This post
was first published on the IEA blog
Note: the
graphs in this post display correlations only. They are used to discuss
relationships some argue exist, not to draw causal conclusions.
We
are often told that school systems with the highest performance are also the
most equitable. For example, when the PISA 2012 results were released, Janet
Downs, of the Local Schools Network, argued
that ‘PISA found that the most successful school systems tend to be those which
are the most equitable. These systems don’t just concentrate on excellence for
some but provide excellence for all’. But what do we mean by equity? And is the
‘virtuous cycle’ hypothesis true?
Here, I sidestep the issue
of causality, which Downs and the OECD completely ignore, and rather focus on
the relationship that we are told exist. The OECD defines a system combining
quality and equality as (1) having high performance and (2) low impact of pupil
background on achievement, and as a system where (3) all individuals reach a
basic minimum level of skills. But while (2) might be an appropriate definition
of equality, (3) has nothing to do with it properly speaking. In traditional
terms, if country A has a lower mean score than country B, but smaller
differences between pupils/schools, country A is still more equal. A high
performance floor may very well be the result of a strong focus on efficiency
instead of equality. Indeed, a trade-off between the two is often assumed in
economic theory.
To investigate the
relationship between equality and efficiency in international surveys, I
instead look directly at the relationship between performance and inequities in
outcomes within education systems. That can give us an indication of whether
equality in results does indeed go hand in hand with higher performance.
I use the latest PISA
results, which tend to be considered the ultimate yardstick for whether or not
school systems perform well (although I disagree). In the first graph, we find
that there is in fact a weak but statistically significant positive correlation between
between-school variance and performance. The measure here is the variance
between schools as a percentage of the total variance in the country (in itself
expressed as the percentage of the average variance in all countries).
In the below graph, I hold
constant the performance variance within schools, but there is still no
relationship between equality between schools and performance. In fact, the
between-school variance is now even more strongly and positively correlated
with results. Thus, there is no support for the argument that low
between-school variation in performance is related to high average scores.
But what happens if we
focus on differences between pupils, which I argue is a better measure of
equity in the education system? Well, that doesn’t change the picture. In the
graph below, I look at the relationship between within-school variation and
performance, holding between-school variation constant. The relationship is
even stronger than the positive relationship between between-school variation
and mean performance.
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.
Another way to measure the
relationship between performance and equality is to look at the relationship
between the strength of the impact of pupils’ background on scores and average
performance. The below graph shows that while the trend line points downwards,
the relationship is not significant.
In other words, there is no relationship between the impact of background and
performance.
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.
To sum up, therefore, it
does not seem to be the case that high equality and high average performance
walk hand in hand. If anything, we find a negative correlation. Again, I want
to emphasise that the above has nothing to do with causality. I have also
ignored the (different) question of how changes in equality are related to
changes in performance, to which I will come back in a future piece. But I do
question the argument that the highest performing education systems are those
that combine quality with equity, as is often contended in the debate. This
contention is simply not supported by the data.