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.
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.
Two features decide everything: the DATA TYPE and the STRUCTURE. Categorical count → $z$-proportion or chi-square; quantitative average → $t$-mean; two quantitative variables' trend → slope $t$. Then: how many samples/variables, and interval or test. Nearly every lost mark on inference is a wrong choice, not wrong arithmetic — decide deliberately.
"Is there a linear relationship between temperature and ice-cream sales?"
- Data: two quantitative variables; the question is about a linear trend.
- → slope $t$-inference (a test of $H_0: \beta = 0$, or an interval for $\beta$).
- (Had it compared mean sales on hot vs. cold days → a two-sample $t$; proportions of days → a $z$ or chi-square.)
Choose from all the course's methods by data type (proportion → $z$; mean → $t$; categorical table → chi-square; two quantitative variables' trend → slope $t$) and structure (samples, variables, interval-vs-test). Then implement fully and communicate the reasoning and conclusion clearly, in context.
One family among many
Two quantitative variables' trend → slope t-inference.
A question about a linear relationship between two quantitative variables calls for...
Two quantitative variables + a trend → slope inference.
Comparing the mean of a measured quantity for two independent groups calls for...
Measured average, two independent groups → two-sample t.
Two categorical variables in one sample, testing association, calls for...
Two categorical variables, one sample → independence.
Which questions help you pick the right inference procedure?
Data type, structure, and goal — not the graph's color.
Most lost marks on inference come from choosing the wrong procedure, not from arithmetic.
Decide the procedure deliberately from data type and structure.