Continuing our investigation, we find also find a strong positive relationship between test score inequality, measured as the difference between the 95th and the 5th percentile, and average performance. The higher the difference between pupils, the higher average performance. The same analysis can be found in the PISA report, although it compares the 90th and the 10th percentiles. The results are very similar. I also looked at the absolute standard deviation in scores as a measure of inequality. Again, results are very similar.
We only find a different picture if we look at the coefficient of variation (sometimes called the relative standard deviation). The coefficient of variation is the ratio of standard deviation divided to the mean. This variable is indeed correlated with average performance in a way that suggests a virtuous equality-efficiency relationship. But the measure is not too interesting if we are interested in inequalities per se, simply because it takes into account (and indeed ‘rewards’) countries’ performance. That is tantamount to mixing apples and oranges, performance and equality, which is untenable. Either we focus on variation between pupils and/or schools in the different systems, or we focus on their achievement.