ประสิทธิภาพของสถิติทดสอบสำหรับการเปรียบเทียบค่าเฉลี่ยภายใต้สถานการณ์ที่ความแปรปรวนระหว่างกลุ่มไม่เป็นเอกพันธ์

Abstract

The purpose of this research is to compare the efficiency of statistical tests for comparing mean under heterogeneity of variance conditions among the traditional T-test, Welch test, Browne-Forsythe test, James test, Yuen test, Alexander-Govern test, and Structural Mean Model (SMM) based statistical tests. These also included chi-square tests, which are estimated by the Maximum Likelihood method (ML), Weighted Least Squares methods (WLS), and Yuan-Bentler chi-square.The study used simulated data generated by Monte Carlo methods under the following conditions: 1) ratio of variance between two groups were equal to 1, 4, 16 and 64; 2) the mean parameters of each group, set by the magnitude of effect size , which were equal to 0, 0.2 and 0.8; 3) the sample sizes of each group were (10,10), (30,30), (50,50), (100,100), (10,30), (10,50) and (10,100) units; and 4) the significance level was chosen to be .05. The total number of simulations was 96, with 500 repetitions for each situation. The efficiency of the statistical test was based on the rate of type I errors and the statistical power of the test.

          The results revealed that 1) in cases of equal sample size and equal variance, all statistical tests tended to have the same efficiency under both homogeneity and heterogeneity of variances. However, Yuen tended to have lower statistical power than other tests and 2) in cases of unequal sample sizes and unequal variances, T statistics are likely to display lower efficiency compared to James's test, Welch's test, BF-test, and AG-test, which yield the highest efficiency values.