Past exam of the experimental design and methods course of the year 2 of the psychology (experimental) course of the University of Oxford / 2022 / 7

Use cluster analysis to discover groups of observations with similar profiles when no correct group labels have been supplied. For example, it could group lecturers by patterns of reported organizational behavior. Define the analysis unit and features, handle missing data, and choose scaling and a meaningful similarity measure; otherwise a feature with large numerical units may dominate the groups.

K-means clustering partitions observations around centers, whereas agglomerative hierarchical clustering produces nested groupings represented by a dendrogram. Their results include group membership and interpretable profiles, conditional on these choices. Check stability across resampling and reasonable analysis choices and, when possible, in new data. A clustering does not prove that natural psychological types exist: an algorithm can partition a continuous distribution. Its units are cases; factor analysis instead primarily models shared variation among measured variables.

Use logistic regression when the response variable is binary, for example whether a lecturer missed a deadline. It relates the event's log odds to one or more predictors, producing fitted probabilities between zero and one. Exponentiating a coefficient gives an odds ratio for a specified predictor change, conditional on the other model terms. An odds ratio is not generally a ratio of probabilities; the corresponding probability change depends on the starting probability and other predictors.

Report the outcome coding, estimated associations with confidence intervals, and relevant model checks. Sparse events, complete separation and dependent observations can make ordinary estimates or inferential procedures unreliable; repeated observations may need a generalized linear mixed model. For prediction, evaluate calibration and discrimination on data not used to tune the model. An adjusted association in an observational study does not automatically identify a causal effect.

Use factor analysis when several observed measurements may reflect fewer unobserved dimensions, such as related questionnaire items about planning, prioritization and record keeping. A common-factor model separates shared variation represented by latent factors from item-specific variation. Factor loadings describe how measurements relate to those latent factors; communalities summarize their shared-variance contributions.

Exploratory factor analysis investigates a structure not yet fixed; confirmatory factor analysis evaluates prespecified measurement restrictions, preferably in independent data. Extraction, factor count and factor rotation affect interpretation, so report them and justify the sample and measurement assumptions. A statistically convenient factor solution does not alone establish construct validity or demonstrate the existence of a literal psychological mechanism. The distinction from principal component analysis is the common-versus-total-variation objective, and from cluster analysis the modeling of measurement relationships rather than the grouping of cases.