Exact Test Fishers Statistics Exact Tests Favorable Test
Exact Test Fisher’s Statistics
Exact Tests Favorable Test Control Total ►A 10 2 12 Unfavorable 2 4 6 Total 12 6 18 test treatment and a control are compared to determine whether the rates of favorable response are the same. ► The sample sizes requirements for the chi-square tests are not met by these data
► if you can consider the margins (12, 6, 12, 6) to be fixed, then you can assume that the data are distributed hypergeometrically and write ► Pr(nij) = n 1+!n 2+!n+1!n+2!/n!n 11!n 12!n 21!n 22! ► p-value is the probability of the observed data or more extreme data occurring under the null hypothesis ► With Fisher’s exact test, determine the p-value for this table by summing the probabilities of the tables that are as likely or less likely, given the fixed margins.
The following table includes all possible table configurations and their associated probabilities. Table Cell ► (1, 1) (1, 2) (2, 1) (2, 2) Probabilities --------------------------------------► 12 0 0 6 0. 0001 ► 11 1 1 5 0. 0039 --------------------------------------► 10 2 2 4 0. 0533 --------------------------------------► 9 3 3 3 0. 2370 ► 8 4 4 2 0. 4000 ► 7 5 5 1 0. 2560 ► 6 6 6 0 0. 0498 To find the one-sided p-value, you sum the probabilities as small or smaller than those computed for the table observed, in the direction specified by the one-sided alternative. In this case, it would be those tables in which the Test treatment had the more favorable response, or p = 0. 0533 + 0. 0039 + 0. 0001 = 0. 0573
find the two-sided p-value, you sum all of the probabilities that are as small or smaller than that observed, or ► p = 0. 0533 + 0. 0039 + 0. 0001 + 0. 0498 = 0. 1071 ► To
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