Sequential analysis of categorical data

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Virginia Polytechnic Institute


Using a variance-stabilizing transformation of the non-centralχ² distribution and Wald's sequential probability ratio test, procedures have been developed for sequential analysis of categorical data group-wise. These procedures' enables (i) a simple hypothesis to be used for the alternative hypothesis instead of the composite hypothesis commonly used in goodness-of-fit tests, contingency tables, and Mood's non-parametric generalization of the one-way analysis of variance, (ii) calculation or a power function, and (iii) calculation of the greatest expected ASR's and the non-centrality parameter requiring this sample size in addition to the ASN's when the null or alternative hypothesis is true. Application of these procedures to the three types of analysis given in (i) give the right decisions with sample sizes near the calculated ASN’s.

The ASN's for when the expected number of groups equals one compare favorably with those obtained by Jackson (1959) using Bhate’s conjecture and those obtained empirically by Appleby (1960). In general, the sequential approach will require smaller sample sizes than fixed sampling if the non-centrality parameter is equal to or less than the group size and the group size is large enough to meet minimum expectation requirements.