Preview
Inferential Statistics — Tests of Difference
IB DP Psychology — Research Methods | HL | Paper 3
🎯 Learning Intentions By the end of this note, you will be able to:
- Define inferential statistics, the null hypothesis, and statistical significance using IB-aligned terminology.
- Explain the logic of hypothesis testing and why researchers use probability thresholds to make decisions about data.
- Distinguish between parametric and non-parametric tests of difference and identify the conditions under which each is appropriate.
- Identify the appropriate test of difference (Mann-Whitney U, Wilcoxon Signed-Ranks, independent samples t-test, related samples t-test) given a research scenario.
- Interpret the output of a test of difference, including the calculated value, critical value, and p-value, to reach a justified conclusion.
- Evaluate the strengths and limitations of parametric versus non-parametric approaches using the concept areas of Measurement, Causality, and Bias.
- Apply knowledge of tests of difference to a stimulus-based research scenario in Paper 3 format.
- Analyse methodological decisions in research using the concept areas of Measurement, Causality, Perspective, and Responsibility.
Introduction & Context
Imagine a researcher wants to know whether a new mindfulness programme reduces stress in university students. She runs the programme with one group and leaves a second group untouched, then measures stress levels in both groups at the end. The mindfulness group scores lower on average — but here is the critical question: is that difference real, or could it have happened by chance even if the programme had no effect at all? This is the fundamental problem that inferential statistics exists to solve.
Descriptive statistics — means, medians, standard deviations — can only tell us what happened in the specific sample we measured. They cannot tell us whether the pattern we observed reflects something genuine about the broader population, or whether it is simply the result of random variation. Inferential statistics provides a principled, mathematical framework for making that judgement. Tests of difference, in particular, allow researchers to decide whether the gap between two sets of scores is large enough — and consistent enough — to be taken seriously as evidence of a real effect.
In IB Psychology HL, understanding tests of difference is not about performing complex calculations by hand. It is about understanding the logic of statistical decision-making: why we set probability thresholds, what it means for a result to be "significant," and how the choice of test reflects the nature of the data and the design of the study. These skills are assessed directly in Paper 3, where you are given a stimulus research scenario and asked to justify methodological choices and interpret findings.
🔍 Analogy — The Courtroom Standard Think of inferential statistics like a courtroom verdict. The null hypothesis is the presumption of innocence — the default assumption that nothing interesting is happening, that any difference between groups is just noise. The data you collect is the evidence. A test of difference asks: how likely is this evidence if the null hypothesis were actually true? If the answer is "very unlikely" (typically less than a 5% chance), you reject the null hypothesis — just as a jury convicts when the evidence is strong enough to overcome reasonable doubt. Statistical significance is not proof of an effect; it is a principled decision that the evidence is strong enough to act on.
Core Concepts
Before choosing any statistical test, a researcher must first articulate what they expect to find — and, crucially, what they would conclude if they found nothing. This is the role of hypothesis testing, and it begins with two competing statements about the world.
📖 Key Definition — The Null Hypothesis (H₀) The null hypothesis is a formal statement that