Diskriminationsparameter

Diskriminationsparameter is a statistical quantity used to quantify how well one or more variables differentiate between two or more predefined groups. It appears most commonly in analysis of variance (ANOVA), multivariate pattern classification, and item analysis in educational testing. The parameter is generally defined as the ratio of the variance between group means to the residual or within‑group variance. For two groups, the formula can be written as D = (μ₁−μ₂)²/(σ₁²+σ₂²), where μ and σ² are the means and variances of the groups. In the case of multiple groups, a generalized form involves the eigenvalues of the between‑group scatter matrix divided by the within‑group scatter matrix.

The discriminationsparameter provides a dimensionless measure of class separation; values close to zero indicate poor discrimination, whereas larger values suggest that the variable(s) carry substantial information about group membership. In classification problems such as linear discriminant analysis (LDA), the parameter informs the selection of features that maximize separation. In educational measurement, a related concept is the point‑biserial correlation between an item score and a total test score, which is also interpreted as a discrimination index. The term is sometimes confused with Fisher’s F‑ratio, which is essentially the same ratio expressed in a different form.

Historically the concept dates back to the early twentieth century work of Karl Pearson, Ronald Fisher, and others on multivariate distributions and hypothesis testing. It remains a staple in statistical tables, software packages, and research literature dealing with group comparison and classification. Despite its long history, the discriminationsparameter is still sometimes misused or interpreted incorrectly, especially in exploratory data analysis where the assumptions of homoscedasticity and normality may be violated.