what is the level of measurement (nominal, ordinal or interval)?

The five OCR tests are the sign test (difference, related, nominal), Wilcoxon (difference, related, ordinal), Mann-Whitney U (difference, unrelated, ordinal), chi-square (^2, difference or association, unrelated, nominal) and Spearman's rho (correlation, ordinal). :::

A researcher uses p ≤ 0.01 rather than p ≤ 0.05. Explain one effect of this choice. [3 marks]

EnglandPsychologySyllabus dot point

How do psychologists summarise data and decide whether a result is statistically significant?

Descriptive statistics (central tendency, dispersion, graphs) and inferential statistics: choosing and interpreting the sign test, Mann-Whitney U, Wilcoxon, Spearman's rho and chi-square.

An OCR A-Level Psychology answer to statistics, covering mean, median, mode, range and standard deviation, choosing the correct inferential test (sign test, Mann-Whitney, Wilcoxon, Spearman, chi-square) from level of measurement and design, significance, critical values and Type 1 and Type 2 errors for Component 1.

Generated by Claude Opus 4.816 min answerUpdated 2026-06-02

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

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Quick answer

Descriptive statistics summarise data: central tendency (mean, median, mode) and dispersion (range, standard deviation), shown with bar charts, histograms, scattergrams and the normal distribution. Inferential statistics test whether a result is unlikely due to chance. The OCR test follows from difference versus correlation, related versus unrelated design, and level of measurement: sign test (related, nominal), Wilcoxon (related, ordinal), Mann-Whitney (unrelated, ordinal), chi-square ( $\chi^2$ , nominal, association) and Spearman's rho (correlation). A result is significant at $p \leq 0.05$ ; the calculated value must beat the critical value (equal to or less for sign, Mann-Whitney and Wilcoxon; equal to or greater for chi-square and Spearman). A Type 1 error is a false positive and a Type 2 error a false negative.

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What this dot point is asking

OCR Component 1 includes the maths of psychology: summarising data with descriptive statistics, then testing whether a result is unlikely to be due to chance with an inferential test chosen from the OCR list. At least 10 per cent of the marks across the course assess these skills, so the test-choice decision and the significance rule must be automatic.

The answer

Descriptive statistics

Graphs display data: bar charts for categories, histograms for continuous data, scattergrams for correlations, and a normal distribution curve when data are symmetrically spread around the mean (mean, median and mode coincide).

Choosing an inferential test

Significance and errors

Calculating the mean and standard deviation

A psychologist records test scores of $4, 6, 8, 10, 12$ and wants the mean and standard deviation.

step 1 Calculate the mean

$\bar{x} = \frac{4 + 6 + 8 + 10 + 12}{5} = \frac{40}{5} = 8$ .

step 2 Find the deviations and square them

Deviations from the mean: $-4, -2, 0, +2, +4$ . Squared: $16, 4, 0, 4, 16$ . Sum of squares $= 40$ .

step 3 Compute the variance

Using the sample formula (divide by $n - 1 = 4$ ): variance $= \frac{40}{4} = 10$ .

step 4 Take the square root and interpret

Standard deviation $= \sqrt{10} \approx 3.16$ . This is the typical distance of a score from the mean of $8$ : a small standard deviation means consistent scores, a large one means widely spread scores.

Examples in context

Example 1. Reading a chi-square ( $\chi^2$ ) result. A study categorises participants by whether they were primed (yes or no) and whether they recalled a target (yes or no). These are nominal frequency counts in an unrelated design, so chi-square is correct. With a $2 \times 2$ contingency table the degrees of freedom are $df = (2 - 1)(2 - 1) = 1$ , and the critical value at $p \leq 0.05$ is $3.84$ . If the calculated $\chi^2 = 5.20$ , then because $5.20 > 3.84$ the result is significant: there is a significant association between priming and recall, with less than a 5 per cent probability it is due to chance.

Example 2. Interpreting Spearman's rho. A researcher measures revision hours and exam mark for 20 students and finds Spearman's $rho = +0.78$ ( $p \leq 0.05$ ). Spearman is correct because the data are ordinal and the aim is a relationship, not a difference. The coefficient $+0.78$ is a strong positive correlation (more revision is associated with higher marks), and significance means the relationship is unlikely to be chance. It does not prove revision causes higher marks, because a third variable such as motivation could drive both, so causation cannot be claimed from a correlation.

Try this

Q1. Name and justify the inferential test for ordinal data from a repeated measures design testing a difference. [3 marks]

Cue. Wilcoxon, because the data are ordinal, the design is related (repeated measures) and the aim is a difference.

Q2. Explain what is meant by a Type 1 error. [2 marks]

Cue. A false positive: rejecting the null hypothesis and accepting a difference or relationship that is not actually real.

Q3. A researcher uses $p \leq 0.01$ rather than $p \leq 0.05$ . Explain one effect of this choice. [3 marks]

Cue. It makes a Type 1 error less likely but a Type 2 error more likely, because the stricter level demands stronger evidence before a result is called significant.

Exam-style practice questions

Practice questions written in the style of OCR exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

OCR 20196 marksA researcher compares ratings (treated as ordinal) from two separate groups to test for a difference. Identify the appropriate inferential test, justify the choice, and explain how to decide whether the result is significant. [6 marks]

Show worked answer →

A test-choice and significance item (AO2 and AO3).

Test: Mann-Whitney U. Justification: the design is unrelated (two separate, independent groups), the data are ordinal, and the aim is to test a difference. Mann-Whitney is the OCR test of difference for an unrelated design with ordinal data (Wilcoxon would be wrong because it is for related designs).

Deciding significance: compare the calculated U value with the critical value from the statistical table for the relevant $N$ values and significance level. For Mann-Whitney the result is significant if the calculated U is equal to or less than the critical value at $p \leq 0.05$ . If so, reject the null hypothesis; if not, retain it.

Markers reward the correct named test, a justification referring to ordinal data and an unrelated design, and the correct rule (calculated equal to or less than critical for Mann-Whitney).

OCR 20226 marksEight participants' recall scores were

7, 9, 5, 8, 6, 10, 4, 7

. Calculate the mean and the range, and explain one reason a researcher might report the standard deviation rather than the range. [6 marks]

Show worked answer →

A full worked calculation (AO2) plus a reasoned point (AO3).

Mean: $\bar{x} = \frac{7 + 9 + 5 + 8 + 6 + 10 + 4 + 7}{8} = \frac{56}{8} = 7$ .

Range: highest minus lowest $= 10 - 4 = 6$ (some specifications add $1$ for the inclusive range, giving $7$ ; either is creditworthy if stated).

Reason to prefer standard deviation: the range uses only the two most extreme scores, so a single outlier distorts it, whereas the standard deviation uses every score and so gives a more sensitive, representative measure of how spread out the data are around the mean.

Markers reward the correct mean ( $7$ ), a correct range ( $6$ or $7$ with method shown), and a valid reason that the standard deviation uses all the data and is less distorted by extremes.

Related dot points

Sources & how we know this

OCR Level 3 Advanced GCE in Psychology (H567) specification — OCR (2015)