Discriminant functions.

Discriminant Functions (DFs), first described by Fisher in 1936, have been applied to the classification of microcytic disorders such as iron deficiency and heterozygous thalassemia. Mathematically DFs are weighted linear combinations of variables. If the underlying assumption of multivariate normality is valid DFs provide the best possible classification. Variables may need to be transformed before the DF is derived. When two groups have to be classified it is easy to visualise the DF. With one variable the DF is represented by the point which provides the best separation. In the bivariate situation the two groups form ellipses and the DF is the best line of separation whilst in the trivariate case the two groups are ellipsoids and a plane forms the best separation. Ratios and power functions are equivalent to DFs but they are less efficient and less rigorously derived. To apply DFs in hematological practice it is necessary to carefully select the measurements to be included and to define the case selection criteria. Once the DF has been derived it should be tested on a new data set and its transferability assessed. Like any single test the DF will have sensitivity and specificity which may need to be adjusted by changing the "cut-off" if the DF is used for screening rather than for differential diagnosis.