This is a question that often arises when using structural equation models in practice, sometimes once a study is completed but more often in the planning phase of a future study. To think about power, we must first consider ways in which we can make errors in hypothesis testing (Cohen, 1992). Briefly, the Type I error rate is the probability of incorrectly rejecting a true null hypothesis; this is the probability that an effect will be found in a sample when there is truly no effect in the population. In contrast, the Type II error rate is the probability of accepting a false null hypothesis; this is the probability that an effect will not be found in a sample when there truly is an effect in the population. Statistical power is one minus the Type II error rate and represents the probability of correctly rejecting a false null hypothesis; this is the probability that an effect will be found in the sample if an effect truly exists in the population. It is important to determine whether a proposed study will have sufficient power to detect an effect if an effect really exists. Although power is quite easy to compute for simple kinds of tests such as a t-test or for a regression parameter, it becomes increasingly complicated to compute power for complex SEMs. (more…)