His research interests included multivariate statistics, multidimensional scaling and measurement, quantitative behavior genetics, test theory and mathematical tools for social scientists.
In particular, he claimed that (1) Arthur Jensen and others routinely confuse the first principal component (PC1) with g as Charles Spearman defined it, and that (2) the high IQ heritability estimates reported in the literature derive from restrictive formal models whose underlying assumptions are rarely tested and usually violated by the data.
[8] Spearman's hypothesis asserts a correlation between the g-loadedness of IQ tests and measures of their hereditability, a concept put to work in Arthur Jensen's discussion of black—white race differences from the 1980s.
[9] The important proviso for Spearman's claim that such a g qualifies as an "objective definition" of "intelligence", is that all correlation matrices of "intelligence tests" must satisfy this necessary condition, not just one or two, because they are all samples of a universe of tests subject to the same g. Schönemann argued that this condition is routinely violated by all correlation matrices of reasonable size, and thus, such a g does not exist.
[10] In a number of publications, Schönemann argued that the statistical heritability estimates used in most twin studies rest on restrictive assumptions which are usually not tested, and if they are, often are found to be violated by the data.