The aim of this article is to show that the $T$-test can be misleading. We argue that normal or Student’s approximation to the distribution $\mathcal{L}\left(t_n\right)$ of Student’s statistic $t_n$ does not hold uniformly over the class ${\mathcal{P}}_n$ of samples $\{X_1,\dots ,X_n\}$ from zero-mean unit-variance bounded distributions. We present lower bounds to the corresponding error.

We suggest a generalisation of the $T$-test that allows for variability of possible approximating distributions to $\mathcal{L}\left(t_n\right)$.

中文翻译：

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在 T 检验上

本文的目的是表明$吨$-test 可能会产生误导。我们认为正态或学生对分布的近似$\mathcal{大号}\left({吨}_n\right)$学生统计${吨}_n$不统一地控制班级${\mathcal{磷}}_n$样品数$\{X_1,\dots ,X_n\}$从零均值单位方差有界分布。我们给出了相应误差的下限。

我们建议对$吨$-测试允许可能的近似分布的可变性$\mathcal{大号}\left({吨}_n\right)$.