Budanmış Ortalamalar için Karşılaştırma Testleri

Abstract

Statistical significance tests, such as Student’s t test, ANOVA-F test, are widely used in many disciplines, including medicine, psychology, and biology. For these tests to exact control over the rate of a Type I error, normality and homoscedasticity must be satisfied. Type I error and power rates are adversely affected when these assumptions are violated. These problems are greatly reduced when using trimmed mean that is a robust measure of location. Also, the results could be improved by combining bootstrap methods with the tests based on trimmed means.

In this study, the tests for mean and trimmed mean equality were compared in terms of Type I Error probability in the case of dependent and independent groups. In comparison of independent groups Student's t test, Welch test, Yuen test, Yuen test with bootstrap-t, ANOVA-F test, Welch test with trimmed mean, Welch test with trimmed mean and bootstrap-t were used. In comparison of dependent groups paired sample t test, Yuen test, Huynh-Feldt(ϵ ̃ )-adjusted ANOVA-F test, ϵ ̃-adjusted ANOVA-F test with trimmed mean, ANOVA-F test with bootstrap-t, ANOVA-F test with trimmed mean and bootstrap-t were used. According to results of simulation study, within the context of independent groups designs, to avoid the problems of assumption violation, in the case of two independent groups, the recommended tests are Yuen test and Yuen test with bootstrap-t, while in the case of k independent groups Welch test with trimmed mean is recommended. Within the context of dependent groups designs, in the case of two dependent groups, the suggested test is Yuen test for skew-heavy tailed distribution, on the other hand, in the case of k dependent groups, ANOVA-F test with trimmed mean and bootstrap-t is recommended.

It is considered that this study will contribute to the literature in terms of including independent group comparison as well as dependent group comparison.