Tests of the hypothesis that group-specific <i>R</i> matrices have more structure than expected by chance (noise analysis).

<p><i>i</i> is an index for three partitions (groupings) of the data based on amino acid physiochemical properties. is the observed distance between a <i>i</i>^th group-specific rate matrix (<i>R_i</i>) and the rate matrix for the complete data (<i>R</i>₀). is the distance between a the <i>j</i>^th random partition (denoted by *) of the complete data and the and the rate matrix for the complete data (<i>R</i>₀). <i>j</i> is an index of 50 different random partitions of the data. The <i>t</i>-statistic is for a one-sample <i>t</i>-test. <i>p</i>_Bonf is the Bonferroni adjusted <i>p</i>-value.