Selecting Any Inference Procedure

The whole toolbox

• By now you've met four families of inference — this lesson picks among all of them.
• Proportions ($z$), means ($t$), chi-square (categorical counts), and slopes ($t$).
• The right choice comes from the type of data and the structure of the question.
• Master this and you can attack any inference problem on the exam.

Start with the data type

• Categorical, and you want a proportion / count? → a $z$-procedure (proportions) or chi-square (tables).
• Quantitative average? → a $t$-procedure for means.
• Two quantitative variables, a linear trend? → slope $t$-inference.
• The data type narrows it to a family immediately.

Choosing any inference procedure: type of data, number of groups, then estimate or test

Then count samples and variables

• One or two groups? Independent or paired?
• One categorical variable vs. a distribution → goodness-of-fit; two variables / several groups → homogeneity/independence.
• A relationship between two quantitative variables → slope inference.
• These structural questions pin down the exact procedure.

Implement and communicate

• Interval or test? — estimate a value, or judge a claim.
• State hypotheses/parameter, check conditions, compute, and conclude in context.
• Name the procedure and justify why the data fit it.
• Clear reasoning earns as much credit as the right number.

Write from a regression t procedure

• Both variables are quantitative.
• The question is whether the population slope is zero.