The 95% Illusion: Why Your Confidence Interval Isn't What You Think It Is

The common interpretation of a 95% confidence interval is incorrect, as it does not represent a 95% probability that the true parameter lies within that specific range. Instead, this frequentist concept means that if the same procedure were repeated many times, 95% of the resulting intervals would contain the true parameter. This approach contrasts with Bayesian credible intervals, which do offer a direct probability statement about the parameter but are dependent on a chosen prior belief. This distinction is critical in applications like A/B testing, where large sample sizes can lead to statistically significant but practically meaningless results, an issue known as the Jeffreys-Lindley paradox.