Abstract
ABSTRACTIn an informal way, some dilemmas in connection with hypothesis testing in contingency tables are discussed. The body of the article concerns the numerical evaluation of Cochran's Rule about the minimum expected value in r × c contingency tables with fixed margins when testing independence with Pearson's X2 statistic using the χ2 distribution.
Highlights
This article uses an example to challenge statisticians, in an informal way, to reflect on their belief in statistics and to ask themselves whether they practice what they preach. This example serves as an introduction to a numerical investigation into the quality of Cochran’s well-known rule of thumb about the minimum expected value needed for using the χ 2 distribution as an adequate approximation to that of Pearson’s X2 statistic when testing independence in a contingency table
As indicated above, we look only at conditional tests with fixed margins
A general point is that programs with exact tests are not too time-consuming
Summary
This article uses an example to challenge statisticians, in an informal way, to reflect on their belief in statistics and to ask themselves whether they practice what they preach. This example serves as an introduction to a numerical investigation into the quality of Cochran’s well-known rule of thumb about the minimum expected value needed for using the χ 2 distribution as an adequate approximation to that of Pearson’s X2 statistic when testing independence in a contingency table. The article will conclude with some advice on what to do if a contingency table has many expected values smaller than 5
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