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预测变量排序抽样、过度集中的 t 统计量与协方差分析AI 解读

In this article we revisit a method of sample allocation that has long been known to statisticians and has recently been “discovered” by wood strength researchers. The method allocates experimental units to blocks on the basis of the values of a variable, x, that is known to be correlated with the response, y We call this allocation method “predictor sort sampling.” We demonstrate that the associated paired T analysis recommended in statistical texts is deficient if the…

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删失数据正态性检验相关统计量的临界值表与大样本理论AI 解读

Plotting order statistics versus some variant of the normal scores is a standard graphical technique for assessing the assumption of normality. To obtain an objective evaluation of the normal assumption, it is customary to calculate the correlation coefficient associated with this plot. The Shapiro—Francia statistic is the square of the correlation between the observed order statistics and the expected values of standard normal order statistics, whereas the Shapiro—Wilk…

若干修正 Shapiro–Wilk 统计量的渐近等价性：完整与删失样本AI 解读

The Shapiro-Wilk statistic and its modifications are widely applied in tests for normality. We establish the asymptotic equivalence of a class of statistics based on different choices of normal scores. In particular, we conclude that the Shapiro-Francia, Filliben, Weisberg-Bingham and de Wet-Venter versions of the statistic are asymptotically equivalent. Our results also apply to the Type I and Type II censored data cases.