Comparación entre COBIT 4.1 y COBIT 5

To cope with variations in the slope parameter across population groups and regions, and possibly at various levels of learner changes, I sort them by population groups, to the extent that the sample size of each group can permit analysis. In preliminary analyses, I found that if I used primary and secondary schools separately, sample sizes for non-African schools at the provincial levels became too small.9

Figure 2.3 depicts relationships between changes in primary-school edu- cators and learners in 1996–2000 for all races and for different racial groups. The samples I use in this exercise are constructed as follows. Among schools that are successfully matched between SRN 1996 and 2000 by EMIS codes and province codes, I use only those classified by funding type as state or state-aided in 1996, those that show learner changes in the range of –1,000 to 1,000, and those that show educator changes in the range of –100 to 100. I dropped observations with missing values for the total number of educators in 1996 or 2000. Primary schools include normal primary (grades 1–7), junior primary (grades 1–4), and senior primary (grades 5–7) in the 1996 survey. Similarly, secondary schools include secondary (grades 8–12), junior second- ary (grades 8–10), and senior secondary (grades 11–12) in 1996. If schools changed the range of grades offered during the period, they experienced large increases or decreases in learners.

In Figure 2.3 the relationship is close to linear but shows a slightly con- vex shape. However, it is asymmetric between the point at which the num- ber of learners increases and the point at which it decreases. The response of educators to increases in the number of learners is larger than that to

9 _{In nonparametric analysis of cross-provincial differences among African schools (Eastern Cape,}

Free State, KwaZulu-Natal, Northern Province (Limpopo), North West, and Western Cape), I used the same criteria used in Figures 2.1 and 2.2. In all provinces, changes in educators responded to those in learners positively. Though we find some variations in the slope across provinces, the magnitude is very small among African schools. Strong nonlinearity cannot be detected in these figures. However, it seems that while some provinces, such as Eastern Cape, Northern Province, and North West, did not experience large changes in learners at the school level, other prov- inces, such as Free State, KwaZulu-Natal, and Western Cape, have gone through large changes in number of learners.

For African secondary schools by province, it is also found that changes in educators responded to those in learners positively in all provinces. However, except in KwaZulu-Natal, the variations in educator change seem to be larger in this case than those for primary schools. In this sense, the equity-improving interventions were larger in secondary schools, and thus worked to narrow the gaps across schools.

⫺49

⫺973 992

Change in number of educators 33

Sources: Republic of South Africa, Department of Education (1996, 2000).

⫺49

⫺973 992

33

Change in number of learners

Change in number of educators Figure 2.3B Dynamic changes: Primary school, African

⫺22

⫺535 606

19

Change in number of educators

Sources: Republic of South Africa, Department of Education (1996, 2000).

⫺21

⫺646 805

25

Change in number of learners

Change in number of educators Figure 2.3D Dynamic changes: Primary school, colored

⫺18

⫺487 514

24

Change in number of educators

Sources: Republic of South Africa, Department of Education (1996, 2000).

⫺15

⫺412 617

12

Change in number of learners

Change in number of educators

Figure 2.3F Dynamic changes: Primary school, new schools

decreases in the number of learners. In Figure 2.3B, in African schools, we have the same observations. However, for white, colored, and Indian/ Asian schools, nonlinearity becomes very strong (Figures 2.3C, 2.3D, and 2.3E). In white schools, while most observations show small changes in the number of learners, the overall shape is kinked with concavity (that is, there is slower adjustment when the number of learners increases). Among colored and Indian/Asian schools, however, the relationship is kinked and convex. Most observations in these groups also show small changes. In new schools that were established after 1994, the plot of results is nearly a straight line.

Figure 2.4 depicts results for secondary schools. As in the case of primary schools, a nearly linear but slightly convex relationship is observed in all schools in the country (Figure 2.4A). The basic relationship holds among Afri- can schools (Figure 2.4B). Figure 2.4C shows white schools: it looks strikingly similar to the case of primary schools. Though observations are less concen- trated in showing small learner changes than those for primary schools, the shape is kinked and concave. Strikingly, the number of educators does not respond significantly to large changes in the number of learners, but it does respond to small changes.

One interesting observation from all these figures is that the cross-school variations in educator changes are quite large. The variations are large even with small changes in learners. One way to explain this finding is that govern- ment interventions narrow the initially existing differences in LER, and that LER does not directly respond to changes in the number of learners. Alter- natively, even without government intervention, schools might have made efforts to weaken their liquidity (budget) constraints in order to adjust the number of educators. In either case, we expect that larger 1996 LERs induce larger subsequent increases in the number of educators.