Selecting a Categorical Procedure

Which categorical procedure?

• For categorical data, choose among proportion $z$-procedures and chi-square tests.
• The decision hinges on how many variables and how many samples.
• Get those right and the procedure follows.
• This skills lesson ties Units 6 and 8 together.

Count the variables and samples

• One variable, one sample, matched against a claimed distribution → goodness-of-fit.
• One variable, several separate samples → homogeneity.
• Two variables, one sample → independence.
• A single proportion (two categories, one sample) can also be a one-proportion $z$-test.

Choosing a categorical inference procedure

Chi-square vs. two-proportion z

• Comparing two groups on a two-category variable? Two valid options overlap here.
• A two-proportion $z$-test works and gives a direction (one-sided possible).
• A chi-square test of homogeneity also works (a $2\times2$ table) but is only non-directional.
• For a directional two-group proportion question, prefer the $z$-test.

Implement and communicate

• State hypotheses, check conditions, compute the statistic and p-value, conclude in context.
• Name the procedure explicitly and justify why it fits the data.
• Word the conclusion to match the test (fit / difference / association).
• Clear communication is graded as heavily as the arithmetic.

Write from goodness of fit

• There is one categorical variable.
• There is one random sample, and several category proportions are claimed.