Schönemann's PhD thesis "A solution of the orthogonal Procrustes problem with applications to orthogonal and oblique rotation," proposed a solution to the orthogonal Procrustes problem. Other Schönemann papers include "A generalized solution of the orthogonal Procrustes problem", "The minimum average correlation between equivalent sets of uncorrelated factors", and "Some new results on factor indeterminacy" co-authored with M.M. Wang. Schönemann wrote also numerous book chapters, including the "Psychometrics of Intelligence" chapter in Encyclopedia of Social Measurement and the “Heritability” chapter in Encyclopedia of Human Intelligence.
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. Schönemann regarded this work as resting on a conceptual confusion. Schönemann argued for the non-existence of psychometric g. He wrote that there is a fundamental difference between g, first defined by Charles Spearman as a latent one-dimensional variable that accounts for all correlations among any intelligence tests, and a first principal component of a positive correlation matrix. Spearman's tetrad difference equation states a necessary condition for such a g to exist. 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.
Twin studies
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. He argued that this was true for the monozygotic twins raised apart vs. together studies as well as for the more widely used MZT vs dizygotic twins raised together studies. For example, the narrow heritabilities of responses to the question "did you have your back rubbed" work out to 0.92 heritable for males and 0.21 heritable for females. Using the statistical models published in Loehlin and Nichols the question "Did you wear sunglasses after dark?" is 130% heritable for males and 103% for females.