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计数数据的趋势检验：多项分布情形AI 解读

Given k multinomial probabilities pi (Σ pi = 1), let pi be a known continuous function f (wi, πi ) of a known weight constant wi and an unknown constant π i . The function f is assumed strictly monotone in π. The maximin statistic for testing the homogeneity of the π i 's versus a trend in the π i 's is derived. The Armitage statistic for testing linear trend is maximin for a certain alternative hypothesis space. The methods are applied to lying habit data (Maxwell 1961),…

计数数据的趋势检验：多项分布情形AI 解读

Given k multinomial probabilities pi (Σ pi = 1), let pi be a known continuous function f (wi, πi ) of a known weight constant wi and an unknown constant π i . The function f is assumed strictly monotone in π. The maximin statistic for testing the homogeneity of the π i 's versus a trend in the π i 's is derived. The Armitage statistic for testing linear trend is maximin for a certain alternative hypothesis space. The methods are applied to lying habit data (Maxwell 1961),…

随机排序约束下的无分布检验AI 解读

A two-sample distribution-free procedure is proposed for testing equal locations under a stochastic ordering restriction. The test statistic M is an estimator of P(X ≤ Y) based upon maximum likelihood estimators of stochastically ordered distribution functions. Some properties of the M test are developed and critical values are provided for selected sample sizes. A Monte Carlo power study indicates that the M test is more effective (for shift alternatives) than the…