Looking times (LTs) are frequently measured in empirical research on infant cognition. We analyzed the statistical distribution of LTs across participants in order to develop recommendations for their treatment in infancy research. Our analyses focused on a common within-subject experimental design, in which longer looking to novel or unexpected stimuli is predicted. We analyzed data from two sources: an in-house set of LTs that included data from individual participants (47 experiments, 1584 observations), and a representative set of published papers reporting group-level LT statistics (149 experiments from 33 papers). We established that LTs are log-normally distributed across participants, and therefore should always be log-transformed before parametric statistical analyses. We estimated the typical size of significant effects in LT studies, which allowed us to make recommendations about setting sample sizes. We show how our estimate of the distribution of effect sizes of LT studies can be used to design experiments to be analyzed by Bayesian statistics, where the experimenter is required to determine in advance the predicted effect size rather than the sample size. We demonstrate the robustness of this method in both sets of LT experiments.