Experimental psychologists routinely simplify the structure of their data by computing means for each experimental condition so that the basic assumptions of regression/ANOVA are satisfied. Typically, these means represent the performance (e.g. reaction time or RT) of a participant over several items that share some target characteristic (e.g. Mean RT for high-frequency words). Regrettably, analyses based on such aggregated data are biased toward rejection of the null hypothesis, inflating Type-I error beyond the nominal level. A preferable strategy for analyzing such data is random coefficient analysis (RCA), which can be performed using a simple method proposed by Lorch and Myers (1990). An easy to use SPSS implementation of this method is presented using a concrete example. In addition, a technique for evaluating the magnitude of potential aggregation bias in a dataset is demonstrated. Finally, suggestions are offered concerning the reporting of RCA results in empirical articles.