The Study on Reasonability of Retrospective Power

There is an increasingly concern with the use of retrospective power. Some researchers suggested calculating the retrospective power after conducting hypothesis testing, particularly in meta-analysis. They considered that retrospective power can be used to determine whether the sample size is sufficient in an experiment and that the combination of retrospective power and prior power can enhance the power of current and future studies. Furthermore, the commonly used statistical software packages, such as SPSS and SAS, provide retrospective power analysis in some modules. However, some pointed out the abuse of retrospective power. In this study, we used Monte Carlo technique to estimate the retrospective power in t-test and ANOVA to address this issue. We found that four styles of retrospective powers, including observed power, plug-in power, unbiased power and median power, are highly positive correlated. They dispersed distribute in the range of (0.05, 1). The width of 25th-75th percentages achieved 0.38-0.54, the standard deviations 0.25-0.30 for 0.7 of the statistical power. However, they all monotonously decreased in respect to P value. The retrospective powers were negatively correlated with P values with Pearson coefficients ranged from -0.753 to -0.831 (p < 0.001). The nonlinear regression models can be built with R squares all above 0.97. We conclude that retrospective power calculation yield no additional insights if P value is available, and can not be used to estimate the statistical power.