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AS & A Level · AS/A Level

Psychology

Data analysis and inference

Name: ____________________Date: October 10, 2026
  1. 1.

    Fictional recall scores are 4, 5, 5, 6 and 10 words. Calculate the mean and median and identify which is more affected by the highest score.

    [3 marks]

    Answer explanation

    Draft walkthroughs are based on marking guidance, not independently verified derivations.

    1. Order the scores to locate the middle observation. The high score pulls the arithmetic mean upward while the median stays at the central ranked value.

    Marking points

    • Mean = 30/5 = 6 words.
    • Median = 5 words.
    • The mean is more affected because every score contributes to the sum.

    Examiner tip: With five ordered observations the median is the third score.

  2. 2.

    Fictional survey: hours of social-media use correlate positively with reported loneliness. Explain why this alone does not establish that use causes loneliness.

    [3 marks] · no calculator

    Answer explanation

    Draft walkthroughs are based on marking guidance, not independently verified derivations.

    1. A shared pattern fits several causal stories. Without identifying temporal ordering and ruling out plausible confounds, the survey supports association rather than a unique causal explanation.

    Marking points

    • Direction may be reversed: lonely people may spend more time online.
    • A third variable such as social circumstances could influence both.
    • Correlation measures association without experimental manipulation or control of all alternatives.

    Examiner tip: Give a specific alternative explanation for the observed association.

  3. 3.

    Fictional study: in 20 paired observations, 16 show improved scores, 2 worse scores and 2 ties. For a sign test discard ties and define S as the less frequent sign count. Calculate N and S. A supplied critical S is 4 at the chosen significance level; reject when S <= 4. State the decision and one limitation.

    [4 marks]

    Answer explanation

    Draft walkthroughs are based on marking guidance, not independently verified derivations.

    1. Remove ties before choosing the applicable sample size. Compare the smaller sign count with the supplied lower-tail threshold; the conclusion concerns evidence against the null, not proof that every participant improves.

    Marking points

    • N = 20 - 2 = 18 non-tied pairs.
    • S = 2, the less frequent sign count.
    • 2 <= 4, so reject the null hypothesis under the supplied decision rule.
    • Accept any explained valid sign-test limitation, such as ignoring change magnitudes or potentially lower power than an appropriate magnitude-sensitive test; significance is not an effect-size estimate.

    Examiner tip: Small S, not large S, triggers rejection under this rule.

  4. 4.

    Fictional independent-group result: mean scores are 18 and 14; both groups have standard deviation 5. Using d = (mean A - mean B)/5 for this equal-SD case, calculate d. Explain why the effect size alone does not show statistical significance or causation.

    [4 marks]

    Answer explanation

    Draft walkthroughs are based on marking guidance, not independently verified derivations.

    1. Standardise the mean difference by the common SD supplied. This expresses relative magnitude, whereas significance asks about uncertainty and causation asks about design.

    Marking points

    • Mean difference = 4 points.
    • d = 4/5 = 0.8 standard-deviation units.
    • Significance also depends on sample size and sampling uncertainty.
    • Causal inference requires suitable design and confound control, not a large d alone.

    Examiner tip: Do not read d = 0.8 as an 80% improvement.

  5. 5.

    Fictional case: researchers obtain p = 0.04 and announce a theory is 96% likely to be true. Evaluate this interpretation and the evidence needed for a stronger conclusion.

    [4 marks] · no calculator

    Answer explanation

    Draft walkthroughs are based on marking guidance, not independently verified derivations.

    1. The claimed 96% reverses the conditioning. A small p can challenge a null model without validating every part of a theory; inspect the methods, effect estimate and replication record.

    Marking points

    • Indicative: p concerns the probability of results at least as extreme under the null model and assumptions.
    • It is not the probability that the theory or null hypothesis is true.
    • Effect size, uncertainty, design quality and multiple-testing decisions affect interpretation.
    • A justified conclusion treats the finding as limited evidence requiring replication rather than proof.

    Examiner tip: State what p is conditioned on before interpreting it.

  6. 6.

    Fictional case: a researcher tests many outcomes, reports only the significant one and calls the finding confirmatory. Evaluate the reliability of this evidence and propose improvements.

    [4 marks] · no calculator

    Answer explanation

    Draft walkthroughs are based on marking guidance, not independently verified derivations.

    1. Exploration can generate hypotheses, but selecting after seeing results is not the same as a planned confirmatory test. Report all analyses and test the selected hypothesis in new data.

    Marking points

    • Indicative: multiple tests increase the chance of obtaining at least one false-positive result.
    • Selective reporting hides the full evidence and makes the result appear more decisive.
    • Preregistered outcomes and transparent reporting distinguish planned from exploratory analyses.
    • A justified conclusion calls for suitable multiplicity handling and independent replication.

    Examiner tip: Do not condemn exploration itself; identify undisclosed selection.