A comparative study of computation approaches of the generalized F-test

Abstract

The Generalized F-test is derived based on the Generalized P-value Method to test the equality of normally distributed group means under unequal variances. There are two approaches to compute the p-value of the GF test, based on beta and chi-squared random numbers. From prior art in the literature, it appears that the two computation approaches of the Generalized tests are equivalent. In this study, the equivalence of these approaches is investigated in an extensive Monte-Carlo simulation study in terms of Type I error probability and penalized power. It is found that the equivalence of the computation approaches is not quite correct and that there is a difference between their conclusion, and researchers should decide which one is powerful than the others according to the structure of data, such as sample size, and the number of groups. Also, real data examples are given to show the opposite decisions of the computation approaches.

Keywords:

• Generalized F-test
• chi-square distribution
• beta distribution
• penalized power

2010 Mathematics Subject Classification:

• 62K05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This study is supported by the Eskisehir Technical University Scientific Research Projects Commission under grant No. 19ADP049.