By Cyrus R. Mehta and Nitin R. Patel
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Additional info for SPSS Exact Tests 7.0 for Windows
Sample text
The width of the confidence interval can be made arbitrarily small, by sampling more tables from the reference set. 4. In principle, you could narrow the width of the confidence interval to such an extent that the Monte Carlo p value becomes indistinguishable from the exact p value up to say the first three decimal places. For all practical purposes, you could then claim to have the exact p value. Of course, this might take a few hours to accomplish. 5. In practice, you don’t need to go quite so far.
00 Test Prop. 05 Exact Sig. 05 is rejected at the 5% significance level. One-Sample Inference for Binary Data 51 Runs Test Consider a sequence of N binary outcomes, (y i,y 2, …y N) , where each y i is either a 0 or a 1. A run is defined as a succession of identical numbers that are followed and preceded by a different number, or no number at all. For example, the sequence (1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1) begins with a run of two 1’s. A run of three 0’s follows, and next a run of one 1.
For the 2 × 2 table, Fisher noted that under the null hypothesis of independence, if you assume fixed marginal frequencies for both the row and column marginals, then the hypergeometric distribution characterizes the distribution of the four cell counts in the 2 × 2 table. This fact enables you to calculate an exact p value rather than rely on an asymptotic justification. Let the generic four-fold table, { x ij } , take the form x 11 x 21 x 12 x 22 xm 1 m2 n1 n2 N with ( x 11, x 12, x 21, x 22 ) being the four cell counts; m 1 and m 2 , the row totals; n 1 and n 2 , the column totals; and N , the table total.