:= 0
670:= 0
634:)/(
505:by
110:= 1
92:= 0
78:= 0
1008::
976:.
966:75
964:.
960:.
927:3
913:1
872:9
858:1
800:0
797:30
756:10
742:10
701:10
687:40
614:OR
605:+
597:–
589:=
581:=
574:.
570:OR
565:=
561:=
553:=
318:.
235:bc
233:/(
231:ad
227:OR
46:.
984:.
972::
937:Y
924:1
919:U
910:3
905:U
897:V
891:V
869:3
864:U
855:3
850:U
842:V
836:V
811:0
806:U
792:U
784:V
778:V
751:U
737:U
729:V
723:V
696:U
682:U
674:V
668:V
647:Y
640:b
636:a
632:b
628:a
624:Y
620:Y
607:b
603:a
599:b
595:a
591:c
587:b
583:d
579:a
563:d
559:a
555:c
551:b
543:Y
532:)
526:(
521:)
517:(
513:.
499:.
455:.
447:Q
439:2
435:Q
428:1
420:1
414:=
411:Y
390:,
379:2
375:Y
371:+
368:1
363:Y
360:2
354:=
351:Q
338:Y
334:Q
329:Q
323:Y
308:Y
288:1
285:+
280:R
277:O
270:1
262:R
259:O
251:=
248:Y
220:Y
203:.
195:c
192:b
187:+
182:d
179:a
170:c
167:b
157:d
154:a
146:=
143:Y
130:Y
119:d
114:c
108:U
101:b
96:a
90:U
82:V
76:V
63:V
59:U
23:Y
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
