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Correlation Statistics

A number of measures of correlation are implemented for nucleotide and morphological characters and their states.

Statistics for measuring morphological character and state associations, first described by Huelsenbeck et al. (2003), have been implemented in SIMMAP to test for state-by-state associations (see measures shown on the right of Figure 1 below). D is the overall association between character i and j. d is a measure of the association between the individual states of each character. a is the observed (o) or expected (e) association between character state i and j (n is the number of states for character 1 and m is the number of states for character 2. The association between one state and another is the frequency of occurrence of states on the phylogeny.

The association measure for molecular (nucleotide) characters is simply the Chi-square statistic with a Yate's correction term (C = 0.5).

Alternatively, SIMMAP 1.5 implements a statistic similar in form to the mutual information content statistic (MIC) for both nucleotide and morphological data types. As implemented in SIMMAP 1.5, this statistic evaluates the correlation between character histories along the phylogeny for two characters (M) and their states (m) where f is the fraction of time one state is associated with another in a character history.

                        Figure 1.