Four experiments tested the hypothesis that people's appreciation for the statistical law of large numbers may at times lead them to ignore other important statistical information when making inferential judgments. In Experiment 1 subjects were presented with either a small or a large dataset that detailed the performance of two racquetball players, each of whom played a different number of games in two different leagues. Results indicated that, compared to large dataset subjects, small dataset subjects were more likely to aggregate across situations and thus less likely to take into account the confounding effects of the league. Experiment 2 demonstrated that this effect occurs even under conditions in which people are explicitly informed about the differing situational constraints. Experiment 3 again replicated the effect, and examined more closely the effects of sample size on within-situation performance assessments as well as on statistical inference strategies. Experiment 4 replicated the sample size effect in a more socially relevant judgment domain involving inferences about intelligence. These results illuminate an intriguing and ironic relation between different aspects of everday statistical reasoning. Discussion focuses on the implications for inference processes and social judgment. © 1992.