Revision sheet

Population and sample

• Population → parameter (usually unknown).
• Sample → statistic (an estimate).

Watch out: a number from the sample is a statistic.

Bias

Voluntary response, convenience, undercoverage, nonresponse, response bias.

Watch out: a bigger biased sample is still biased.

Comparing two groups

• Two proportions: pooled $\hat{p}$ in the SE.
• Paired: test the differences.

Watch out: pool counts, not proportions.

z-scores and the normal model

• $z = (x - \mu)/\sigma$; $x = \mu + z\sigma$.
• 68–95–99.7 within 1, 2, 3 SDs.

Watch out: the percentages are for both sides together.

Studies

• Observational: record. Experiment: assign.
• Confounding hides cause in observational data.

Watch out: association is not causation.

Experimental design

Compare · randomize · replicate · block. Treatments = combinations of factor levels.

Watch out: blocks (experiments) vs strata (samples).

Sampling variability

• Statistics vary from sample to sample.
• Sampling distribution: a statistic over all samples.
• Larger $n$: less variability.

Watch out: data distribution vs sampling distribution.

Interval estimates

Estimate ± ME, ME = critical value × SE; ME = half the width.

Watch out: width = 2 × ME.

Interval for p

$\hat{p} \pm z^*\sqrt{\hat{p}(1 - \hat{p})/n}$; check random and large counts.

Watch out: "confident", not "probability", for a computed interval.