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• W3117354560 abstract "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 $,Ł(t_n)$." @default.
• W3117354560 created "2021-01-05" @default.
• W3117354560 creator A5051011328 @default.
• W3117354560 date "2020-12-28" @default.
• W3117354560 modified "2023-09-27" @default.
• W3117354560 title "On the T-test" @default.
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• W3117354560 hasPublicationYear "2020" @default.
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