The P-P Plot as a Method for Comparing Treatment Effects
本文研究了概率-概率图（p-p图）在比较处理效应中的应用，通过实例对比分位数-分位数图（q-q图），发现p-p图能进行尺度不变比较、不受异常值干扰，并包含对照组分布信息，理论证明其是最大不变统计量。
Abstract This article examines the use of the probability-probability plot (p-p plot) as a method for comparing treatment effects. To begin in the context of three examples the p-p plot is contrasted with the quantile-quantile plot (q-q plot), which is an alternative means of describing treatment effects. In these examples it is shown that p-p plots representing different experimental conditions or patient populations allow scale-invariant comparisons of treatment effects but q-q plots do not; that the presentation of the treatment effect by the p-p plot is not obscured by outliers, whereas it may be in the q-q plot; and that the p-p plot encompasses information in the control distributions that is important for the assessment of treatment effects but that is not incorporated in the q-q plot. Theoretical considerations are presented that show that under appropriate assumptions, the p-p plot is a maximal invariant and contains all the information necessary to make scale-invariant comparisons of treatment effects. Further, statistical methods for assessing patterns observed in the p-p plots are presented and illustrated in two examples.