Selecting Inference Procedures
IntroducedThe same data can answer different questions
- Two independent groups have measured completion times. Asking how much the population means differ calls for an interval; asking whether the difference is zero calls for a test.
- First define the population parameter and the question. Do not choose a test merely because a formula is familiar.
Classify the parameter, not just the data format
- A binary success proportion is a population proportion. The average of measured completion times is a population mean.
- For the normal-approximation procedures covered in these two sequences, independent proportions use z and means with unknown population SD use t. This is a bounded menu, not every possible inference method.
The question asks 'how much larger is the mean?' You should build a...
Estimating a value → interval; judging a claim → test.
Read the study design before choosing a formula
- Two unrelated random samples support an independent-samples comparison after conditions are checked. Repeated measurements on the same people are paired.
- For paired quantitative measurements, calculate one difference per pair and use the one-sample t framework on those differences. Paired binary responses need a different categorical method, not an independent two-proportion formula.
To infer a measured population mean with unknown population SD using the normal-theory method taught here, use...
Measured average → mean → t-procedure.
Match each question and design to the method in this course.
Classify the parameter, purpose and relationship of the observations.
Carry out the selected method completely
- For a test, state population hypotheses and the prechosen alternative. For an interval, name the population parameter and confidence level.
- Check design, independence and the appropriate shape or count conditions; then calculate and report the uncertainty. The 10% check applies when sampling without replacement.
Estimating a mean before-minus-after change uses a paired t interval on differences. Testing whether that mean change is zero uses a paired t test.
Two independent treatment groups, judging a difference in means. The procedure is...
Independent groups + means + a claim → two-sample t-test.
Check what the result actually supports
- Use a p-value and a prechosen threshold to make a test decision. Use an interval to describe plausible parameter values under that method.
- A non-rejection does not prove equality; a narrow interval does not fix a biased sample. Random assignment and random sampling support different kinds of conclusions.
The procedures taught here do not cover every design. Identify pairing before applying an independent-samples formula.
Arrange the questions in the suggested procedure-selection workflow.
This is the suggested workflow: define the goal, classify the parameter, then check sample structure. Other coherent workflows can consider design earlier.
Which require revisiting a proposed independent two-proportion calculation?
Pairing, selection bias and inadequate approximation are method issues. Different sample proportions are expected and do not by themselves invalidate the method.
A random sample alone proves that a measured group difference was caused by the group label.
Random sampling supports population generalization under its design. Causal inference requires a suitable randomized experiment or another justified causal design.
Make the procedure visible in the report
- State the question, parameter, design, chosen procedure, conditions, calculation and contextual conclusion. Include units for measured means.
- A wrong procedure can invalidate a result even when the arithmetic is correct. No evidence here establishes whether procedure errors are more common than arithmetic errors.
Question, parameter and design select a candidate procedure; its assumptions still need checking.
A wrong inference procedure can invalidate a conclusion even when its arithmetic is correct.
The method must fit the study design and assumptions. Correct arithmetic alone does not establish a valid inference.