Computational Ecology and Software (Dec 2022)
Dilemma of t-tests: Retaining or discarding choice and solutions
Abstract
The t-test theory has laid the foundation of modern statistics and it is one of the main contents of statistics. This theory can be found in all statistics textbooks and is at the core of almost all applied statistics courses. At the same time, almost all statistical software or tools have t-test content, such as Matlab, SAS, SPSS, R, etc. However, t-test theory has been widely criticized in recent years due to its theoretical flaws and misuse. The t-test is only used for the problems of normal distribution population with small sample size. Even so, its sample size cannot be too small due to problems such as t-transformation distortion. In terms of significance test, the t-test has the general defects of statistical significance tests, coupled with the inherent fallacies of confidence intervals, and the peculiar uncertainty problems of t-intervals, make the t-test methodology obviously insufficient. The t-test theory is faced with the retaining or discarding decision in statistics, and some statisticians have advocated and abolished the t-test theory from statistics textbooks. As a statistical significance test, the solutions of t-tests include using Bayesian methods, performing meta-analyses, using effect sizes, stressing statistical validity, using nonparametric statistics, using good experimental and sampling designs and determining appropriate sample size, the network methods are used instead of the reductionist method to obtain and analyze the data, and the statistical conclusions are combined with the mechanism analysis to draw scientific inferences, etc. As a t-interval uncertainty problem, its solutions include using the Bayesian credible interval method, using the Bootstrap credible interval method, inferring directly from the central limit theorem, using the unified theory of uncertainty, etc.
