A priori vs. post hoc analysis Statistical power

power analysis can either done before (a priori or prospective power analysis) or after (post hoc or retrospective power analysis) data collected. priori power analysis conducted prior research study, , typically used in estimating sufficient sample sizes achieve adequate power. post-hoc analysis of observed power conducted after study has been completed, , uses obtained sample size , effect size determine power in study, assuming effect size in sample equal effect size in population. whereas utility of prospective power analysis in experimental design universally accepted, post hoc power analysis fundamentally flawed. falling temptation use statistical analysis of collected data estimate power result in uninformative , misleading values. in particular, has been shown post-hoc observed power one-to-one function of p-value attained. has been extended show post-hoc power analyses suffer called power approach paradox (pap), in study null result thought show more evidence null hypothesis true when p-value smaller, since apparent power detect actual effect higher. in fact, smaller p-value understood make null hypothesis relatively less true.