Explaining Anomalous GCSE Results

How educational statistics have been used to mislead about race in the United Kingdom

Britain’s Black African student population does much better on General Certificates of Secondary Education (GCSE) examinations than on IQ tests. The gap on IQ tests tends to be somewhere between 7 and 10 points, whereas lately there’s generally no gap or higher performance for Black Africans relative to White Britons when it comes to the GCSEs. I’m not the first to notice this fact, nor that the gap between the two types of tests has grown over the years. Some people have argued that GCSE results show Black Africans living in the U.K. are just as smart as White Britons, but that idea conflicts with the observations from IQ tests, so what’s the deal?

One possibility is that the discrepancy is due to sampling: the people who take the GCSEs may not be the same sorts of people who take IQ tests. While this is a possible explanation, it is also an unlikely one, as we have norming sample data for Britain’s Cognitive Abilities Test (CAT), we have representatively sampled data from the OECD’s Programme for International Student Assessment (PISA), and we know that known GCSE results apply only to public schoolers in England, thus underrepresenting the abilities of White Britons relative to Black Africans.

Sampling is an unlikely explanation, but some people still believe it. The truth is that there’s absolutely no reason to believe it and good reason to not believe it, but this is about the only way the discrepancy can be explained if you’re committed to the idea that the GCSEs show Black Africans and White Britons are intellectual equals.

To remove the sampling argument from play, we merely have to observe high Black African GCSE performance and relatively low IQ test performance in the same sample.

It just so happens that the 2018 wave of the Millennium Cohort Study (MCS) provides us with exactly that in a nationally representative sample of 17-year-olds. These kids took cognitive tests in each wave of the study from the earliest years of their lives and their educational data has been linked to them.

So let’s see how GCSE performance in the required maths and English courses looks compared to measured general intelligence for this cohort:

Black Africans do relatively better on the GCSEs than in terms of measured general intelligence and the GCSE gaps in this sample are similar to the ones for the broader population of test-takers in English public schools in the 2016/2017 school year.¹

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Why This Result?

This finding tells us nothing new; those who have put any amount of thought into this topic were already aware the discrepancy was real and not driven by sampling concerns. This explicit finding simply takes away any room to debate the discrepancy exists. Now we have to explain it.

The short, simple explanation for this finding is that the GCSEs are biased indicators of general intelligence. This does not imply that they are biased in general, only that some of the group differences in results on them cannot be fully explained by differences in general intelligence. For clarity, imagine this hypothetical factor model:

If the Spatial Ability factor underlies performance on Q1 and Q2, failing to model it might lead to poor model fit. If it’s replaced by a covariance between the residuals of Q1 and Q2, that can make the model fit even when the factor that should be shown isn’t. But if the mean for Spatial Ability in one group is much higher than in another group, failing to model it could result in Q1 and Q2 having biased intercepts even if it was previously able to be modeled as a residual covariance.

If we’re talking about classroom assignments, tests, projects, and pretty much anything else where being a diligent student helps, there’s likely to be a bias in favor of girls over boys. Grades are related to intelligence, but at all levels of intelligence, girls tend to earn better grades than boys in the same classrooms. Part of this difference can sometimes be controlled away by adjusting for conscientiousness, but the point remains: if you tried to use classroom grades alongside IQ test results, the model would be biased in favor of girls.

A simplification of my MCS factor model

Similarly, when GCSE results are included alongside IQ tests, the result is evidence of bias in favor of girls relative to boys and Black Africans relative to White Britons. We know there’s bias when these variables are used to indicate intelligence, but we don’t have explicit knowledge of why. All we know is that there’s bias, and in both of these cases, it results in certain groups scoring better than they should for their smarts.

Many people have predicted this and, frankly, it was bound to be true. This resolves the mystery of why Black Africans in Britain appear to do so well on the GCSEs even though IQ tests don’t provide evidence that they’re that intelligent. The explanation is simply psychometric bias.

As an explanation, psychometric bias is not exactly satisfying since bias could be due to anything. If you want to know more, keep scrolling.

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Table of Contents

1. The Faulty GCSE Syllogism

2. GCSEs, CAT Performance, and Non-Invariant Correlations

3. Transitivity and IQ-Achievement Discrepancies

4. Revising the GCSE Syllogism

5. Freedom of Information Requests for Other British IQ Tests

6. Earlier Explanations

7. The Importance of Theory for Forming Hypotheses

8. Why I Am So Good At Making Predictions

9. The Millennium Cohort Study: Description and Parental Replication