Skewness, and transformations of Farnsworth-Munsell 100-Hue test scores

Abstract

In the past, suggested transformations of Farnsworth-Munsell 100-Hue Test (FM 100-Hue) test scores distributions have been limited to a square root transformation. In this study, the choice of transformations of total error scores (TES) are considered by identifying a possible source of skewness. Several distributions of FM100-Hue Test TES were assessed for skewness (third moment). The error score (ES) distributions for the 85 individual caps in each of the populations were also analysed for skewness (Figs. 3 and 4). There is no single transformation which will normalise all TES distributions. The single cap ES distributions with low mean ES (such as those achieved normals and, for some regions of the test, by anomalous trichromats and dichromats) are symmetrical because most subjects can organise the cap perfectly (and could do even better given smaller colour differences). The distributions of ESs where the mean ES is in the moderate range (such as those achieved by diabetics) are skewed because some ESs at the lower end of the range represent performance which could also be better than the test allows. ES distributions with a high mean (such as random distributions and some regions of the test by congenital dichromats) are symmetrical being unaffected by the limitations of the test. TES distributions of diabetics are asymmetrical and comprise skewed cap ES distributions. A suggestion for a transformation is made.