Abstract
The study highlighted three essential roles of retrospective analysis in hypothesis testing, particularly as a priori analysis, post hoc analysis, and sensitivity analysis. These approaches were applied to the Gini ratio data sourced from the National Socioeconomic Survey Indonesia 2023 to examine the income inequality level in Indonesia. The sample size, statistical power, and effect size for the one-sample t-test are evaluated by aid G*Power software. The test results show that for a sample size of 10, at the 95% confidence interval, there is not enough evidence to show that the Gini ratio in 2023 is smaller than 0.4. A retrospective analysis using G*power software reveals that for a sample size of 20 at the same confidence interval, there is enough evidence to suggest that the Gini ratio is statistically significant at less than 0.4 with a power of analysis of 90.8% and an effect size of 0.76. This study has important implications in hypothesis testing, especially in retrospective analysis, since understanding the effect of sample size and effect size makes it possible for academics or practitioners to optimize hypothesis testing and generate more accurate and reliable test results.
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