On the Application of Multivariate Test of Hypothesis to Compare Advanced Mathematical Abilities (Published)
The multivariate test of means, using the Hotelling’s T2 distribution, has vast applications in many real-life situations; education inclusive. Prominent amongst them is the test of means between two groups; say treatment and control groups in tests scores given an intervention. The objective of this study was to apply the Hotelling’s T2 distribution to compare the performance of mathematical science students in Kaduna Polytechnics, Nigeria in Advanced Mathematics. In specifics terms, the study wishes to determined the mean difference between the students’ Advanced Mathematical abilities for treatment and control group in tests scores using three variables; Linear Algebra, Calculus I and Calculus II. The treatment intervention is an introductory algebra taught for ten weeks. In order to compare only two populations, multiple t-tests may be considered, but such analyses may result in an unacceptably high probability of Type I error. To avoid this problem, a single multivariate hypothesis testing procedure (omnibus test) serves better. This omnibus test of two group means is conducted using the Hotelling’s T2 distribution. After the data analysis using the SPSS, the results have revealed that the treatment group produces better results than the control group in Advanced Mathematical abilities. Furthermore, the descriptive statistics have also affirmed that the treatment group produces better results of Advanced Mathematical performance than the control group. Moreover, this was further confirmed by the individual Analysis of Variance (ANOVA) test. In general, the treatment has enhanced performance in Advanced Mathematics. Hence, the treatment in form of tutorial (In Introductory Algebra) for ten weeks, has significantly improved the performance of students in Advanced Mathematics. By extension, we conclude that the treatment (In Introductory Algebra) is effective.
Keywords: Analysis of Variance (ANOVA) test, Hotelling’s T2 distribution, Multivariate test, covariances, dispersion matrix, mean vectors, omnibus test, univariate test, variance-covariance matrix