การเปรียบเทียบสถิติทดสอบความเท่ากันของสัมประสิทธิ์การแปรผัน / อรไท พลเสน = A Comparison on test statistics for testing the equality of coefficients of variation
The objective of this research is to compare four test statistics for testing the equality of coefficients of variation for two populations by considering their ability to control probability of type I error and power of the test. The four test statistics are Modified Bennet test statistic, Likelihood Ratio test statistic, Wald test statistic, and Asymptotic test statistic. Both populations are normal distributions, gamma distributions, and Weibull distributions. Sample sizes are 10, 20, 30, 50, 70 and 100. Coefficients of variation range is [0.05, 2]. Eleven levels of ratio of coefficients of variation are given. Significance levels are 0.01, 0.05, and 0.10. For this research, Monte Carlo technique is used by repeating 8,000 times for each case. The results of this research can be summarized as follows: 1. The ability to control probability of type I error When populations have normal distributions, Modified Bennet test statistic can control the probability of type I error when coefficients of variation are in range [0.05, 0.8], Likelihood Ratio test statistic can control the probability of type I error for all levels of coefficient of variation [0.05, 2] except when sample sizes are small (n<20), Wald test statistic can control the probability of type I error when coefficients of variation are in range [0.05, 0.2], and Asymptotic test statistic can control the probability of type I error when coefficients of variation are in range [0.05, 0.6]. When populations have gamma or Weibull distributions, all of the test statistics can control the probability of type I error when population distributions close to normal distribution 2. Power of the test Power of the test of every test statistic varies according to sample size, the ratio of coefficients of variation, and significance level. Power of the test of all test statistics are nearly the same when sample size or the ratio of coefficients of variation increases. In most cases, Likelihood Ratio test statistic has highest power of the test except for the following cases: - Case of populations have normal distributions, small sample sizes (10<n<20), and significance level of 0.01. - Case of populations have gamma distributions, small sample sizes (10<n<20), coefficients of variation are in range [0.05, 0.3], and significance level of 0.01. - Case of populations have Weibull distributions, small sample sizes (10<n<20), coefficients of variation are in range [0.25, 0.3], and significance level of 0.01.
