What is in the Hypothesis Testing area?

This area teaches the formal procedure for testing claims about populations. It covers the testing framework (null and alternative hypotheses, significance level, test statistic, p-value, one- and two-tailed tests, critical region, and Type I and Type II errors), the one-sample, two-sample and paired t-tests for means, the one- and two-sample tests for proportions, the non-parametric Mann-Whitney and Wilcoxon signed-rank tests, and the chi-squared goodness-of-fit and contingency-table tests. It also stresses communicating conclusions clearly in context.

How do I decide which hypothesis test to use?

Match the test to the data and the question. For a mean with unknown standard deviation, use a t-test (one-sample, two-sample for independent groups, or paired for matched data). For a proportion, use a proportion test with the normal approximation. When the data are not normal or are ranks, use a non-parametric test (Mann-Whitney for two independent samples, Wilcoxon signed-rank for paired data). For counts in categories, use a chi-squared test (goodness of fit for one variable, contingency table for association between two). Choosing and justifying the test is a major source of marks.

What is the difference between a Type I and a Type II error?

A Type I error is rejecting the null hypothesis when it is actually true, a false positive, and its probability is the significance level alpha. A Type II error is failing to reject the null hypothesis when it is actually false, a false negative, with probability beta. The power of a test is one minus beta, the chance of correctly detecting a real effect. For a fixed sample size, lowering alpha raises beta, so there is a trade-off between the two; increasing the sample size lowers both.

When should I use a non-parametric test instead of a t-test?

Use a non-parametric test when the t-test's assumption of approximate normality cannot be justified, typically when the sample is small and the data are clearly skewed or contain outliers, or when the data are ordinal (ranks or ratings). Non-parametric tests such as Mann-Whitney and Wilcoxon work on the ranks of the data rather than the raw values, so they do not assume a normal population. The cost is a small loss of power when the data really are normal, in which case the t-test remains preferable.

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Hypothesis Testing: study guide to the SQA Advanced Higher Statistics third area

A study guide to the third area of SQA Advanced Higher Statistics, Hypothesis Testing. Covers the testing framework, the t-tests, proportion tests, non-parametric tests and chi-squared tests, with advice on choosing the right test and communicating conclusions.

Generated by Claude Opus 4.89 min readAdvanced Higher: Hypothesis TestingUpdated 2026-06-16

Reviewed by: AI editorial process; not yet individually human-reviewed

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What the area covers
How the topics connect
How to study this area
Where to go next

Hypothesis Testing is the third of the three areas of SQA Advanced Higher Statistics and the culmination of the course. It teaches the formal machinery for deciding whether sample data give convincing evidence against a claim, and the judgement to pick the right test for the situation. This guide maps the area and links to the full topic pages.

What the area covers

The area starts with the shared framework, then works through the families of test.

The hypothesis testing framework. Null and alternative hypotheses, the significance level, the test statistic and p-value, one- and two-tailed tests, the critical region, and Type I and Type II errors.
The t-tests. The one-sample, two-sample (independent) and paired t-tests for population means, with degrees of freedom and the normality assumption.
Proportion tests. Tests for a single proportion and for the difference between two proportions, using the normal approximation and a pooled estimate.
Non-parametric tests. The Mann-Whitney U test for two independent samples and the Wilcoxon signed-rank test for paired data, for when normality fails.
Chi-squared tests. The goodness-of-fit test and the contingency-table test for association, with expected frequencies and degrees of freedom.

How the topics connect

Everything in the area is built on the framework page: every test states hypotheses, computes a statistic, finds a p-value or critical value, and reaches a conclusion, differing only in how the statistic is formed. The t-tests and proportion tests are parametric, resting on the sampling distributions and standard errors developed in the inference area; the central limit theorem is what justifies the normal approximation in the proportion tests. The non-parametric tests are the fallback when the normality those tests need cannot be justified, swapping raw values for ranks. The chi-squared tests handle the categorical data that none of the others can, reusing the observed-versus-expected idea. Choosing among them is the single most examined skill, so the connections matter as much as the individual methods.

How to study this area

Master the framework first. Hypotheses, significance level, p-value rule, tails and the two error types are common to every test, so learn them once thoroughly.
Build a "which test?" decision habit. For each scenario ask: mean or proportion or count? one sample or two? paired or independent? normal or not? That sequence picks the test.
Memorise the test statistics. The t-statistic $\dfrac{\bar{x} - \mu_0}{s/\sqrt{n}}$ , the proportion z-statistic and the chi-squared $\sum \dfrac{(O - E)^2}{E}$ should be automatic.
Check assumptions every time. Note normality for a t-test, large expected counts for chi-squared, and independence versus pairing; the justification carries marks.
Write conclusions in context. Never stop at "reject $H_0$ "; state what it means for the original question and note any limitation.

Where to go next

Work through the five topic pages from this area, then test yourself with the area quiz. Return to the Data Analysis and Modelling and Statistical Inference guides to see how the distributions and sampling theory underpin every test here.

Sources & how we know this

SQA Advanced Higher Statistics Course Specification (C803 77) — SQA (2023)
SQA Advanced Higher Statistics Course Overview and Resources — SQA (2023)