**4. Identification and removal of legitimate contaminants in PDA**

#### **4.1 Correction for bias of discriminant weights in PDA**

In general, extreme scores or outliers bias estimates of any parameter. One notable way to correct for bias is to change the data by changing the scores so as to reduce the impact of the extreme scores or adjust the shape of the distribution. Notable variants of changing the scores method include transforming the data, trimming the data and winsorizing the data. However, in PDA, where one is interested in differences between set of variables or groups, transformation may not be a good choice to correct for bias of discriminant weights. This is because, transformation can change the units of measurements, which may in turn affects the interpretation of the data because the data now relate to a different construct compared to the original data [47]. Similarly, trimming of data seemed odd since one could just discard lots of data. To overcome these inherent drawbacks associated with both methods, the winsorization method was adopted. These approach involves replacing a percentage of the highest score with the next highest score in the data and the same percentage of the lowest score are

replaced with the next lowest score in the data. One major challenge with this method is that even the next higher or lowest score might still be an extreme score. Another variant of the winsorization involves replacing extreme score with a score three standard deviations from the mean. This variant of winsorization also suffers a major drawback. As noted by Field [47], the standard deviation will be biased by extreme scores, so this means that you are replacing scores with a value that has been biased by extreme scores. To address the observed shortcomings of both variants of the winsorization method, Iduseri and Osemwenkhae [6] proposed the modified winsorization with graphical diagnostic (MW-GD) method. The method proved very effective in identifying and removing legitimate contaminants.
