The hypothesis is tested using arrest statistics of the Uniform Crime Reports for the years 1953-1984. Statistics on the Index crime rate and on the individual Index crimes are included in the analysis. The age-period-cohort analysis reveals large age and period effects but small cohort effects. The statistical tests demonstrate that cohort size is not a good predictor of cohort variability. No cohort size effects emerges on the Index crime rate or the individual Index crimes. Thus, the data do not support the hypothesis. We suggest possible explanations for this contrary findings and speculate that the cohort size thesis is flawed on theoretical grounds. (Author abstract)