Werdelin, L. and B.S. Tullberg. 1995. A comparison of two methods to study correlated discrete characters on phylogenetic trees. Cladistics 11: 265-277.

We use a simulation approach to study two methods proposed for the analysis of correlated discrete characters on cladograms, the concentrated changes test (CCT) and the contingent states test (CST). Both of these consider the case where there is an independent and a dependent character and assign probabilities to various events in the dependent character given one or the other state of the independent character. The CCT gives different results for symmetric and asymmetric cladograms. In the latter case, the proportion of branches reconstructed as having the derived state has less influence on the resulting probabilities. The CST is only sensitive to the proportion of derived branches, regardless of whether the tree is symmetric or asymmetric. The CCT calculates probabilities by considering character state reconstructions which are not allowed by parsimony algorithms, thereby increasing the probability of rejecting a true null hypothesis (type I error rate). We discuss some alternative questions that could be studied using these tests and also derive equations for calculating the number of possible events in the dependent character for unresolved parts of the phylogeny.