Comparison of the performances of parametric k-sample test procedures as an alternative to one-way analysis of variance

Year 2023, Volume: 9 Issue: 1, 39 - 48, 04.01.2023

Gökhan Ocakoğlu , Aslı Ceren Macunluoglu

https://doi.org/10.18621/eurj.1030038

Abstract

Objectives: The performances of the Welch test, the Alexander-Govern test, the Brown-Forsythe test and the James Second-Order test, which are among the parametric alternatives of one-way analysis of variance and included in the literature, to protect the Type-I error probability determined at the beginning of the trial at a nominal level, were compared with the F test.

Methods: Performance of the tests to protect Type-I error; in cases where the variances are homogeneous and heterogeneous, the sample sizes are balanced and unbalanced, the distribution of the data is in accordance with the normal distribution and the log-normal distribution, how it is affected by the change in the number of groups to be compared has been examined on simulation scenarios.

Results: The Welch test, the Alexander-Govern test and the James Second-Order test were not affected by the distribution and performed well in situations where variances were heterogeneous. The Brown-Forsythe test was not affected by the distribution, it performed well when the variance was homogeneous and the sample size in the groups to be compared was not equal.

Conclusions: The Welch test, the Alexander-Govern test and the James Second-Order test are the tests that can be recommended as an alternative to the F test.

Keywords

Analysis of variance, conformity of normal distribution, parametric k-sample tests

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