Performance evaluation of classication methods: the case of equal mean discrimination.

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This study considered the equal mean discrimination problem by evaluating the performance of Bartlett and Please method, Bayesian Posterior Probability Ap-proach, the Quadratic Discriminant Function (QDF) and the Absolute Euclidean Distance Classi er method (AEDC) under equal and unequal prior probabilities and non normality contamination. Stocks (1933) twin data recorded in London on 832 children based on ten selected measurements was used because it satis- es the assumptions of the equal mean populations. Four discriminant functions were derived and their error rate estimates determined using the Cross Valida-tion (CV) and Balanced Error Rate (BER) methods. Results from equal prior probability showed the Bayesian Posterior Probability classi er performing bet-ter than the three other classi ers, thus it provides maximum separation with a recorded mean error rate of 0.149. Under the unequal prior probability situa-tion, Bartlett and Please method outperformed both the QDF and the Bayesian posterior probability classi ers under the sampling ratios, 1:2, 1:3 and 1:4. For non-normality, all four classi cation methods recorded higher mean error rates indicating abysmal performance of the methods. However, Bartlett and Please method was found to be very sensitive to outliers. We recommend the Bayesian approach and the AEDC methods for classifying observations with equal prior probabilities, Bartlett and Please method under unequal prior probabilities and QDF for non-normal contamination with equal prior probabilities.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfilment of the requirement for the degree of MPhil Mathematical Statistics,.