Statistics (NZ Scholarship Statistics)
What this domain tests
The NZ Scholarship Statistics exam rewards statistical judgement, not recipe-following. You are expected to critique study designs and reports, select and justify methods, interpret output in context, and communicate uncertainty. The single domain draws on study design, exploratory and multivariate data, probability, inference, and regression.
Core rules
- Random sampling supports generalisation to a defined population; random allocation supports causal claims. Confounding, selection bias, non-response, and measurement error can invalidate either.
- A confidence interval gives a range of plausible values for a parameter and shows precision; a p-value is evidence against a null hypothesis, not the probability that the null is true.
- Statistical significance is not practical significance: report effect sizes with units and judge them against context.
- In regression, check linearity, independence, constant variance, outliers/influential points, and multicollinearity; interpret coefficients as estimated changes holding other predictors fixed.
- For reports, trace the claim back to the design, the sample, the question wording, and the analysis actually performed.
Worked example
A report claims a tutoring programme raised pass rates from 70% to 78% (n = 120, p = 0.04). The 8-point rise is statistically significant at the 5% level, but the confidence interval may include trivial effects, and without random allocation or a control group, selection or maturation could explain the gain. Ask whether the 120 students were representative, whether many outcomes were tested, and whether the pass standard changed. The defensible conclusion is "promising association", not "programme caused the rise".
Traps
Do not treat p < 0.05 as proof of importance or truth. Do not make causal claims from observational data. Avoid post-hoc subgroup stories, ignoring non-response, extrapolating beyond the observed range, and reading a CI as a probability. Check whether a graph's scale or a summary statistic hides variability.