On the T-test

Novak, Serguei ORCID: https://orcid.org/0000-0001-7929-7641 (2022) On the T-test. Statistics & Probability Letters, 189 , 109562. ISSN 0167-7152 [Article] (doi:10.1016/j.spl.2022.109562)

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Official URL: https://doi.org/10.1016/j.spl.2022.109562

Abstract

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 L(tn) of Student's statistic tn does not hold uniformly over the class Pn of samples fX1; :::;Xng 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 L(tn).

Item Type:	Article
Sustainable Development Goals:	Goal 9: Industry, Innovation, and Infrastructure
Theme:	Other
Keywords (uncontrolled):	Hypothesis testing, T-test, Student’s statistic
Research Areas:	A. > School of Science and Technology
Item ID:	36843
Notes on copyright:	Accepted manuscript: Copyright © 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
Useful Links:	Publisher's T&Cs
Depositing User:	Serguei Novak
Date Deposited:	28 Nov 2022 10:33
Last Modified:	07 Dec 2022 14:05
URI:	https://eprints.mdx.ac.uk/id/eprint/36843

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