ความแกร่งของสถิติทดสอบที เมื่อประชากรมีการแจกแจงไม่เป็นโค้งปกติ / สามารถ พันคง = Robustness of t-test with non-normal population distribution / Samad Phunkhong
To examine robustness of the t-test when populations violate the assumption of normality and to examine the skewness and kurtosis that keep the t-test robust. For one sample and two equal samples (n₁ = 10, 30, 60) and two unequal samples n₁ = 10, 30, 60 n₂= n₁ x 130% and n₁ x 150%, skewness = 0, 0.5, 1.0, 1.5, 2.0, 2.5 and 3.0, kurtosis = 3, 4, 5, 6 and 10, alpha = .01, .05 and .10, the Monte Carlo simulation experiment was repeated 5,000 times. The results showed that : 1)The t-test was robust against the normal distribution assumption accounting for 1,047 of 1,125 cases. 2) For all case of studies regard as. 2.1) For one population, t-test was robust when skewness = 0, 0.5 and 1.0 with 100%, 100% and 88.89%, respectively. 2.2) For two independent populations with equal sample sizes, t-test was robust when skewness = 0, 0.5, 1.0, 1.5, 2.0 and 2.5 with 100%, 100%, 100%, 100%, 88.89% and 88.89%, respectively. 2.3) For two independent populations with unequal sample sizes 30%, t-test was robust when skewness = 0, 0.5, 1.0, 1.5, 2.0 and 2.5 with 100%, 100%, 100%, 97.78%, 96.30% and 88.89%, respectively. 2.4) For two independent populations with unequal sample sizes 50%, t-test was robust when skewness = 0, 0.5, 1.0, 1.5, 2.0 and 2.5 with 100% at all. 2.5) For two dependent populations, t-test was robust when skewness = 0, 0.5, 1.0, 1.5 and 2.0 with 100%, 100%, 100%, 95.56% and 92.59%, respectively. 3) For high skewness, t-test was robust when data had high kurtosis or large sample size or high significance level.
