论文标题
在t检验上
On the T-test
论文作者
论文摘要
$ t $检验可能是最受欢迎的统计测试。教科书通常建议它。测试的适用性取决于正常或学生近似对学生统计$ \，T_N $的分配的有效性。但是，后一个假设的有效期不如假设。我们表明，即使在类$ \，{\ cal p} _n \ $中，正常或学生对$ \，$也不均匀地保持$，$也不均匀地保持。我们向相应的误差提出下限。非参数测试不适用于类$ \，{\ cal p} _n \的样本，这一事实似乎是第一次建立。这意味着$ t $ - 检验可能会产生误导，不应以目前的形式推荐。我们建议对测试的概括，以使可能的限制/近似分布变异到$ \，（t_n）$。
The $T$-test is probably the most popular statistical test; it is routinely recommended by the textbooks. The applicability of the test relies upon the validity of normal or Student's approximation to the distribution of Student's statistic $\,t_n$. However, the latter assumption is not valid as often as assumed. We show that normal or Student's approximation to $\,Ł(t_n)\,$ does not hold uniformly even in the class $\,{\cal P}_n\,$ of samples from zero-mean unit-variance bounded distributions. We present lower bounds to the corresponding error. The fact that a non-parametric test is not applicable uniformly to samples from the class $\,{\cal P}_n\,$ seems to be established for the first time. It means the $T$-test can be misleading, and should not be recommended in its present form. We suggest a generalisation of the test that allows for variability of possible limiting/approximating distributions to $\,Ł(t_n)$.
