Addressing common inferential mistakes when failing to reject the null-hypothesis

Failure to reject a null-hypothesis may lead to erroneous conclusions regarding the absence of an association or inadequate statistical power. Because an estimate (and its variance) can never be exactly zero, traditional statistical tests cannot conclusively demonstrate the absence of an association. Instead, estimates of accuracy should be used to identify settings in which an association and its variability are sufficiently small to be clinically acceptable, directly providing information on safety and efficacy. Post-hoc power calculations should be avoided, as they offer no additional information beyond statistical tests and p-values. Furthermore, post-hoc power calculations can be misleading because of an inability to distinguish between results based on insufficient sample size and results that reflect clinically irrelevant differences. Most multiple testing procedures unrealistically assume that all positive results are false positives. However, in applied settings, results typically represent a mix of true and false positives. This implies that multiplicity corrections do not effectively differentiate between true and false positives. Instead, considering the distributions of p-values and the proportion of significant results can help to identify bodies of evidence unlikely to be driven by false-positive results. In conclusion, rather than attempting to categorize results as true or false, medical research should embrace established statistical methods that focus on estimation accuracy, replication, and consistency.