The extent to which certain phenotypes are more likely to be attained than others (evolutionary “bias”) is among the central questions in evolutionary biology. Character covariation plays a pivotal role in quantitative investigations on evolutionary bias, and dispersion (variance) of eigenvalues of a covariance matrix, standardized to the number of variables, is often used as a measure of bias. However, sampling properties of this measure are not well known, complicated by the fact that eigenvalues are not stochastically independent of one another in a sample covariance matrix. Here, sampling properties of the dispersion of eigenvalues of a covariance matrix are investigated with simulations of i.i.d. or Brownian-motion-based normal samples for a range of moderately low p/n (number of variables / sample size) ratio, and a simple framework is proposed for detecting evolutionary bias from comparative datasets. Simulations showed that, as expected, the dispersion measure tends to be overestimated, especially when its population value is small. The upward estimation bias decreased markedly with increasing n, but did not vary prominently with p in the conditions examined. The (apparent) precision increased with increasing n and p. For empirical cases, observed values of the dispersion measure can be compared with parametric bootstrapping and Monte Carlo null distributions to assess estimation bias and to test hypothesis of no evolutionary bias, respectively. When dealing with comparative datasets, phylogenetic generalized least squares-based estimation of covariance was found to be by far superior to the non-phylogenetic counterpart, at least in idealistic situations where the true tree is known and assumed evolutionary model is correct. Influence of stabilizing selection and high p/n ratio should be investigated in the future.