Abstract:

Introduction
The evaluation of academic yield for a given subject has been determined traditionally by means of a final exam. However, this scenario is changing. Nowadays, university students are often requested to make different kinds of assignments along the year that are assessed by the lecturer in order to obtain partial scores that contribute to the final mark. As a result of this continuous assessment, at the end of the year, the lecturer may have a set of about 10 to 20 partial marks available from each student that, properly weighted, lead to the final mark. If this mark reaches a certain threshold, the student passes the subject. If the final mark is very close to this threshold, the exam is reviewed with more detail and the lecturer has to decide with some criterion, which might be a bit subjective sometimes, whether or not the student passes the subject.
Principal component analysis (PCA) is a useful technique for explaining the data variability of a matrix, as well as for the interpretation of relationships among observations and variables. The first principal component (PC1) is the combination of the original variables that explains the highest amount of the total data variability. In this paper, PCA was applied to a real dataset of academic marks. This paper analyzes if PCA might be useful as a complementary tool to decide whether or not students with a final mark close to the threshold should pass the subject.

Materials and methods
The dataset for this study corresponds to partial marks of 80 students in their first-year subject ‘Applied Physics’, corresponding to the degree of Agricultural Engineering at the Universidad Politécnica de Valencia in the academic year 2007-2008. As a result of the continuous assessment, 19 marks were available from each student at the end of the academic year. A PCA was applied to this matrix using the program SIMCA-P 10.0 (www.umetrics.com) after centering the data and scaling to unit variance. The cross-validation criterion was used to determine how many principal components account for the relevant information in the dataset.

Results and conclusions
PC1 explains 43.6% of the total data variance. After projecting all students over the direction determined by PC1, it was observed that the scores were strongly correlated with the final mark, which indicates that PC1 reflects the academic yield of students. The variables with highest loadings in PC1 correspond to the final mark followed by the semester marks and the fourth partial marks. These marks are the most representative, as it could be expected. PC1 discriminates between students who passed the subject versus those who failed, but the borderline between pass and fail is not very well determined. Some students close to this borderline, who failed the subject according to the final mark criterion, would have passed according to the PC1 criterion. Thus, this suggests that the marks of these students should be revised because their final result (i.e., pass or fail) might change with a slight modification of the initial assignment weight coefficients. The second principal component (PC2), which is orthogonal to PC1, explains 10.3% of the data variance. PC2 discriminated between marks corresponding to the first versus the second semester, which means that students did not devote the same effort to prepare both semesters.
The proposed methodology could be used as a complementary tool for decision making in academic yield evaluation.

Keywords:

yield assessment, multivariate statistics, principal component analysis.