Past exam of the experimental design and methods course of the year 2 of the psychology (experimental) course of the University of Oxford / 2022 / 3

Use one-way analysis of variance to compare a quantitative response variable across levels of one categorical factor; for example, compare task accuracy across three independently assigned teaching methods. The ordinary independent-groups procedure tests the null hypothesis that all group population means are equal. Its F-test compares variation associated with the group factor against within-group error variation; a significant result indicates that not all population means are equal, without identifying which groups differ.^[ref]

The classical one-way normal linear model assumes independent observations and within-group errors approximately following a normal distribution with a common variance. Repeated observations on the same people require a different dependence structure; pronounced unequal variances may call for Welch's one-way analysis of variance. Planned contrasts or appropriately controlled follow-up comparisons identify scientifically relevant differences. Report the means, differences and confidence intervals, not just significance. Causal interpretation depends on the design of experiments, particularly randomization, rather than on the F-test alone.

Use a bivariate correlation to describe the direction and strength of association between two measured variables, such as study time and test score. The Pearson correlation coefficient describes linear association between two quantitative variables: its sign gives direction, and its magnitude reflects linear association on a standardized scale. A confidence interval describes estimation uncertainty; a corresponding hypothesis test can assess a specified null association under its sampling assumptions.

Inspect a scatter plot for curvature, clusters, influential observations and restriction of range. A coefficient near zero does not exclude a strong nonlinear relationship. For ordered or markedly nonnormal measurements, a Spearman rank correlation can describe monotone association, using ranks; it does not require a linear relation in the original units. Ordinary inferential procedures require independent observational units and appropriate assumptions for their chosen method. Correlation alone does not identify a causal direction or exclude confounding.

Use a Student t-test to assess a mean or mean difference relative to its standard error. A one-sample version compares a population mean with a specified reference. An independent two-sample version compares two separate groups, such as groups assigned different instructions; Welch's t-test permits unequal group variances. A paired t-test uses within-pair differences, such as each participant's before/after scores, rather than pretending those measurements are independent.^[ref]

The relevant normality assumption concerns within-group errors for the independent-groups model or the distribution of within-pair differences for the paired model. Independent participants or pairs remain essential. Report the estimated difference and its confidence interval together with the test result. A small p-value indicates incompatibility with the specified null hypothesis under the model; it does not measure the size of the difference, the probability that the null hypothesis is true, or whether the difference matters practically.