Many psychometricians and behavioral geneticists believe that high heritability of IQ test scores within racial groups coupled with environmental hypotheses failing to account for the differences between the mean scores for groups lends plausibility to explanations of mean differences in terms of genetic factors. I show that heritability estimates and the statistical analysis of variance on which they are based have limited relevance in exposing genetic and environmental factors operating within any single group or population. I begin with agricultural investigations, (...) where replication of genetic types and control over environmental factors are possible, and highlight the difficulties of moving from AOV of observed traits to investigation of measurable genetic factors. The difficulties can only be exacerbated for human data sets, which are equivalent to a crop trial in which each variety is replicated in only one or two of the locations. (shrink)