33. Hypothesis Testing — p-Values, Alpha, Type I and II Errors and Power

The reasoning: the testing framework

1. State H₀ (no difference/association) and H₁ (two‑sided unless strongly justified).
2. Pre‑specify α (usually 0.05).
3. Compute a test statistic (t, χ², Z) from the data.
4. p‑value = probability, under H₀ and the model assumptions, of obtaining a statistic at least as extreme as observed.
5. If p < α, reject H₀ ("statistically significant"); otherwise "fail to reject".