## The Power of T-Test with Large Sample Size under the Different Condition of Sample Size and Significance Level between Real Data, Transformed Data, and Data from Monte Carlo Simulation Technique.

#### Natcha Mahapoonyanont, Suwichaya Putuptim

 ABSTRACT The power of the test is the probability that the test rejects the null hypothesis (H0) when a specific alternative hypothesis (H1) is true. The probability of occurrence of a type I error is modeled on medical research that tried to avoid the type I error, such as testing of new medicines, etc. The statistical significance level must be set to be as small as possible, and the probability of type II error would be considered later. In behavioral sciences and social sciences research, the researcher wants to avoid a type I error by determining the level of statistical significance. There are arguments of statistical significance that could affect the errors of the findings. Independent variables may have a real influence on the dependent variables but the researcher could not detect them because statistical significance was setting at a low level. Therefore, in some situations, more attention should be paid to the occurrence of the type II error, and less interest in the type I error. This may demonstrate more realistic and valid results. The objectives of this research were to compare the power of test on t – test under the condition of different sample size (n; 30, 60, 90), statistical significance (sig; .001, .01, .05), and type of data (real data, transformed data, simulation data (Monte Carlo Simulation Technique)). The research findings were found that the level of significance, sample size, and type of data had a statistically significant effect on the power of test of the t-test. The interaction between sample size and the level of significance had a statistically significant effect on the power of test of the t-test. The interaction between sample size and the type of data had a statistically significant effect on the power of the test of the t-test. The interaction between the level of significance and the type of data had a statistically significant effect on the power of the test of the t-test. The interaction between the level of significance, sample size, and type of data had a statistically significant effect on the power of the test of the t-test.
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