**6. Conclusions**

This paper addresses the issue of achieving a statistically optimal classification accuracy in PDA by first achieving an optimal training sample. For the first real dataset, a training sample of four variables was obtained using the SPSS stepwise method. The training sample gave a hit rate of 86.0%. When all legitimate contaminants in one of the four variables have been identified and eliminated using the MW-GD method, an optimal training sample was achieved. The optimized training sample was used to construct the PDF, *Zopt* (13) which gave a classification accuracy of 97.0% when tested on the initial training sample of four variables. This significant increase in classification accuracy suggests that the use of the WM-GD method seems to effectively enhance the similarity of each predictor variable variances between groups, thus taken into account the basic assumptions needed to achieve a statistically optimal classification accuracy. Using the second real dataset, a training sample of three variables was obtained and used to construct the PDF, *Z* (16), which yielded 85.0% hit rate. When the modified mean values of the three variables were plotted, the bar shape of the three variables in the two groups was similar. This means that the PDF, *Z* (16) hit rate of 85.0% cannot be increased further because the training sample that gave birth to it was statistically optimal.

The uniqueness of the MW-GD method lies in its ability to effectively identify and eliminate legitimate contaminants in one or several predictor variables, thus resolving any significant differences in the variances of the predictor variables between the groups. In other words, the MW-GD method is unique in its ability to sufficiently account for the basic assumptions required to achieve statistically optimal classification accuracy in PDA. As a result, an optimal training sample obtained from the first real dataset gave a statistically optimal hit rate of 97.0% compared to an initial maximum hit rate of 86.0%. For the second real dataset, the method was successful in confirming the optimality of the initial training sample obtained using the SPSS stepwise method. Similarly, the graphical diagnostic was able to identify the predictor variable(s) whose variance was not similar within the groups. Consequently, the graphical diagnostic associated with the proposed method could be used as an alternative graphical test of homogeneity of variances in PDA.

Another important contribution to the MW-GD method in this paper was the proposed alternative statistical interpretation for the graphical diagnostic associated with the MW-GD method demonstrated in Subsection 5.2. This proposed alternative statistical interpretation proved very effective in terms of identifying the variable with legitimate contaminants, and could serve as a useful alternative tool for identifying variables with legitimate contaminants in the event of any difficulties in differentiating between a variable shape in the groups of the 2-D area plot.

Finally, two real training samples have been used. Consequently, the validity of the experimental results is limited to the scope of the datasets used. Therefore, this paper believes that more experimental results are needed in order to reach a final conclusion on the efficiency of the MW-GD method compared to classical alternatives known to improve classification accuracy in PDA.
