We present a simple mathematical technique that we call granularity-related inconsistency of means (GRIM) for verifying the summary statistics of research reports in psychology. This technique evaluates whether the reported means of integer data such as Likert-type scales are consistent with the given sample size and number of items. We tested this technique with a sample of 260 recent empirical articles in leading journals. Of the articles that we could test with the GRIM technique (N = 71), around half (N = 36) appeared to contain at least one inconsistent mean, and more than 20% (N = 16) contained multiple such inconsistencies. We requested the data sets corresponding to 21 of these articles, receiving positive responses in 9 cases. We confirmed the presence of at least one reporting error in all cases, with three articles requiring extensive corrections. The implications for the reliability and replicability of empirical psychology are discussed.