การเปรียบเทียบอำนาจการทดสอบของตัวสถิติ ที่ใช้ในการทดสอบการแจกแจงปกติหลายตัวแปร / จรรยา เกศเกษมกุล = A comparison of power of some standard goodness-of-fit test of multinormality / Junya Kaskasamkul
The objective of this research is to compare power of the test for test of multinormality. The test statistics are MK test, N test and KTT test. Underlying distribution are multivariate normal distribution, multivariate lognormal distribution, multivariate student-t distribution and multivariate chi-square distribution with various parameters. Number of variable are 2 and 3. Sample sizes are 20, 30, 40, 50, 60, 70, 80, 90, 100. The data of the experimental were obtained through the Monte Carlo simulation technique. It was used to calculate the probability type - I error and power of the test. The experiment was repeat 2,000 times under each condition at five percent and ten percent significant level. The result of this research can be summarized as follows : 1. Probability of type - 1 error : All of 3 test statistics could control probability of type - 1 error in all case. 2. Power of the test : Case of two variables N test has the highest power of the test when - the correlation (p12) equal to 0.1 - 0.3 and sample sizes are 20 - 39. - the correlation equal to 0.4 - 0.9 and sample sizes are 20 - 29. MK test has the highest power of the test when - the correlation (p12) equal 0.1 - 0.3 and sample sizes are 40 - 100. - the correlation equal to 0.4 - 0.9 and sample sizes are 30 - 100. 3. Power of the test : Case of three variables N test has the highest power of the test when - the correlation (P12, P13, P23) equal to (0.1-0.3, 0.1-0.3, 0.1-0.3) and sample sizes are 20- 39. - the correlation equal to (0.1-0.6, 0.1-0.6, 0.4-0.9) and sample sizes are 20 -29. MK test has the highest power of the test when - the correlation (P12, P13, P23) equal to (0 1-0.3, 0.1-0.3, 0.1-0.3) and sample sizes are 40- 100. - the correlation equal to (0.1-0.6, 0.1-0.6, 0.4-0.9) and sample size are 3 0 - 100. - the correlation equal to (0.7-0.9, 0.7-0.9, 0.7-0.9) all of sample sizes.
