Lies, Damned Lies and #WomenED Statistics Part 2February 3, 2016
Last time I discussed how, despite 66% of headteachers being women, it was claimed that there were too few female heads. In this post I will deal with a couple of cherry picked statistics used to justify this claim. Both of these statistics tend to be accurate, but misleading.
The first statistic is the difference between the proportion of women teachers and the proportion of women headteachers. 75% of classroom teachers are women, so why 66%, not 75%, of heads? My immediate response has always been to ask “why would they be?” Heads are not a random sample of teachers; headship is not a universal aspiration for all teachers. Many factors could explain the difference without any women losing out just because they are women, not least an acceptance that wanting a career in management is not necessarily a good thing, and that those without this ambition are not “failures” or being deprived by not having this ambition.
However, before I go too far down this route of explaining the alleged “discrepancy” in terms of human behaviour, I should point out there is no need for this sort of explanation. Statisticians are familiar with the rule of “regression to the mean”. I should be careful here, “regression to the mean” is defined in different ways, some of which may not apply here. However, the basic principle is that when you measure something and get an extreme value, then further measurements (even if related to the first measurement) are likely to be less extreme. This is why, if you look at the students who did best in one test, they are likely to do less well in the next test, and those who did worst in the first test are likely to do better in the next test. This is why the children of very tall parents are, on average, less tall than their parents and the children of very short parents are likely to be taller than their parents. (This also came up here.) Extreme measurements are not easily repeated, even when the first measurement is likely to be correlated to the second. Whether or not what I have been describing here can be labelled as “regression to the mean”, there is definitely a similar problem here. Because the population of classroom teachers is so skewed towards being women, it is highly unlikely that the population of heads would be skewed to the same degree.
Without any need for discrimination against women, or a prejudice against women leaders, or a reason for some women not becoming heads, we would expect the population of headteachers to be skewed towards being women, but not to the same degree as classroom teachers. And that’s what we’ve got, a large majority of heads are women, but not in the same proportions as classroom teachers. This is not unfairness or inequality; this is just how statistics work. We should be very careful to watch out for attempts to obscure this. A number of people have referred to the ratio of female heads to female teachers as a measure of the “likelihood of promotion” or “the prospects of promotion” as if it measured opportunities for advancement. To assume that an individual’s opportunities are measured by the statistics for their gender is to assume that appointments are made on the basis of gender, the very claim that is at issue here. What we have here are two connected, but distinct populations, and while the number of women classroom teachers is likely to affect the number of women heads, it was never likely to determine it and, given the extreme gender imbalance among classroom teachers, it would have been highly unlikely that there would have been the same imbalance among heads.
The second figure used to suggest a shortage of women is that for secondary heads. According to the workforce survey, only 37% of secondary heads are female (it might be 36%, as my figures are rounded and I have heard that figure quoted a lot). This is probably the best evidence of an actual discrepancy between men and women in educational leadership, although why the dominance of men in secondary is more of a problem than the even greater dominance of women in primary is not usually explained. But, again, we should hesitate, and remind ourselves how statistics work. Secondary heads account for only a sixth of heads, and we can expect at least some subsets of any population to depart from the rest of the population just by chance. This is why statisticians warn about “subgroup analysis”. There are bound to be anomalous subsets, and if it hadn’t been found by subdividing by sector, could we have found one by subdividing by region? Age? Race? Type of school? Without knowing what else would have been considered a cause for concern it’s hard to judge whether this should be. All we do know is, it is unreasonable to assume that all possible subsets of headteachers would have as many (or more) women as men. That’s not to say there is nothing to be explained here. The “regression to the mean” argument I used earlier does not apply in the secondary sector and the problems of subgroup analysis may not be enough to explain why the proportions in secondary are so different to the proportions in primary, but the mere fact that there is a subset of schools with more men than women as heads should not, in itself, be of concern.
Even after all this, I cannot rule out that there are no issues relating to gender that affect women’s opportunities to become school leaders. All I can say is that we are yet to have reliable evidence for this. I’m happy to endorse any (rigorous) effort to acquire that evidence, and research into application rates and differences in ambition would be a good place to start. But until that evidence is found, then #WomenEd remains a campaign against a problem that may not even exist and the question of why people want to convince others that the problem exists should be asked.