Overview
Hypothesis testing fails when researchers confuse "failing to reject H0" with "accepting H0." These are not the same: failing to reject the null hypothesis means the evidence is insufficient to conclude a difference exists — it does not mean no difference exists. Stating that a non-significant result "proves the null hypothesis" is a logical error that systematically misleads. Hypothesis testing has two error types with asymmetric default control: Type I errors (false positives) are controlled at the significance level; Type II errors (false negatives) require deliberate power analysis to control.
The Null Hypothesis Framework builds correctly formulated hypotheses, selects appropriate tests, calculates required power, and produces conclusions stated with correct error-probability language.