DA Calculations Demonstrated with a Simple Example

This section is dedicated to the interested reader who wants to follow the major steps of discriminant analysis and also to inform him of further mathematical details. (For the calculations we use a pocket calculator and sometimes rounded values small differences may, therefore, occur if other precision or programmed algorithms are used.) Again we start from the raw data we first used in cluster analysis, Tab. 5-10. 

We have five objects each with two features. The objects are classified according to the result of cluster solution 1 class 1 contains objects Kl, K3 and K4 (n1 = 3), class 2 has the two elements K2 and K5 (n2 = 2). With the objects written as 

As we mentioned in the preceding section, multivariate analysis of variance, like discriminant analysis, uses the scatter matrices B and W. 

Unfortunately, test statistics are not easy to understand and critical values are normally not available from standard -tables. However, in our two-class case we have the advantage that Fexp of Eq. 5-34 is / -distributed with 

With sp (BW 1) = 12.9868, Fexp = 12.9868 (C = 1) is to be compared with Fcnt (2 2 0.95) = 19. Therefore, at a significance level of a = 5%, we have to conclude that the variance encountered in B and fkoccurs only by chance, in other words, from the statistical point of view the classes are not separable. 

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