THE INVERTED STUDENT DENSITY AND TEST SCORES

Abstract

ABSTRACTThe inverted student density is one whose contour lines are spheroidal as in the normal distribution, but whose moments differ from those of the normal in that its conditional arrays are not homoscedastic, being quadratic functions of the values of the linear regression functions. It is also platykurtic, its measure of kurtosis ranging from that of the normal to that of the uniform depending on the value of a parameter: as that parameter increases the inverted student distribution approaches normality. Measures of kurtosis are given for distributions of scores on a number of cognitive tests, and they are almost all seen to be platykurtic. Data are presented showing that a quadratic term contributes substantially to the regression of conditional variances on test scores in a bivariate distribution. These data suggest that the inverted student distribution may provide a better description of distributions of test scores than does the normal.