A vector-based goodness-of-fit metric for interval-scaled data

Abstract

With interval-scale data, goodness-of-fit is conceptualized as the degree of dissimilarity between a set of n idealized values and a set of suitably scaled sample scores. Depending on the choice of the idealized values, the dissimilarity statistic, h, can encompass a number of extant statistics (e.g., all probability-plot statistics, and normal model Shapiro-Wilk W and Shapiro-Francia W statistics). In gerneral, however, two other methods of defining the idealized markers can be utilized (i.e., a method based on the mean-value theorem, and a method based on the concept of zonal medians). Evidence is provided that the resulting h statistic is both computationally straightforward and powerful.

Keywords:

• testing distributional models
• probability plots
• dissimilarity metric
• expected-order values