Hypothesis testing is one of the topics where students often understand each individual step but lose marks because they can't articulate why they're doing it — and IB mark schemes reward that reasoning explicitly. This guide walks through the logic, not just the mechanics.
The core logic, in plain terms
You start by assuming nothing interesting is happening — this assumption is the null hypothesis (H₀). You then look at your sample data and ask: "if H₀ were actually true, how likely is it that I'd see data this extreme just by chance?" That likelihood is the p-value. If it's small enough, you conclude the data doesn't fit comfortably with H₀, and you reject it in favour of the alternative hypothesis (H₁).
Key vocabulary
- Null hypothesis (H₀) — the default assumption, usually "no difference" or "no relationship"
- Alternative hypothesis (H₁) — what you conclude if you reject H₀
- Significance level (α) — the threshold you compare your p-value against, commonly 5% or 1%, always given in the question
- p-value — the probability of observing data this extreme (or more extreme) assuming H₀ is true
- Test statistic — the calculated value (e.g. from a chi-squared or t-test) used to determine the p-value
If p-value < significance level → reject H₀ (the result is "statistically significant"). If p-value ≥ significance level → do not reject H₀ (insufficient evidence). This single comparison is the entire decision — get comfortable stating it exactly this way, since mark schemes are strict about the direction of the inequality and the precise conclusion wording.
Common test types you'll meet
- Chi-squared test for independence — tests whether two categorical variables are related (e.g. is favourite subject independent of gender?). Involves comparing observed vs expected frequencies in a contingency table.
- Chi-squared goodness-of-fit test — tests whether observed data fits an expected distribution (e.g. is a die fair?).
- t-test for the mean — tests whether a sample mean differs significantly from a claimed population mean (AI HL, and some AI SL contexts with technology).
Mistake 1: Wording the conclusion incorrectly
A conclusion should never say you "prove" or "accept" H₀ — you either reject H₀ or you find insufficient evidence to reject H₀. Statistical tests never prove the null hypothesis true; they only fail to find enough evidence against it. Examiners specifically watch for this distinction, and "accept H₀" style wording commonly loses a mark even when the numerical work is correct.
Mistake 2: Forgetting to state the significance level in the conclusion
A complete conclusion references the significance level explicitly — e.g. "Since the p-value (0.032) is less than the 5% significance level, we reject H₀" — rather than just stating the decision on its own. The comparison is the reasoning; without it, the conclusion looks like a guess rather than a justified statistical decision.
Mistake 3: Mixing up degrees of freedom
For a chi-squared test for independence, degrees of freedom = (rows − 1)(columns − 1) — a frequent source of errors, especially with larger contingency tables. Getting this wrong shifts your entire critical value or p-value calculation even if every other step is correct, so it's worth double-checking on every table-based question.
Practise hypothesis testing questions
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✦ Try it freeFrequently asked questions
Is hypothesis testing only in AI, or also AA?
Hypothesis testing is an AI-specific topic (both SL and HL) — it does not appear in the AA syllabus.
Do I need to calculate p-values by hand?
No — in AI, a GDC is used throughout, and you're expected to use your calculator's built-in statistical tests to find test statistics and p-values directly, then focus your working on interpreting and justifying the result.