Fig. 5.

Comparison of Bayesian mixed-effects model with summary statistics for detection of changes on the group level, i.e. finding a negative slope for different ground truth effect sizes. Posterior probabilities (upper part) and p-values from summary statistics (lower part) are shown under variations of first (left) and second (middle) level error variances and design types (right). Summary statistics here means using independent linear models for every subject and calculating p-values from a one-sample t-test of obtained slope parameters. Realizations of ensembles of 64 subjects with 5 annual scans per person. These were sampled under balanced/unbalanced designs and subsequently modeled. Balanced here means that every subject has the same average age at measurements while unbalanced means a uniform distribution of each subject's average age across the whole study interval [20, 80]. All probabilities are shown as a function of (from left to right increasing) ground truth effect size, i.e. increasing steepness of decline. Results are obtained from averaging across 200 realization of ensembles for each parameter configuration. Color shading indicates the manipulation of the variable of interest, i.e. error sizes (left and middle) and balanced design property (right). Here, p-values and posterior probabilities show similar dependence on effect sizes in balanced designs (see black curves right plot). Posterior probabilities show a gain of sensitivity when designs become unbalanced (see ochre curves in right plot) while summary statistics perform similarly for both designs. Probabilities in left and middle plot are averages across multiple design types.