NZ Scholarship Statistics common mistakes
NZ Scholarship Statistics · Understand the traps and how to avoid them.
When asked to compare two groups, the candidate describes each group's centre and spread separately and then stops, without making an explicit comparative statement (e.g., 'the median of group A is 5 units higher than group B').
Candidates treat the task as two separate 'describe the distribution' questions, a habit reinforced by earlier years where description alone earned credit. Under Scholarship, the comparative judgement is the point, and separate descriptions do not demonstrate it.
What to do instead
Before writing, force a sentence frame: 'Compared with [group], [group] tends to be [higher/lower/more variable] by [specific amount/measure], which matters because [context].' Practise by writing only the comparison sentence for ten past-style prompts, then checking that every sentence contains a comparative word (higher, more variable, narrower) and a quantified difference.
The candidate interprets a p-value as the probability that the null hypothesis is true, or as the probability the results occurred by chance, and then uses that interpretation to make the conclusion.
The phrase 'probability of getting this result by chance' is repeated in many school resources, so it feels safe. The subtlety that the p-value is conditional on H0 being true is easily lost under time pressure.
What to do instead
Memorise and rehearse the exact conditional sentence: 'If H0 were true and the study were repeated many times, about p of those repetitions would produce a result at least as extreme as observed.' Then write the conclusion in two parts: the decision about H0, and the contextual claim about the population, keeping them separate.
The candidate writes a conclusion that asserts a causal relationship ('the new programme increased scores') from an observational study, or generalises beyond the sampled population without acknowledging the design.
Candidates focus on the statistics and treat the study design as background. The word 'effect' in the question prompt is often taken as licence to use causal language.
What to do instead
Build a two-line template before writing the conclusion: (1) 'For [population], there is evidence of an association between X and Y'; (2) 'Because the data came from [design], we cannot conclude causation; [confounding variable] could explain part of the difference.' Use this template until it becomes automatic, and always name at least one plausible confounding variable.
When planning a study or interpreting an interval, the candidate ignores the sampling method and treats a convenience or voluntary-response sample as if it were a random sample, then makes precision statements based on n.
The formula for a confidence interval is salient and feels like the 'real' statistics, while sampling method is treated as a preamble. Candidates also confuse sample size with representativeness.
What to do instead
Before any calculation, write one sentence naming the sampling method and its consequence: 'This is a voluntary-response sample, so the interval's coverage property does not apply and non-response bias may dominate.' In planning questions, specify the randomisation mechanism explicitly (e.g., 'randomly select 40 students from the enrolment list using a random number generator') rather than saying 'choose a random sample'.
The candidate uses a hypothesis test to answer a question about the size of an effect, concluding 'no effect' from a non-significant result, or treating a tiny significant difference as important.
The decision framework (reject/not reject) is over-learned, and candidates collapse 'not statistically significant' into 'no difference'. They also rarely connect the confidence interval to the practical question.
What to do instead
Always report and interpret the confidence interval alongside the p-value. Write the conclusion as: 'The estimated difference is [value] (95% CI [a, b]). This interval [does/does not] include values that would be practically important, so [practical conclusion].' Practise with examples where significance and practical importance disagree.
The candidate reads a scatterplot or regression output and describes the relationship as 'strong positive' without checking whether a linear model is appropriate, ignoring curvature, outliers, or unequal spread.
Candidates equate 'correlation coefficient close to 1' with 'linear model fits'. They do not routinely inspect residual plots because these are often supplied only as an afterthought.
What to do instead
Adopt a fixed four-step check before interpreting r or a regression line: (1) plot or inspect the scatter for curvature; (2) identify high-leverage or influential points; (3) check whether the spread changes with x; (4) only then comment on strength and direction. In writing, state the check explicitly: 'The scatter shows a curved pattern, so r understates the relationship and a linear model is not appropriate.'
The candidate interprets a regression slope as a correlation or as a statement about individuals ('each student's score increases by 3 marks') rather than about the average change in the response for a one-unit increase in the predictor.
The slope and the correlation are both 'how much y changes with x' in informal language, and the distinction between group-level and individual-level statements is rarely tested explicitly in internal assessment.
What to do instead
Write the slope interpretation with the exact template: 'On average, [response] changes by [slope] [units] for each additional [one unit of predictor], among [population].' Then add a sentence about prediction error: 'Individual predictions vary about the line with residual standard deviation [s].' Do not use the word 'correlation' in a slope sentence.
The candidate chooses a two-sample t-test or ANOVA without checking the required conditions, or applies a chi-square test to expected counts below 5 without comment.
Candidates match the test to the data type (numeric vs categorical) but skip the conditions because they are listed in a textbook and not in the question. Under time pressure, conditions feel optional.
What to do instead
Create a one-page test-selection table with three columns: data structure, test, and conditions to check. For each practice question, write the condition check as a sentence in the answer ('The sample sizes are 18 and 22, the histograms show no strong skew or outliers, so the t-test is reasonable'). This earns communication marks and catches invalid applications.
The candidate answers a probability question by listing outcomes without defining the sample space or the event, and consequently double-counts or omits outcomes, especially in 'at least one' or conditional problems.
Candidates rely on intuition for simple probability and do not build a formal representation. Conditional probability in particular invites reversing the condition.
What to do instead
For every probability question, write the sample space or a tree diagram first, label each branch with its probability, and state the event in set notation before calculating. For 'at least one', use the complement explicitly. For conditional probability, write P(A|B) and circle B as the denominator before substituting numbers.
The candidate uses a normal approximation for a proportion or mean without checking np and n(1-p), or uses a binomial calculation when the sampling was without replacement from a small population.
The normal approximation is presented as the default, and the conditions are often stated once and then forgotten. The finite population correction is rarely practised.
What to do instead
Before any normal approximation, write the check numerically: 'np = 8, which is less than 10, so the normal approximation is unreliable; use the exact binomial.' For without-replacement sampling, compare n with N and state whether the finite population correction is needed. Keep a checklist of approximation conditions and tick each one in the answer.