A statistical analysis of the renumeration of teaching/research staff at Stellenbosch University for the years 2002 to 2005

Walters, Idielletta Sophia (2007-03)

Assignment (MSc) -- University of Stellenbosch, 2007.

Thesis

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.

AFRIKAANSE OPSOMMING: Die vergoeding van permanent-voltydse onderrig/navorsingspersoneel (C 1-personeel) by Stellenbosch Universiteit word in hierdie studie statisties ontleed. Daar word spesifiek gekyk na verskille in die vergoeding van manlike en vroulike personeel asook verskille in die vergoeding van die onderskeie fakulteite. 'n Datastel wat die totale koste van indiensname, voor enige aftrekkings, van permanent-voltydse onderrig/navorsingspersoneel bevat vir Desember 2002, 2003, 2004 en 2005 is deur die Afdeling Menslike Hulpbronne voorsien. Verskeie statistiese tegnieke is gebruik om die omvang en oorsake van die verskille in akademiese posisies by die Universiteit te ondersoek. Die enkel-veranderlike eienskappe van die vergoeding en ouderdom veranderlikes was ondersoek deur middel van beskrywende data analises. Hauer-en-punt stippings is gekonstrueer vir die vergoedings -en ouderdomsverdelings van permanent-voltydse onderrig/navorsingspersoneel by die Universiteit volgens fakulteit en geslag vir 2002 tot 2005. 'n Benaderde 95% vertrouensinterval is bereken vir die mediaan van elk van die verdelings en is aangedui met a kerf op elk van die houer-enpunt stippings. Die houer-en-punt stippings reflekteer duidelike verskille in die toename van die mediaan en gemiddelde vergoeding tussen die onderskeie fakulteite. Hierdie verskille is hoofsaaklik die gevolg van verskillende ouderdoms en geslagprofiele en verskillende rangstrukture binne die onderskeie fakulteite. Uitdienstreding van personeel en nuwe aanstellings wat gemaak word be"invloed oak die posisie van elke fakulteit verskillend. Die enkel-veranderlike ouderdom verdelings van die Universiteit en van elke fakulteit is oak ondersoek deur houer-en-punt stippings te konstrueer. Hierdie grafiese voorstellings reflekteer duidelike verskille tussen die mediane van die onderskeie fakulteite. Hauer-en-punt stippings wat gekonstrueer is vir die vergoedingsverdelings van manlike en vroulike personeel dui aan dat 'n algemene patroon voorkom tussen die verdelings van mans en vroue. Hierdie grafiese voorstellings onthul dat die mediaan en gemiddelde vergoeding van mans deurgaans hoer is as die vir vroue. Dit geld vir 2002, 2003, 2004 en 2005 in al nege fakulteite. Hierdie patroon kom oak voor in die houer-en-punt stippings wat die ouderdomsverdelings van mans en vroue reflekteer. Die mediaan en gemiddelde ouderdom van mans is deurgaans hoer as die van vroue. Nie-parametriese digtheidsfunksieberamings is gebruik om die onderliggende digtheidsfunksies van die vergoeding van elk van die fakulteite en van manlike en vroulike personeel binne elke fakulteit te ondersoek. Die digtheidsfunksies reflekteer verskeie van die eienskappe van die onderliggende verdelings wat deur die houer-en-punt stippings onthul is. Dit was voordelig om vir hierdie studie nieparametriese data gedrewe digtheidsfunksieberamings te gebruik in plaas van parametriese beramings soos die normaal verdelings aangesien baie van die vergoedingsverdelings skeet is. Die waarskynlikhede om meer te verdien as die vergoedingswaardes by die hoof modusse is bereken vir elke digtheidsfunksie met behulp van numeriese integrasie tegnieke. 'n Hoer gemiddelde vergoeding vir mans word gereflekteer deur die beraamde verdelings vir mans wat meer na regs gelee is as die verdelings vir vroue. Hierdie resultaat geld vir alle onderrig/navorsings personeel by die Universiteit en vir elke fakulteit vir 2002, 2003, 2004 en 2005. Bevorderings, nuwe aanstellings en salarisverhogings wat plaasgevind het van 2002 na 2005 word gereflekteer deur digtheidsfunksieberamings wat wyer word met swaarder sterte en hoof modusse wat na hoer vergoedingswaardes beweeg van 2002 na 2005. Die hoof doelwit van hierdie studie is om te bepaal watter faktore is verantwoordelik vir die verskille tussen die vergoeding van manlike en vroulike onderrig/navorsingspersoneel. 'n Beter begrip van die verwantskappe tussen die veranderlikes word verky deur 'n meerveranderlike analise op die datastel uit te voer. Die enkel-veranderlike houer-en-punt stippings het nie die verwantskap tussen ouderdom en vergoeding in ag geneem nie. Die houer-en-punt stippings van ouderdom en vergoeding vir die Fakulteite van Natuurwetenskappe, AgriWetenskappe en Gesondheidswetenskappe het aagedui dat daar moontlik 'n verwantskap tussen vergoeding en ouderdom is. Hierdie verwantskap word ondersoek deur twee-veranderlike 'bagplots' te konstrueer vir elke fakulteit sowel as vir manlike en vroulike onderrig/navorsingspersoneel by die Universiteit en binne elke fakulteit. Die 'bagplot' verskaf 'n opsomming van die eienskappe van die onderliggende twee-veranderlike verdeling van vergoeding en ouderdom. Die vergoedingsdatastel bestaan uit die volgende veranderlikeis: vergoeding, ouderdom, rang, akademiese kwalifikasies en navorsingsuitsette van onderrig/navorsingspersoneel. Die verwantskappe tussen hierdie veranderlikes word bestudeer deur hoofkomponentanalise bistippings te konstrueer. Hierdie bistippings reflekteer die meerveranderlike variasie van die nege fakulteite en van manlike en vroulike personeel in die vergoedingsdatastel vir 2005. Die meerdimensionele verandering in die vergoedingsdatastel van 2002 to 2005 is gemeet deur kanoniese variasie analise bistippings waarop alpha-sakkies gesuperimposeer is. Kanoniese variasie analise bipstippings verskaf 'n twee-dimensionele voorstelling wat die nege fakulteite sowel as manlike en vroulike onderrig/navorsingspersoneel optimaal skei. Die bistippings vir die nege fakulteite is gekonstrueer met 90% alpha-sakkies wat daarop gesuperimposeer is. Hierdie alpha-sakkies dui die lokaliteit van elke fakulteit aan en kwantifiseer die oorvleueling of skeiding van die nege fakulteite. In die kanoniese variase analise bistippings vir manlike en vroulike personeel is 50% alpha-sakkies gebruik. Kanoniese variasie analise bistippings met 50% alpha-sakkies is oak gekonstrueer vir onderrig/navorsingspersoneel met die range Junior Lektor en Andere, Lektor, Senior Lektor, Medeprofessor en Professor. Kanoniese variasie analise bistippings kan slegs gekonstrueer word as die aanname van gelyke binnegroepe kovariansie matrikse geld. lndien hierdie aanname nie geld nie word 'n analise van afstand bipstipping gekonstrueer om die groep of klas verskille te ondersoek.

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