Non-Parametric Statistics

Abstract

Beginning statistics students are usually introduced to what are called “parametric” statistics methods. Those methods utilize “models” of score distributions such as the normal (Gaussian) distribution, Poisson distribution, binomial distribution, etc. The emphasis in parametric statistical methods is estimating population parameters from sample statistics when the distribution of the population scores can be assumed to be one of these theoretical models. The observations made are also assumed to be based on continous variables that utilize an interval or ratio scale of measurement. Frequently the measurement scales available yield only nominal or ordinal values and nothing can be assumed about the distribution of such values in the population sampled. If however, random sampling has been utilized in selecting subjects, one can still make inferences about relationships and differences similar to those made with parametric statistics. For example, if students enrolled in two courses are assigned a rank on their achievement in each of the two courses, it is reasonable to expect that students that rank high in one course would tend to rank high in the other course. Since a rank only indicates order however and not “how much” was achieved, we cannot use the usual product–moment correlation to indicate the relationship between the ranks. We can estimate, however, what the product of rank values in a group of n subjects where the ranks are randomly assigned would tend to be and estimate the variability of these sums or rank products for repeated samples. This would lead to a test of significance of the departure of our rank product sum (or average) from a value expected when there is no relationship.