Absolute numbers need proportions to inform policy

SOUTH Africa has undoubtedly made major strides since it shed the yoke of apartheid. An important achievement has been the higher rate of literacy, the result of adult basic education programmes and compulsory schooling. Almost 97 percent of children of school-going age attend school.

An important indicator of this achievement is not only the absolute increase in the number of children who have attained basic education, but also the proportional increase in each successive cohort.

Figure 1 shows the progress made in the attainment of basic education. The graph shows that, from 2001 to 2016, disadvantaged race groups moved upwards. This is also true in terms of absolute numbers.

The graphs for Indians, coloureds and black Africans show a progressive increase. In terms of absolute numbers, growth has been marked since the mid1990s, particularly among coloureds and black Africans.

Despite the improvements, in terms of both absolute numbers and proportionally, the quality of primary education remains a sore point.

At tertiary level, particularly at universities, enrolment has increased dramatically. The number of black African graduates is more than double the number of white graduates. The trend among coloureds and Indians has been flat trend in figure 2 graph on the left.

Dr Nick Spaull, an education researcher in the economics department at Stellenbosch University, in his analysis treated us to this important picture on the right graph.

In order to demonstrate that proportionality matters, let us look at figure 2, which has a graph on the left and a graph on the right. Many are deceived by what the graph on the left purports to show.

Although the absolute numbers are correct – the number of black African graduates has indeed grown four times over 28 years – they have not been rebased to take each population group’s contribution into account, as shown in the graph on the right.

Second, the representation has not been judged by the performance of cohort across time. The numbers are correct, but their graphical display by race represents a misleading analysis, and, in the current discourse, is at best deceptive, because it fails to show that black Africans are more than ten times the number of whites. So, if the number of black African graduates is twice the number of white graduates, the inequity has hardly been addressed.

The correct way of displaying this graphically would be, first, to represent them as a total figure, without a breakdown by racial group. Once they are broken down by race, they represent a comparison. But in order to compare apples, oranges, bananas and pears, you have need a common currency by which to define them. In this regard, the size of each population group must be the denominator, while the number of students from each group who graduate is the numerator. Then the comparison stands. But the graph on the left in figure 2 is mischievous and uneducated, to say the least.

Relook at the scorecard Many, like Spaull, equate an increase in an absolute number with progress. This fallacy of absolute numbers needs to be addressed. As a standalone figure, a score of 50 is bigger than a score of 40. But what if the 40 you scored was out of 45, and the 50 you scored was out of 60? The numbers alone are meaningless until you know the total out of which they are scored. A score of 40 out of 45 represents performance of 89 percent, which is higher than a score of 50 out of 60, which represents performance of 83 percent.

This demonstrates Spaull’s fallacious comparison in the graph on the left. Comparing a bigger number with a smaller one is meaningless, unless the two are juxtaposed against their relative denominators.

The reality of the situation is depicted in the graph on the right, which shows that, for every one black African who graduates, 4.5 whites graduate. Ratios matter, and progression ratios matter even more.

Let us now turn to progression ratios. We are applying the same analysis done in figure 1 to university education. Below is performance of the system for Whites as shown in figure 3.

Although the number of whites who graduate from university is less than half the number of black Africans who do so, based on figure 2 graph to the right from Mr Nick Spaull, their graph for Bachelors shows improving performance for all three data points.

Let us turn to black Africans, who, in terms of figure 2, have quadrupled as graduates, from about 12 000 a year to 48 000. This is an impressive achievement when measured in terms of absolute numbers. But the analysis shows a regression of each successive cohort. This puts paid to the notion that performance at 40/45 is indeed better than performance of 50/60. If such performance is sustained, it matters less what numbers succeed. For as long as the progress is an increasingly declining one then the danger signs of trouble ring across the system.

What is more troubling with the assertion by some analysts, is that despite the evidence obtained in this long-term analysis that in the eighties the performance of blacks was higher than currently,, they wish to deny this evidence shown on figure 4.

Progresively what figure 4 shows is that in the 1980s those classes of black Africans were progressively having a bigger proportion passing compared with the previous year. Currently, a smaller proportion succeeds, compared with the previous year. This is why progression ratios are a more accurate reflection of educational attainment than absolute numbers.

They unambiguously inform policymakers of the challenges of the performance of the system and not only its outputs which are totally unrelated to the inputs of the total system.

To conclude, I am reminded of the national anthem of Lesotho, a gift from a French missionary, the Reverend Francois Coillard, to the then Basotholand protectorate. Shortly after independence, three verses from the national anthem had to be removed because they were patronising and derogatory. Only two verses remained. The English translation of one of the offending verses ran: “Even though others consider Lesotho as small, for us it is big and is enough, we have ploughing fields, we have cattle and we are content.”

The unscientific optical illusion of the graphic representing numbers that have doubled in Spaull’s graphic on figure 2 as progress is really absurd, because it downplays equity as an objective of transformation. Second, it does not look at how the system is performing. Essentially, it is performing regressively for black Africans. In many ways, the arguments are like the three verses that had to be removed from the national anthem of Lesotho.

Hankering after absolute numbers without proportions and progression ratios is a perilous adventure in the policy space.