Craig’s theorem

Craig’s theorem provides a way to compare two different statistical tests to see which one is more effective at detecting a true effect. Specifically, it states that under certain conditions, the combined likelihood of two independent tests can be used to create a more powerful overall test, potentially reducing the likelihood of missing a real effect (increasing power) without increasing false positives (maintaining significance level). In essence, it guides researchers on how to optimally combine evidence from separate tests to make better, more reliable conclusions in statistical analysis.