🟢 Stats: Hypothesis Testing Step-by-Step

1. State hypotheses: H₀ (null — no effect) vs H₁ (alternative — there IS an effect)
2. Choose significance level: α = 0.05 (accept 5% false positive risk)
3. Collect data and compute test statistic
4. Find p-value
5. Decision: p < α → reject H₀. p ≥ α → fail to reject H₀.

P-Value — The Most Misunderstood Concept

What it IS: The probability of seeing data this extreme or more extreme, assuming H₀ is true.

What it is NOT: - ❌ NOT the probability that H₀ is true - ❌ NOT the probability your result is due to chance - ❌ NOT the probability of making an error

Example: P-value = 0.03 means: "If there were truly no effect, there's only a 3% chance we'd see results this extreme." Since 0.03 < 0.05, we reject H₀.

P-value = 0.06: We fail to reject H₀ at α = 0.05. But this does NOT mean "no effect." It means insufficient evidence. Say "we don't have sufficient evidence to conclude there's an effect" — never say "the null is true."