順序カテゴリーデータにおける2標本検定 : 検出力に関する若干の考察

概要

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Several methods have been proposed to test equality of two population distributions when responses are obtained as ordered categories. Among these , four tests, that is, conditional Wilcoxon test (W), normal test based on preassigned scores (T), cumulative chi-square test (Q) and ordinal chi-square test (X^2) are investigated from the following aspects. (1) Large sample approximating distributions and power formulas are obtained. Limiting distributions and limiting power formulas in Pitman's sense are also derived. (2) Powers of the tests against some families of hypotheses are compared based on the model with successive categories on underlying continuum. W has higher powers than Q against the location shift alternatives in normal distributions. In the case of scale shift alternatives in exponential distribution, Q gives higher powers than W for some cases. and conversely W is more superior to Q for another, depending on the form of class alternatives. (3) For the cumulative chi-square test, we have numerically investigated actual limiting sizes of the two and three moment chi-square approximating tests. (4) For the T test, some meaning of equi-spaced scores is considered through optimal scores.
社団法人日本品質管理学会の論文
1980-07-15