20:
663:, revealed that in the actual experiment the lady succeeded in identifying all eight cups correctly. The chance of someone who just guesses of getting all correct, assuming she guesses that any four had the tea put in first and the other four the milk, would be only 1 in 70 (the combinations of 8 taken 4 at a time).
450:
indicating an incorrect cup which is chosen). Thus a selection of any one correct cup and any three incorrect cups can occur in any of 4×4 = 16 ways. The frequencies of the other possible numbers of successes are calculated correspondingly. Thus the number of successes is distributed according to the
28:
644:
The critical region for rejection of the null of no ability to distinguish was the single case of 4 successes of 4 possible, based on the conventional probability criterion < 5%. This is the critical region because under the null of no ability to distinguish, 4 successes has 1 chance out of
343:
The frequencies of the possible numbers of successes, given in the final column of this table, are derived as follows. For 0 successes, there is clearly only one set of four choices (namely, choosing all four incorrect cups) giving this result. For one success and three failures, there are four
94:
The experiment provides a subject with eight randomly ordered cups of tea – four prepared by pouring milk and then tea, four by pouring tea and then milk. The subject attempts to select the four cups prepared by one method or the other, and may compare cups directly against each other as
652:
the lady properly categorized all 8 cups was Fisher willing to reject the null hypothesis – effectively acknowledging the lady's ability at a 1.4% significance level (but without quantifying her ability). Fisher later discussed the benefits of more trials and repeated tests.
79:. Her future husband, William Roach, suggested that Fisher give her eight cups, four of each variety, in random order. One could then ask what the probability was for her getting the specific number of cups she identified correct (in fact all eight), but just by chance.
541:
257:
113:
The test statistic is a simple count of the number of successful attempts to select the four cups prepared by a given method. The distribution of possible numbers of successes, assuming the
82:
Fisher's description is less than 10 pages in length and is notable for its simplicity and completeness regarding terminology, calculations and design of the experiment. The test used was
779:
ii. 19, "We may speak of this hypothesis as the 'null hypothesis' the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation."
753:
751:
440:
387:
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171:
145:
601:
581:
561:
473:
790:
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397:
denoting a correct cup that is not chosen); and independently of that, there are four incorrect cups of which three are selected, which can occur in
176:
826:
478:
736:
1033:
645:
70 (≈ 1.4% < 5%) of occurring, whereas at least 3 of 4 successes has a probability of (16+1)/70 (≈ 24.3% > 5%).
838:
760:, Chapter II. The Principles of Experimentation, Illustrated by a Psycho-physical Experiment, Section 8. The Null Hypothesis.
23:
The experiment asked whether a taster could tell if the milk was added before the brewed tea, when preparing a cup of tea.
1012:
992:
912:
875:
76:
797:
1028:
979:. Institute of Mathematical Statistics Lecture Notes - Monograph Series. Hayward, CA.: IMS. pp. 13–31.
1038:
452:
65:, which is "never proved or established, but is possibly disproved, in the course of experimentation".
775:
57:
400:
347:
107:
699:" was "one of the two supporting pillars ... of the randomization analysis of experimental data."
1043:
103:
102:
is that the subject has no ability to distinguish the teas. In Fisher's approach, there was no
83:
723:
48:
36:
958:
Statistical
Information and Likelihood : A Collection of Critical Essays by Dr. D. Basu
1003:
683:
8:
961:
618:
615:
th row of Pascal's triangle, such that each integer in the row is squared. In this case,
150:
124:
942:
925:(1980a). "Randomization Analysis of Experimental Data: The Fisher Randomization Test".
718:
586:
566:
546:
458:
1008:
988:
908:
871:
834:
745:, II. The Principles of Experimentation, Illustrated by a Psycho-physical Experiment.
713:
344:
correct cups of which one is selected, which by the combination formula can occur in
1004:
The Lady
Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century
980:
968:
934:
708:
583:
is the number of success states in the population or four cups of either type, and
68:
The example is loosely based on an event in Fisher's life. The woman in question,
972:
603:
is the number of draws, or four cups. The distribution of combinations for making
95:
desired. The method employed in the experiment is fully disclosed to the subject.
678:
114:
99:
62:
953:
922:
674:
656:
649:
72:
984:
1022:
900:
822:
688:
52:
956:(1980b). "The Fisher Randomization Test", reprinted with a new preface in
61:(1935). The experiment is the original exposition of Fisher's notion of a
118:
69:
946:
40:
117:
is true, can be computed using the number of combinations. Using the
27:
977:
Current Issues in
Statistical Inference – Essays in Honor of D. Basu
938:
692:
536:{\displaystyle X\sim \operatorname {Hypergeometric} (N=8,K=4,n=4)}
19:
641:
because 4 teacups are selected from the 8 available teacups.
446:
interpreted as an incorrect cup which is not chosen, and
252:{\displaystyle {\binom {8}{4}}={\frac {8!}{4!(8-4)!}}=70}
973:"Intervention experiments, randomization and inference"
563:
is the population size or total number of cups of tea,
403:
350:
263:
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589:
569:
549:
481:
461:
179:
153:
127:
695:
wrote that "the famous case of the 'lady tasting tea
442:
ways (as shown in the second column, this time with
77:
whether the tea or the milk was added first to a cup
687:, which describes Fisher's experiment and ideas on
633:
595:
575:
555:
535:
467:
434:
381:
251:
165:
139:
196:
183:
1020:
927:Journal of the American Statistical Association
475:equal to the number of successes, we may write
975:. In Malay Ghosh and Pramod K. Pathak (ed.).
782:
420:
407:
367:
354:
666:
389:different ways (as shown in column 2, with
967:
393:denoting a correct cup that is chosen and
611:available selections corresponds to the
26:
18:
852:
850:
1021:
899:
821:
788:
757:
742:
455:. Specifically, for a random variable
921:
815:
333:
868:R.A. Fisher, The Life of a Scientist
847:
659:reports that a colleague of Fisher,
865:
827:"Mathematics of a Lady Tasting Tea"
13:
831:The World of Mathematics, volume 3
763:
411:
358:
304:ooxx, oxox, oxxo, xoxo, xxoo, xoox
187:
14:
1055:
89:
870:. New York: Wiley. p. 134.
1034:Statistical hypothesis testing
884:
859:
833:. Courier Dover Publications.
530:
494:
435:{\textstyle {\binom {4}{3}}=4}
382:{\textstyle {\binom {4}{1}}=4}
234:
222:
1:
829:. In James Roy Newman (ed.).
729:
75:, claimed to be able to tell
16:Famous randomized experiment
7:
1007:, W.H. Freeman / Owl Book.
907:(9th ed.). Macmillan.
890:Basu (1980a, p. 575; 1980b)
702:
453:hypergeometric distribution
10:
1060:
271:Combinations of selection
905:The Design of Experiments
866:Box, Joan Fisher (1978).
776:The Design of Experiments
273:
270:
267:
58:The Design of Experiments
55:and reported in his book
964:, editor. Springer 1988.
985:10.1214/lnms/1215458836
274:Number of Combinations
259:possible combinations.
173:cups chosen, there are
108:Neyman–Pearson approach
635:
607:selections out of the
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577:
557:
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469:
436:
383:
315:oxxx, xoxx, xxox, xxxo
293:ooox, ooxo, oxoo, xooo
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104:alternative hypothesis
32:
24:
1029:Design of experiments
823:Fisher, Sir Ronald A.
724:Binomial distribution
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598:
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49:randomized experiment
37:design of experiments
31:Ronald Fisher in 1913
30:
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1001:Salsburg, D. (2002)
684:The Lady Tasting Tea
668:The Lady Tasting Tea
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1039:Science experiments
634:{\displaystyle k=4}
264:
166:{\displaystyle k=4}
140:{\displaystyle n=8}
84:Fisher's exact test
791:"Lady Tasting Tea"
719:Randomization test
661:H. Fairfield Smith
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33:
25:
969:Kempthorne, Oscar
901:Fisher, Ronald A.
840:978-0-486-41151-4
789:Sturdivant, Rod.
714:Random assignment
596:{\displaystyle n}
576:{\displaystyle K}
556:{\displaystyle N}
468:{\displaystyle X}
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998:
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933:(371): 575–582.
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796:. Archived from
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709:Permutation test
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106:, unlike in the
45:lady tasting tea
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803:on 10 July 2004
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115:null hypothesis
100:null hypothesis
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63:null hypothesis
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773:R. A. Fisher,
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681:book entitled
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657:David Salsburg
650:if and only if
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268:Success count
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121:formula, with
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90:The experiment
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73:Muriel Bristol
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9:
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4:
3:
2:
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1044:Ronald Fisher
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1013:0-8050-7134-2
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994:0-940600-24-2
990:
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978:
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914:0-02-844690-9
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877:0-471-09300-9
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689:randomization
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53:Ronald Fisher
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38:
29:
21:
1002:
976:
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926:
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817:
805:. Retrieved
798:the original
784:
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677:published a
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112:
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93:
81:
67:
56:
44:
34:
962:J. K. Ghosh
807:2 September
769:OED quote:
758:Fisher 1971
743:Fisher 1971
318:4 × 4 = 16
307:6 × 6 = 36
296:4 × 4 = 16
119:combination
70:phycologist
51:devised by
1023:Categories
730:References
329:1 × 1 = 1
285:1 × 1 = 1
41:statistics
903:(1971) .
825:(1956) .
492:
486:∼
229:−
971:(1992).
954:Basu, D.
923:Basu, D.
703:See also
693:Deb Basu
543:, where
947:2287648
35:In the
1011:
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945:
911:
874:
837:
648:Thus,
334:Total
43:, the
943:JSTOR
801:(PDF)
794:(PDF)
47:is a
1009:ISBN
989:ISBN
909:ISBN
872:ISBN
835:ISBN
809:2018
771:1935
670:book
326:xxxx
282:oooo
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981:doi
935:doi
337:70
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