Pass/Fail Determination Using Examination Scores

Abstract

In this chapter, we examine the k-fold cross-validation for small sample method (Method 1) by combining the resampling technique with k-fold cross-validation. By this breakthrough, we obtain the error rate means, M1 and M2, for the training and validation samples, respectively, and the 95 % CI of the discriminant coefficient and the error rate. Moreover, we propose a straightforward and powerful model selection procedure where we select the model with minimum M2 as the best model. We apply Method 1 and model selection procedure to the pass/fail determination using examination scores. By setting the intercept to one for seven LDFs, we obtain several good results, as follows: (1) M2 of Fisher’s LDF is over 4.6 % worse than Revised IP-OLDF. (2) The soft-margin SVM (S-SVM) for penalty c = 1 (SVM) is worse than other five MP-based LDFs and logistic regression. (3) We obtain the 95 % CI of the discriminant coefficients. If we select the coefficient median of seven LDFs, with the exception of Fisher’s LDF, the coefficient median is almost the same as the trivial LDF for the linearly separable model. (4) Although these datasets are LSD and show the natural feature-selection, we do not introduce this theme because there are only four independent variables.