Lindley's Paradox

Lindley's Paradox highlights how Bayesian and traditional statistical methods can lead to different conclusions when testing hypotheses. Specifically, it occurs when a small effect appears statistically significant under classical (frequentist) tests, but Bayesian analysis suggests strong support for no effect or the null hypothesis. This discrepancy arises because frequentist tests focus on whether data would be unusual if the null were true, while Bayesian methods incorporate prior beliefs and the overall probability of hypotheses. Therefore, Lindley's Paradox shows that depending on the approach, we can interpret the same data differently, especially in large samples or with weak evidence.