Tag Archives: transposed matrix

Maximization of Systematic Variance in Research Design (Published)

The main focus of a research design, whether in pure or applied sciences, is the study of variances in the collected data. Technically, the systematic variance is maximized, the error variance is minimized and the effects of extraneous variables are controlled. In the pure sciences, the maximization of the systematic or desirable variance is done by a good spread in the level of the factors in the study by pulling them apart. In behavioral sciences it is quite easy when the factor(s) are categorical or inanimate. The levels of the factor(s) are deliberately pulled apart. It is a problem when the factor is continuous. Several methods have been advocated. In this study, five of such methods are compared- the use of sample mean and standard deviation, theoretical mean and standard deviation, the correlation coefficients from the transposition of Person by Item Matrix, factor score and factor analysis methods. Two validated instruments designed to measure students attitude towards mathematics and tendency to cheat in examinations, were administered on a sample of 100 students of Cross River University of Technology, Calabar, Nigeria. The students’ scores were grouped on basis of their attitude towards Mathematics, using the five methods. One-way ANOVA was carried out with the categorized Mathematics Attitude score as factor and their tendency to cheat in examinations as the dependent variable. The proportions, of the total variance, in the dependent variable, accounted for, in each of the five methods, were compared using the Fishers’ Z-test, for all possible pairs of the explained variances. The results showed that four out of the ten paired comparisons were significant, with grouping using sample mean and standard deviation, accounting for the total variance highest. The grouping base on sample mean and standard deviation is recommended and the implications for behavioral research design discussed.

Keywords: Correlation, Factor analysis, factor loadings, factor scores, person by item matrix, systematic variance, transposed matrix