Analyzing the data of individuals has several advantages over analyzing the data combined across the individuals (the latter we term group analysis): Grouping can distort the form of data, and different individuals might perform the task using different processes and parameters. These factors notwithstanding, we demonstrate conditions in which group analysis outperforms individual analysis. Such conditions include those in which there are relatively few trials per subject per condition, a situation that sometimes introduces distortions and biases when models are fit and parameters are estimated. We employed a simulation technique in which data were generated from each of two known models, each with parameter variation across simulated individuals. We examined how well the generating model and its competitor each fared in fitting (both sets of) the data, using both individual and group analysis. We examined the accuracy of model selection (the probability that the correct model would be selected by the analysis method). Trials per condition and individuals per experiment were varied systematically. Three pairs of cognitive models were compared: exponential versus power models of forgetting, generalized context versus prototype models of categorization, and the fuzzy logical model of perception versus the linear integration model of information integration. We show that there are situations in which small numbers of trials per condition cause group analysis to outperform individual analysis. Additional tables and figures may be downloaded from the Psychonomic Society Archive of Norms, Stimuli, and Data, www.psychonomic.org/archive.