There is increasing interest in cumulative approaches to science, in which instead of analyzing the results of individual papers separately, we integrate information qualitatively or quantitatively. One such approach is meta-analysis, which has over 50 years of literature supporting its usefulness, and is becoming more common in cognitive science. However, changes in technical possibilities by the widespread use of Python and R make it easier to fit more complex models, and even simulate missing data. Here we recommend the use of mega-analyses (based on the aggregation of data sets collected by independent researchers) and hybrid meta- mega-analytic approaches, for cases where raw data are available for some studies. We illustrate the three approaches using a rich test-retest data set of infants' speech processing as well as synthetic data. We discuss advantages and disadvantages of the three approaches from the viewpoint of a cognitive scientist contemplating their use, and limitations of this article, to be addressed in future work.
