Browsing by Author "Walters, Idielletta Sophia"
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- ItemA statistical analysis of the renumeration of teaching/research staff at Stellenbosch University for the years 2002 to 2005(Stellenbosch : Stellenbosch University, 2007-03) Walters, Idielletta Sophia; Le Roux, N. J.; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.ENGLISH ABSTRACT: This assignment investigates the gender and faculty remuneration gap of permanent full-time teaching/research staff members at Stellenbosch University. A dataset providing detailed information on teaching/research staff members over the period 2002 through 2005 was used. Several statistical techniques were employed to assess the extent and causes of the remuneration gap in academic positions at the University. The univariate properties of the remuneration and age variables were studied by exploratory data analyses. Boxplots were constructed for the remuneration and age distributions of permanent full-time teaching/research staff at the University and according to faculty and gender for 2002 and 2005. An approximate 95% confidence interval was computed for the median of each of the distributions and is indicated by a notch on each of the boxplots. The notched boxplots reflect clear differences in the increase of the median and average remuneration between the various faculties. These differences are mainly caused by different age and gender profiles and different rank structures in the various faculties. The retirement of older staff members earning high salaries and new appointments also influence the position of each faculty differently. The univariate age distributions of the University and of each faculty were also investigated by constructing notched boxplots. These graphical displays reveal clear differences between the medians of the various faculties. Notched boxplots constructed for the remuneration distributions of male and female staff members indicate that a general pattern occurs between the distributions for men and women. These graphical representations reveal that the median and average remuneration of men is throughout higher than that of women. This holds for 2002, 2003, 2004 and 2005 in all nine faculties. The same pattern occurs in the notched boxplots reflecting the age distributions of men and women. The median and average age of men is throughout higher than that of women. Non-parametric kernel density estimation is used to estimate the underlying densities of the remuneration of each of the faculties and of male and female staff members within each faculty. Most of the properties of the underlying remuneration distributions that were revealed by the boxplots are also reflected by the density estimates. For this study it is advantageous to use non-parametric data driven density estimates instead of parametric estimates like the normal distributions, because many of the remuneration distributions are skew. The probabilities to earn more than the remuneration values at the main peaks were calculated for each density function by numerical integration techniques. Higher mean earnings for men are reflected by the estimated distributions for men that lie more to the right than the distributions for women. This result holds for all teaching/research staff members at the University and for each faculty for 2002, 2003, 2004 and 2005. Promotions, new appointments and salary increases that occurred over the four years are reflected by density estimates that became wider with heavier tails and main peaks that moved towards higher remuneration values from 2002 to 2005. The main goal of this study is to determine which factors are responsible for the difference between the remuneration of male and female teaching/research staff members. A better understanding of the relationships among these variables is obtained by conducting a multivariate analysis on the dataset. The univariate notched boxplots did not take the relationship between age and remuneration into consideration. The notched boxplots of age and remuneration for the Faculties of Science, AgriSciences and Health Sciences indicate that there might be a relationship between remuneration and age. This relationship is investigated by constructing bagplots for each faculty as well as for male and female teaching/research staff members at the University and within each faculty. The bagplot provides a summary of the properties of the underlying bivariate distribution of remuneration and age. The remuneration dataset consists of the following five variables: remuneration, age, rank, academic qualifications and research outputs of teaching/research staff members. The relationships among the variables are studied through construction of principal component analysis biplots. These biplots reflect the multivariate variation of the nine faculties and of male and female staff members in the remuneration dataset for 2005. The multidimensional change in the remuneration dataset from 2002 to 2005 was measured by constructing canonical variate analysis biplots with superimposed alphabags. Canonical variate analysis biplots provide a two-dimensional display that separates the nine different faculties as well as male and female teaching/research staff members optimally. For the nine faculties 90% alpha-bags were superimposed to indicate the location of each faculty and to quantify the overlap or separation between the different faculties. In the canonical variate analysis biplots for male and female staff members 50% alpha-bags were used. Canonical variate analysis biplots with superimposed 50% alpha-bags were also constructed for teaching/research staff members with the ranks of Junior Lecturer and Others, Lecturer, Senior Lecturer, Associate Professor and Professor. However, canonical variate analysis biplots can only be constructed if the assumption of equal within group covariance matrices holds. If this assumption does not hold an analysis of distance biplot can be constructed to investigate group or class differences.