A {\it pure significance test} (PST) tests a simple null hypothesis $H_f:Y\sim f$ {\it without specifying an alternative hypothesis} by rejecting $H_f$ for {\it small} values of $f(Y)$. When the sample space supports a proper uniform pmf $f_\mathrm{unif}$, the PST can be viewed as a classical likelihood ratio test for testing $H_f$ against this uniform alternative. Under this interpretation, standard test features such as power, Kullback-Leibler divergence, and expected $p$-value can be considered. This report focuses on PSTs for multinomial and binomial distributions, and for the related goodness-of-fit testing problems with the uniform alternative. The case of repeated observations cannot be reduced to the single observation case via sufficiency. The {\it ordered binomial distribution}, apparently new, arises in the course of this study.

翻译：纯显著性检验（PST）在未指定备择假设的情况下，通过拒绝小值f(Y)来检验简单零假设$H_f:Y\sim f$。当样本空间支持适当的均匀概率质量函数$f_\mathrm{unif}$时，PST可视为针对该均匀备择假设检验$H_f$的经典似然比检验。在此解释下，可考虑检验功效、KL散度和期望p值等标准检验特征。本报告重点研究多项分布与二项分布的PST，以及均匀备择假设下的相关拟合优度检验问题。重复观测情形无法通过充分性简化为单次观测情形。本研究中新发现的序贯二项分布，具有明显的创新性。