Thesis ((Ph.D. (Mathematics Education)) -- University of Limpopo, 2016 / The focus in this thesis was on the approaches that seek to compare two study arms in the absence of randomisation when the interclass correlation coefficient is greater than zero. Many reports on performance of learners in Grade 12 have used ordinary regression models (such as logistic regression model and linear regression models) which ignore clustering effect, and descriptive statistics (e.g., averages and standard deviations for continuous variables, and proportions expressed as percentages and frequencies). These models do not only bias point estimates but also give falsely narrow confidence intervals. The study was applied to two of the nine provinces of South Africa: Gauteng Province and Western Cape Province in 2008, 2009 and 2010 academic years. Causal models, and in particular, hierarchical models (or disaggregated approach), unlike descriptive analyses, are more powerful as they are able to adjust for individual covariates. For the analysis of continuous variables; Western Cape Province was expected to significantly score higher marks than Gauteng Province in 2008 (Crude estimate: 0.782) and 2009 (Crude estimate: 0.957 ) while Gauteng Province was expected to score higher marks than Western Cape Province in 2010 (Crude estimate: −0.302). Adjusted models indicate that Western Cape Province performed better than Gauteng Province in 2008 and 2009 but not in 2010 where Gauteng Province performed better than Western Cape Province after adjusting for gender. In case of binary outcome; the crude estimates favoured Western Cape Province than Gauteng Province in 2008 (Odds ratio = 1.16) and 2009 (Odds ratio = 1.19). Otherwise, the crude estimates favoured Gauteng Province in 2010 (Odds ratio = 0.11). The proportion of female learners in Gauteng Province ranged between 54.48% and 54.99%, while in Western Cape Province it ranged between 56.78% and 57.16%, in 2008 through 2010 academic years. Proportion of female learners in Western Cape Province were found to be higher than those in Gauteng during this period. At least 70.42% of learners in Gauteng and at least 73.96% of learners in Western Cape Province passed Grade 12 during the years 2008 to 2010. Through the application of causal model we have learned that although gender is not a significant predictor of the overall learner performance in Grade 12, the effect of gender gave the mixed findings depending on the nature of the outcome. The xi effect of gender on continuous endpoint (marks) suggests that a model of single-sex classrooms or single-sex schools may be adopted so as to mitigate the inherent perceptions and stereotype regarding learner-gender. However, the results based on binary endpoint (pass/not pass) suggest that coeducation system is the best bet. A school quintile is a significant predictor of the overall learner performance in the two provinces. The resourceful schools are more likely to produce learners with higher marks. Also, the resourced schools than the less or under resourced schools are more likely to produce the favourable results (higher marks (%) or/and pass) in the two provinces.