Discriminant Analysis

A technique of multivariate analysis in which new variables are calculated from the original, large number of variables and this function is combined with classification. Discriminant functions are especially calculated to show up differences between previously defined groups of items (e.g. artifacts from several different sites), whereas principal components do not make any distinction between groups. The object of the classification is to see how widely separated the multivariate distributions of a number of previously defined groups of items are in hyperspace. The results are presented as a classification results table in which the known grouping of items is compared with the most likely grouping, calculated from the variables supplied from the analysis. An example of useful classification would be in comparing groups of skulls from different sites on the basis of their measurements.

A technque of multivariate analysis. Most discriminant analysis programs perform two operations. One is to calculate discriminant functions and the other is known as ‘classification’. Discriminant Functions. New variables which are calculated from the original, large number of variables. The discriminant functions are somewhat akin to principal components — calculated so that most of the variation in the original distribution is squeezed into the first few functions, which can then be plotted or analysed statistically. The difference between the two methods is that discriminant functions are specially calculated to show up differences between previously defined groups of items (for instance artefacts from several different sites), whereas principal components do not make any distinction between groups. Classification. The object of this operation is to see how widely separated are the multivariate distributions of a number of previously defined groups of items in hyperspace. Each item is taken in turn, and the likelihood of its belonging to a group is calculated for each of the group distributions. The results are presented as a ‘classification results table’ in which the known grouping of items is compared with the most likely grouping, calculated from the variables supplied to the analysis. The smaller the proportion of items ‘correctly classified’ in this way, the more overlapping are the previously defined groups. Conversely, the larger the proportion ‘correctly classified’ the less the groups overlap. Classification is, for example, particularly useful in comparing groups of skulls from different sites, on the basis of their measurements. Discriminant analysis can be, and was originally, done by ‘pencil-and-paper’ methods, but nowadays it is usually carried out by digital computer. See also computer, STATISTICS.