Multivariate normality tests of planktonic foraminiferal data

Abstract

Data of a microfossil group, the planktonic foraminifera, have been tested to determine the conformity of various real data distributions to univariate and multivariate normality and the effects that standard transformations have upon the distributions. Studies of two bivariate samples, one trivariate sample, and two quadrivariate samples of size data indicate that distributions frequently deviate greatly from multivariate normality. Univariate distributions are generally positively skewed and show a tendency for leptokurtosis. A logarithmic transformation improved both univariate and multivariate distributions but the number of distributions conformable to normality increased only slightly—from zero to one in the multivariate case and from one to four in the univariate case (totally 15 distributions). Arcsine (p/100)1/2transformations of percentage data in two samples including 16 and 23 species, respectively, decreased highly significant deviations from multivariate normality but distributions remained greatly non-normal. Although markedly positively skewed and leptokurtic univariate distributions were improved in most instances, the number of normal distributions (two) did not change. It follows that neither of the transformations caused significant increases in the number of normal distributions but if it is assumed that the consequences of non-normality are less severe as the deviation from normality decreases, the transformations are justified.