NUMERICAL CONSEQUENCES OF CHANGING THE UNITS IN WHICH CHEMICAL-ANALYSES OF IGNEOUS ROCKS ARE ANALYZED

Chemical analyses of igneous rocks have been expressed in a variety of units and many previous workers have expressed a preference for one transformation form or another (oxide weight percentages, molecular amounts, grams per 100 cc, etc.). Transformations which operate on the columns of a data matrix (containing the measured chemical constituents) can be described as simple linear transformations which change the means and variances of the columns but not the coefficients of variation of the columns or the correlation coefficients between columns. Such transformations include changing from oxide weight percentage to molecular amounts or normalizing to some constant value. If the investigator applies a numerical or graphical method of analysis to the original and column transformed forms of the same data set any differences must be attributed to the transformation itself. If the column transformed data are converted to percentage form (such as forming molecular percentages from molecular amounts) all of the summary statistics are likely to change. Transformations which operate on a row of the data matrix (such as multiplication by sample density to convert oxide weight percentages to grams/100 cc) result in changes in the summary statistics of each column and the correlations between all pairs of columns. Equations can be written which express the properties of the columns of the row transformed data matrix in terms of the properties of the non-transformed (parent) data matrix. An investigator may have a preference as to the units in which to express chemical variations(s) of igneous rocks but such preference must be based on petrogenetic criteria and not on a comparison of the statistics of the transformed and non-transformed forms of the same data set. © 1979.