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Descriptive statistics tell us what did happen in our sample. Inferential statistics tell us whether we can generalise it — whether a difference or relationship is real or just the kind of fluke that random variation throws up. This is the conceptual heart of Component 01, and the ideas here (significance, probability, the null hypothesis, Type 1 and Type 2 errors, and the logic of choosing a test) are examined every year and underpin the interpretation of every study you will meet.
This lesson builds the reasoning. We look at normal and skewed distributions, the meaning of probability and significance levels (why p≤0.05 is the conventional threshold), how to use a table of critical values, the criteria for a parametric test, the two ways an inferential decision can be wrong (Type 1 and Type 2 errors), and the logic of choosing a statistical test from three questions: is the study looking for a difference or an association, what is the experimental design, and what is the level of data. The next lesson applies that logic to the five named tests.
| This lesson covers | OCR H567 Component 01 sub-area | AO focus |
|---|---|---|
| Normal and skewed distributions | 1.3 — inferential stats: distributions | AO1 |
| Probability and significance levels (p ≤ 0.05) | 1.3 — probability; significance | AO1; AO2 |
| Tables of critical values | 1.3 — statistical tables of critical values | AO2 |
| Criteria for a parametric vs non-parametric test | 1.3 — criteria for a parametric test | AO1; AO2 |
| Type 1 and Type 2 errors | 1.3 — Type 1 & Type 2 errors | AO1; AO3 |
| Logic of choosing a test | 1.3 — choosing an inferential test | AO2 |
Referenced descriptively; see the official OCR H567 specification document for exact wording. This lesson develops AO1 (defining significance, error types and criteria), AO2 (applying the significance level and critical-value logic; selecting a test) and AO3 (evaluating the consequences of Type 1/Type 2 errors and the choice of significance level).
Many psychological variables (height, IQ, reaction time) form a normal distribution — a symmetrical, bell-shaped curve where the mean, median and mode all coincide at the centre, and scores tail off equally on both sides. In a normal distribution, a predictable proportion of scores falls within one, two and three standard deviations of the mean. Normality is one of the criteria for a parametric test.
A skewed distribution is asymmetrical, with a "tail" pulled to one side by extreme scores:
The relationship between the three averages is a reliable way to detect skew: if mean > median > mode, the distribution is positively skewed; if mean < median < mode, negatively skewed. Skew is one reason a dataset may fail the normality criterion and require a non-parametric test.
The normal distribution matters far beyond being a nice shape, because a great deal of statistical theory assumes it. In a normal distribution, the symmetry means the three averages coincide, and — importantly — a predictable proportion of scores falls within each band of standard deviations from the mean (roughly two-thirds within one SD, about 95% within two). This regularity is what parametric tests exploit, which is why "the data are drawn from a normal distribution" is one of the parametric criteria. Many natural human variables — height, IQ, reaction time in a healthy population — approximate normality, which is one reason the distribution is so central. Skewed distributions break the symmetry: a positive skew (tail to the right, toward high values) arises when most scores are low but a few are very high (e.g. income, or reaction times where a few very slow responses stretch the tail), pulling the mean above the median; a negative skew (tail to the left) arises when most scores are high but a few are very low (e.g. an easy test on which most score well but a few fail badly), pulling the mean below the median. Recognising skew from the ordering of the averages, or from the shape of a histogram, is directly examinable, and it feeds the decision about whether a parametric test is legitimate.
graph LR
A["Shape of the distribution"] --> B["Normal<br/>symmetrical; mean = median = mode"]
A --> C["Positive skew<br/>tail to high values; mean > median"]
A --> D["Negative skew<br/>tail to low values; mean < median"]
B --> E["Supports the normality<br/>criterion for a parametric test"]
C --> F["May require a<br/>non-parametric test"]
D --> F
style B fill:#27ae60,color:#fff
style C fill:#e67e22,color:#fff
style D fill:#8e44ad,color:#fff
Probability is the likelihood of an event occurring, expressed from 0 (impossible) to 1 (certain). In inferential statistics, we ask: if the null hypothesis were true (no real effect), how probable is it that we would obtain results as extreme as ours by chance alone?
Probability sits at the heart of inferential statistics because we are always reasoning under uncertainty. We study a sample, but we want to draw conclusions about a population, and the sample could always, by chance, be unrepresentative — a difference between two conditions might reflect a genuine effect, or it might be the kind of random fluctuation that sampling inevitably produces. Inferential statistics is the formal machinery for deciding which is more plausible. It never delivers certainty: it delivers a probability that the observed pattern would have arisen by chance if there were no real effect, and we make a decision based on whether that probability falls below our agreed threshold. This is fundamentally different from the deductive certainty of mathematics — it is probabilistic inference, and every conclusion carries a stated risk of being wrong (the significance level for a false positive). Keeping in mind that we are managing uncertainty rather than proving facts explains why the language of results is always tentative — "the difference was significant, so we reject the null hypothesis" — rather than "we have proven that the IV causes the DV".
The significance level is the threshold probability we set for deciding that a result is unlikely to be due to chance. Psychology conventionally uses p≤0.05 — a 5% level. This means: we will reject the null hypothesis only if the probability of our results occurring by chance is 5% or less. Put differently, we accept up to a 5% risk of wrongly claiming an effect when none exists.
p≤0.05Why 0.05? It is a pragmatic balance between being too willing to claim effects (a lax level like 0.10 catches too many flukes) and being too cautious to detect real ones. For research with serious consequences (e.g. testing a drug), a stricter level such as p≤0.01 (1%) is used to reduce the chance of a false claim; for exploratory research, a more lenient level may be justified. When you read "the result was significant at p≤0.05", it means the null hypothesis was rejected at the 5% level.
It is worth being precise about what the significance level is and is not, because loose thinking here is heavily penalised. The 5% is the probability of obtaining our results (or more extreme) if the null hypothesis were true — that is, if there were really no effect and the result arose purely by chance. It is emphatically not the probability that the null hypothesis is true, nor the probability that we are wrong, nor a measure of how large the effect is. When we reject the null at p≤0.05, we are saying "a result like this would happen by chance less than 5% of the time if there were no effect, so we judge it too improbable to be a fluke and conclude an effect is present" — while accepting that, on 5% of such occasions, we will be wrong (a Type 1 error). The choice of 0.05 is a convention, not a law of nature: it encodes a socially-agreed tolerance for false positives. Where a false positive would be costly (approving an ineffective or harmful treatment), researchers tighten the level to 0.01 or lower; where missing a real effect would be the greater loss, and false positives are cheap, a more lenient level can be defended. Understanding that the significance level is a deliberate trade-off rather than a magic threshold is the mark of genuine statistical literacy.
A related subtlety that distinguishes strong answers: statistical significance and importance are different things. With a very large sample, even a trivially small effect can cross the significance threshold, because large samples make it easy to detect tiny departures from the null; conversely, a genuinely large effect can fail to reach significance in a very small sample. So "significant" means "unlikely to be due to chance", not "big" or "meaningful". A fully critical evaluation of a significant finding therefore asks not only whether the result was significant but how large the effect was and whether it matters in practice.
A crucial subtlety: "significant" is a statistical statement about chance, not a statement about how large or important the effect is. A tiny, trivial effect can be statistically significant with a large enough sample, and a large effect can fail significance in a tiny sample.
Once a test statistic has been calculated, we decide whether it is significant by comparing it against a critical value taken from a statistical table. The tables of critical values are pre-computed reference tables — one for each of the five named tests — that a researcher (or student in an exam) consults rather than deriving the boundary from scratch. Historically they were painstakingly calculated by statisticians and printed in the back of methods textbooks; today software often reports the exact probability directly, but the tables remain the tool used at A-Level and are provided in the exam. Each table is entered using three pieces of information:
The table returns the critical value — the boundary the calculated statistic must reach to be significant. A point students often get wrong: when a result is non-significant, the correct conclusion is that we retain the null hypothesis, not that we have "proven the null true" or "proven there is no effect". Failing to find an effect is not the same as demonstrating its absence — the study may simply have lacked the power, the sample size, or the sensitivity to detect a real but modest effect (a possible Type 2 error). The disciplined phrasing is "the result was not significant, so we retain the null hypothesis and conclude that the evidence does not support an effect", carefully avoiding any claim to have proven a negative. Crucially, which way the comparison goes depends on the test:
Because this direction flips between tests, every critical-values table in the exam is accompanied by a rubric telling you which rule applies. Reading that rubric — rather than assuming "bigger is always significant" — is where careful candidates protect easy marks. (The next lesson covers each test's rule explicitly.)
It is worth understanding why a critical value works the way it does, because it demystifies the whole procedure. A statistical test converts the data into a single number — the calculated or observed value — that summarises how far the results depart from what the null hypothesis predicts. The critical value, read from the table, marks the boundary of "too extreme to be plausibly due to chance" at the chosen significance level. Comparing the two decides the outcome: if the calculated value is more extreme than the critical value (in whichever direction the test defines as "more extreme"), the result is significant and the null is rejected; if not, the result is non-significant and the null is retained. The three pieces of information needed to enter the table all shape where that boundary sits: a stricter significance level pushes the critical value further out (harder to reach); a one-tailed test concentrates the whole rejection region at one end, whereas a two-tailed test splits it, changing the critical value; and the sample size or degrees of freedom adjusts for how much data the estimate rests on. None of this requires you to compute the tests by hand for the exam, but knowing what the comparison means — rather than treating it as an arbitrary ritual — is what allows you to interpret an outcome correctly and explain it in words, which is exactly what the questions demand.
Parametric tests (such as the t-test, which OCR references as an alternative for suitable data) are more powerful — more likely to detect a real effect — but they make stronger assumptions. Think of the criteria below as a checklist: all three boxes must be ticked before a parametric test is justified, and a single failure sends you to a non-parametric alternative. This is a common exam trap — a question may describe data that meet two of the criteria but fail the third (for example, interval-level and normally distributed but with very unequal variances), and the correct answer is still to use a non-parametric test, because the requirement is all three together, not a majority of them or merely most of them. A test is only legitimately parametric if all three criteria are met:
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