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There are two common methods for statistical inference on 2 × 2 contingency tables. One is the widely taught Pearson chi-square test, which uses the well-known χ2statistic. The chi-square test is appropriate for large sample inference, and it is equivalent to the Z-test that uses the difference between the two sample proportions for the 2 × 2 case. Another method is Fisher's exact test, which evaluates the likelihood of each table with the same marginal totals. This article mathematically justifies that these two methods for determining extreme do not completely agree with each other. Our analysis obtains one-sided and two-sided conditions under which a disagreement in determining extreme between the two tests could occur. We also address the question whether or not their discrepancy in determining extreme would make them draw different conclusions when testing homogeneity or independence. Our examination of the two tests casts light on which test should be trusted when the two tests draw different conclusions. [ABSTRACT FROM AUTHOR]

This article presents a simple example that illustrates the key differences and similarities between the Fisherian, Neyman-Pearson, and Bayesian approaches to testing. Implications for more complex situations are also discussed. [ABSTRACT FROM AUTHOR]

Presents the Fisher exact test for unweighted means in a 2[sup k] experiment. Hypothesis testing using linear models; Analysis of variance; Methods in the determination of unweighted mass.

Presents correspondence concerning statistics and statistical methods. Rationale behind the use of transformations in data analysis; Effect of extrapolation to large estimation error; Feasibility of the Fisher exact test.

Presents a practical computer program for the Fisher randomization tests of location. Description and features of the computer program; Disadvantages of randomization tests; Use of heuristics and computing algorithms in the program.

Demonstrates the necessary and sufficient condition for the Fisher information matrix of a causal and invertible ARMA to be nonsingular which is also extended to fractional ARIMA models. Information on ARMA and ARIMA time series models; Nonsingularity of Fisher information; Operator notation of ARMA model.