POWER OF TEST UNDER THE CONDITION OF DIFFERENT SAMPLE SIZES, LEVELS OF SIGNIFICANCE, AND DATA TYPES

Abstract

The objectives of this research article were to: 1) study the testing power of the t-test under sample size conditions, statistical significance level, and different types of data; and 2) to compare the test power and to study the interactions between the three conditions variables. The research was conducted by creating three datasets of 18,000 (9,000 pairs) and examining the properties of the normality distribution. All data were taken for testing at the statistical significance level of .001, .01, and .05, and the power of test was obtained from 27,000 t - tests pairs. The experimental model used in this research was a                   3 - factor factorial experimental plan. The results showed that the three data types are real data, transformed data, and data from the Monte Carlo technique; at the sample sizes of 30, 60, and 90, the power of the t-test was higher, respectively, in all statistical significance levels 001, .01, and .05. As the level of statistical significance increases, the set of test power values ​​tends to be normality distribution. Moreover, the statistical significance level, sample size, and data type had a statistically significant effect on the power of the t - test. It was found that the power of the test at the statistical significance level of .05 was the highest average. The power of the test at the sample size 60 was significantly highest. The power of the test from the Monte-Carlo technique had the highest average. There was an interaction between the sample size and the statistical significance level, interaction between the sample size and the data type, interaction between the statistical significance level and the data type, and interaction between statistically significant levels, sample size, and data type that had a statistically significant effected on the power of test.