Sample Size, Replicability, and Pre-Test Likelihoods—Essential, Overlooked, and Critical Components of Statistical Inference: A Journal of Neurotrauma Guide to Statistical Methods and Study Design

Perhaps one of the most overlooked components of statistical inference is the sample size. While in randomized controlled trials, power analysis is common and sample size justification is an integral component of the core statistical analysis plan, observational and laboratory research studies often rely on convenience samples and/or underpowered analyses. Insufficiently powered studies increase uncertainty associated with the results and limit interpretability. Moreover, they increase the likelihood that the findings might be disproved in future replication studies. A scientific study can be compared with a diagnostic test for the “truth”— i.e., whether a certain effect exists or whether a relationship is actually true. In this diagnostic analogy, the positive predictive value is dependent not only on the statistical power of the study in question, but also on the pre-test likelihood that any true relationship exists at all. The concept of using an estimate of the pre-test likelihood to interpret observed results is another critical and often overlooked component of statistical inference. Even if a statistically significant relationship or an effect is found, however, such finding alone may be insufficient. It often must be replicated, ideally in a more generalizable setting. Further, if the effect size is small, replication often requires sample sizes that are substantially larger than the original study. For most neurotrauma research, thousands of subjects are usually not required, but many studies do require substantially larger sample sizes than are typically presented in published research to increase replicability. In this methodological tutorial, choice of sample size, pre-test probability, and the concept of positive predictive value for scientific findings will be discussed, together with suggestions to improve replicability of neurotrauma research in the future.