Opening
We tossed a coin twenty times and got eighteen heads. Does that prove it is unfair? No. But under a fair-coin model, the observation is sufficiently unusual that we ought to pay attention.
Teaching narrative
Begin by stating a specific null hypothesis and the experimental or sampling conditions under which its reference distribution is appropriate. A p-value measures results at least as extreme as the observed data according to the specified test, conditional on that null model.
An exact binomial test can count all the possible head totals. A chi-square goodness-of-fit test compares observed category counts with expected counts under a specified categorical distribution.
A chi-square independence test instead asks whether two categorical variables appear related, using expected cell counts calculated from row and column totals. It is an association test; it does not identify a cause.
A significant test is not necessarily a scientifically important effect. Report the observed differences, units, sampling design, uncertainty, and the limitations of the model.
Before the experiment
Is a p-value the probability that the null hypothesis is true? Why not?
Live demonstration
Display the binomial null probabilities for twenty tosses, then calculate a six-category die goodness-of-fit statistic, then examine a 2-by-2 commuter table.
Exit question
Write a correct plain-language interpretation of p=.03 that does not mention the probability the hypothesis itself is true.