On Ratio Correlation in Petrography

The same ratio correlation may be generated by many different combinations of relationships between absolute measures, but a single set of absolute-measure statistics leads to one, and only one, correlation between any particular set of ratios formed from these absolute measures. The passage from ratio correlation to inference about relations between absolute measures is ambiguous at best and often misleading. Algebraic statements exhibiting ratio correlation as a function of absolute-measure statistics are offered for types of ratios commonly used in petrography. These statements are all derived from Pearson's general formula for index correlation. They yield good approximations only if the fraction s/x for each absolute measure is suitably small. Several practical examples drawn from petrographic literature are described. In most of these cases the ratios seem to have been used either to order the data or in the hope that they would throw some light on relationships between absolute measures. The results are shown to be on the whole indecisive and ambiguous and in a few cases decidedly misleading. The formation of ratios should be confined to those problems in which hypotheses being tested deal with ratios. Absolute measures are always preferable when large numbers of observations must be recorded without benefit of satisfactory hypothesis. Ratios can always be drawn from tables of absolute measures; frequently, absolute measures cannot be reclaimed from tables of ratios.