Hypothesis test have been shown to be valuable contributors to science (p < .05) but are sometimes abused (p < .05).

Used to assess the degree to which data is consistent with a particular model.

The most widely used tool in statistical inference.

Lay out your model(s).

\(H_0\): null model, business as usual
\(H_A\): alternative model, business not as usual

• Hypotheses are statments about the TRUE STATE of the world and should involve parameters, not statistics.
• Hypotheses should suggest a test statistic that has some bearing on the claim.
• Always use two-tailed tests.

Contruct the appropriate null distribution.

1. Randomization
2. Simulation
3. Exact Probability Theory
4. Normal Approximation

Calculate a measure of consistency between the observed test statistic (the data) and the null distribution (i.e., a p-value).

• If your observed test stat is in the tails > low p-val > data is inconsistent with null hypothesis > "reject null hypothesis".
• If your observed test stat is in the body > high p-val > data is consistent with the null hypothesis > "fail to reject the null hypothesis".

What can go wrong?