NZ Scholarship Statistics study plan

Map the full Statistics domain into a personal topic checklist, marking each subtopic as confident, shaky, or unknown

Write out the formal definition and assumptions of the linear regression model, including the error-term conditions

Derive the ordinary least squares estimator for simple linear regression from first principles

Distinguish between the population regression line and the fitted line, and explain what residuals estimate

Derive the sampling distribution of the sample mean and state the Central Limit Theorem precisely with its conditions

Compute standard errors for means, proportions, and differences, and explain what each measures

Construct and interpret confidence intervals for a mean and a proportion, justifying the critical value chosen

Explain the logic of hypothesis testing, including Type I and Type II errors and the meaning of a p-value

Derive the t statistic for a regression slope and state its null distribution and degrees of freedom

Interpret regression output: coefficients, standard errors, t values, p values, and confidence intervals

Explain R-squared and adjusted R-squared, and identify when each misleads

Diagnose violations of regression assumptions using residual plots and describe the consequence of each violation

Set up and interpret one-way analysis of variance, including the F statistic and its null distribution

Derive the partitioning of total sum of squares into between-group and within-group components

Explain the role of experimental design, randomisation, and blocking in causal interpretation

Compare two groups using both a t test and an ANOVA and show the results agree

Distinguish observational studies from experiments and articulate what each can and cannot establish

Identify confounding variables and explain how randomisation and adjustment address them

Interpret conditional probability, independence, and Bayes' theorem in applied contexts

Explain the difference between statistical significance and practical significance with a concrete example

Compute expected values and variances of linear combinations of random variables

Apply the law of total probability and Bayes' theorem to multi-stage problems

Model counts and proportions with the binomial and Poisson distributions and justify the choice

Derive the mean and variance of the sample proportion and use them for inference

Solve multi-part Scholarship-style problems that combine probability, inference, and regression

Justify modelling choices in writing, stating assumptions and their consequences

Critique a flawed statistical argument and propose a corrected analysis

Manage time across a full-length paper by allocating minutes per mark

Re-derive the ten most examinable results from memory under time pressure

Rewrite and resolve every item in the error log from weeks 4 to 7

Practise concise written justifications that state assumption, method, and conclusion in three sentences

Review the personal topic checklist and confirm every subtopic is marked confident