A Computer Program for Fisher's Exact Probability Test

Abstract

The Fisher test is concerned with data of independent groups and a dichotomous criterion in a fourfold (2 × 2) contingency format. Typically, small samples ( N ≤ 30) are considered. Some tables of critical values of Fisher's test for small samples are available to offset the tediousness of computation. Fisher's test requires determination of a combined probability, that is, the observed set added with all the more extreme (directional) sets. For large samples, an approximation method such as chi square is used. Considered in this paper are a mathematical discussion and algorithm, and a computer program for Fisher's test. The computer program for small and large ( N of about 500) samples is available from the authors. Such technology, in most instances, makes approximation methods unnecessary.

Intra‐oral gingival massage activates human cerebral prefrontal cortex and enhances cognitive performance

“…10,29 Therefore, to clarify the effect of gingival massage on participants' performance in the Stroop cognitive test, we analyzed change ratios of the number of correct answers (%) and oxy-Hb-AUC 60s in the Stroop test for 60 s using the Wilcoxon signed rank method in the gingival massage and control experiments as described previously. 12 Furthermore, to investigate the association of left DL-PFC region activation with cognitive performance, a contingency table for Fisher's exact probability test [30][31][32] was prepared. Conventional correlation analyses were not suitable for our data, as both the number of correct answers in the Stroop cognitive test and the oxy-Hb-AUC 60s entailed substantial individual-level differences.…”

“…A subtraction procedure to emphasize Stroop cognitive performance could have further jeopardized the quantification of each parameter 10,29 . Therefore, we performed Fisher's exact probability test as a robust nonparametric statistical method for determining the significance of a difference for independent groups with discrete data 30–32 . For that, we used the relationship between the change in the number of correct answers and the changes in oxy‐Hb‐AUC 60s in the left DL‐PFC during the Stroop cognitive test in the gingival massage and control experiments.…”

“…Furthermore, to investigate the association of left DL‐PFC region activation with cognitive performance, a contingency table for Fisher's exact probability test 30–32 was prepared. Conventional correlation analyses were not suitable for our data, as both the number of correct answers in the Stroop cognitive test and the oxy‐Hb‐AUC 60s entailed substantial individual‐level differences.…”

Permutation methods

“…While computer algorithms to generate permutation sequences were important, other researchers turned their attention to computing exact probability values for known statistics. Gregory80 and Tritchler and Pedrini,81 for example, confined their applications to the Fisher exact test for 2 × 2 contingency tables, while Agresti and Wackerly,82 Agresti et al,83 Fleishman,84 Howell and Gordon,85 and March86 attempted to extend the Fisher hypergeometric procedure to larger r × c contingency tables, and others applied permutation procedures to, for example, the Pitman test for two independent samples,87 the F test for completely randomized designs,88 the F test for randomized block designs,89 the chi‐squared test for goodness‐of‐fit,90 the Kruskal–Wallis test for ranks,91 and alternative choices of rank scores 92,93. In addition, Edgington provided permutation procedures and examples for an extensive inventory of statistical tests in 1969 (Ref 94, pp.…”

A Program for Computing Fisher's Exact Probability Test and the Coefficient of Association λ for n × m Contingency Tables

“…EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT 1977, 37, 253-256. As noted by Tritchler and Pedrini (1975), Fisher's exact test provides a technique for determining &dquo;the significance of a difference between two independent samples or groups for which the scores fall into two mutually exclusive classes&dquo; (p. 717). Although this statement is correct, it is somewhat misleading in that Fisher's exact test may be extended to larger (greater than 2 X 2) contingency tables.…”