Analyzing students' performance by factor analysis and discriminant analysis

Abstract

The objective of this dissertation is to observe the marks obtained by fourth former girls and boys in their final examination. An interesting analysis is to see whether there exists a difference between the marks obtained by boys and girls attending Junior Lyceum schools and who sat for the same examination paper. The marks were obtained from St.Theresa girls Junior Lyceum School and from Dun Guzepp Zammit boys Junior Lyceum. This data was inserted into the SPPS database and the results were analyzed by Factor Analysis and Discriminant Analysis. These were two techniques which were appropriate to analyze the data. Through principal component analysis, factor scores were obtained, showing us that in general a student who performs well in one subject tends to do well in all subjects. Also, a student who tends to do well in sciences may not perform so well in the language subjects. Taking the means of the examination marks, in all five subjects obtained by girls and boys gives us very interesting results. Evidently, boys performed quite badly with a difference of approximately 20 marks in every subject compared to the girls. Many researchers suggest that boys tend to do better in science subjects rather than in language subjects, while girls tend to do better in the language subjects rather than in the science subjects. We found that girls outperformed boys in all subjects. Discriminant Analysis was useful in finding the best line that separates the girls group from the boys group. There were certain cases were the two groups interacted in their general performance. So, a hypothesis analysis was used so that this could be seen more clearly. However, this was not the only test used because results from discriminant analysis, like sample distances and the classification statistics, were also used to verify our hypothesis. This difference in marks between genders is present since the most intelligent boys do go to church schools instead of Junior Lyceum schools. On the other hand girls have no other choice and the most intelligent girls attend the Junior Lyceum schools. The dispersion of the marks of the boys and girls in all subjects are very much the same. This suggests that boys should be streamed as well as girls to match students with the same ability.