Choosing the Right Procedure: A Decision Framework
- Select the correct inference procedure from the structure of a scenario
- Distinguish one-sample, two-sample and paired designs
- State the conditions each procedure requires
Four questions decide the procedure
Nearly every inference question on the exam is settled by asking four things in order. One: proportion or mean? Counts and percentages point to proportions; measurements point to means. Two: one group, two groups, or paired? Three: interval or test? An interval estimates a value; a test evaluates a claim. Four: what are the conditions? Answering the first three names the procedure; the fourth decides whether you may use it. Working through them explicitly is faster and far more reliable than recognizing the problem by resemblance.
The paired-versus-two-sample fork
This is the fork students get wrong most often, and the test is whether there is a natural link between one observation in the first group and one specific observation in the second. Before and after on the same subject, left and right, twins, two measurements on the same plot of land — paired, and analyzed as a one-sample t procedure on the differences. Two separately chosen groups of different subjects — two-sample. A tell in the wording: if the two groups have the same size and the data are presented side by side in a table with a subject label, suspect pairing.
Conditions, and why they are worth stating
Every procedure needs random data, some form of independence, and a Normality condition. Independence usually requires either random assignment or the 10% condition, that the sample is no more than 10% of the population when sampling without replacement. Normality means large counts (np̂ ≥ 10 and n(1 − p̂) ≥ 10) for proportions, and for means a Normal population, a large sample, or a graph of the data showing no strong skew or outliers. Conditions are worth real points on the free response and are checked, not asserted — stating the condition and the evidence for it.
Free-response inference is scored in four parts: state the hypotheses or parameter, plan by naming the procedure and checking conditions, do the calculation, conclude in context and linked to the p-value or interval. A perfect calculation with no conditions and no context typically earns about half the available credit.
For each scenario, name the procedure. (i) The mean sodium content of a cereal is claimed to be 200 mg; a sample of 25 boxes is tested. (ii) Graduation rates are compared for two independent random samples of schools. (iii) Thirty students take a pretest and a posttest.
- 1.Scenario (i): a measurement, one group, a claim to evaluate — a one-sample t test for a mean.
- 2.Scenario (ii): rates are proportions, two separate groups — a two-proportion z test or interval.
- 3.Scenario (iii): each student contributes two measurements, so the data are naturally linked.
- 4.Reduce each student to one difference and apply a one-sample t procedure on those differences, with df = 29.
A researcher measures the fuel economy of 20 cars using regular fuel and then the same 20 cars using premium fuel. The correct procedure is —
The 10% condition exists to justify —
Answer the 2 checkpoints as you read.
Sign in to save your progress