Data for empirical example in: An effect size for comparing the strength of morphological integration across studies

Understanding how and why phenotypic traits covary is a major interest in
evolutionary biology. Biologists have long sought to characterize the
extent of morphological integration in organisms, but comparing levels of
integration for a set of traits across taxa has been hampered by the lack
of a reliable summary measure and testing procedure. Here we propose a
standardized effect size for this purpose, calculated from the relative
eigenvalue variance, Vrel. First we evaluate several eigenvalue dispersion
indices under various conditions, and show that only Vrel remains stable
across samples size and the number of variables. We then demonstrate that
Vrel accurately characterizes input patterns of covariation, so long as
redundant dimensions are excluded from the calculations. However, we also
show that the variance of the sampling distribution of Vrel depends on
input levels of trait covariation, making Vrel unsuitable for direct
comparisons. As a solution, we propose transforming Vrel to a standardized
effect size (Z-score) for representing the magnitude of integration for a
set of traits. We also propose a two-sample test for comparing the
strength of integration between taxa, and show that this test displays
appropriate statistical properties. We provide software for implementing
the procedure, and an empirical example illustrates its use.