การเปรียบเทียบประสิทธิภาพของตัวสถิติทดสอบสำหรับการทดสอบ ความแตกต่างของค่าเฉลี่ยระหว่างประชากร 2 กลุ่มที่อิสระกัน

The objectives of this study were to calculate the probability of type I error power of a test and to compare the performance of three test statistics: Z Student’s t and Welch’s t. Including the recommending the appropriate test statistic. Classification of the population according to five distribution. The ratios of mean group 1 per group 2 were three levels. The ratios of variance group 1 per group 2 were three levels. The sample sizes of two populations were nine sizes. The significance levels that to study were 0.01 and 0.05. The data were simulated by using SAS programming with 1000 replicates. Results of the research were Z test statistic could control the probability of type I error and had higher power of a test than other test statistics but this test is necessary to know the variances of the two groups. Therefore it was appropriate to apply the other test statistics i.e. Student’s t or Welch’s t. If the variances of the two groups were equal Student’s t was a more appropriate test statistic than Welch’s t. But if the variances of the two groups were not equal Welch’s t was a more appropriate. When both sample sizes were large and the population variances were equal we could use any tests since there is no difference in the performance.