Lies, Damned Lies and #WomenED Statistics Part 2
February 3, 2016Last 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.
Scenes From The Battleground 
If this logic holds, then in male-dominated professions (say, engineering), we should expect there to be a much higher chance of women becoming leaders because of regression to the mean? Is that the right interpretation?
Good point, but actually I’m going to go with “yes” if everything else remains equal and there is no mechanism ensuring those who are promoted resemble those who aren’t. Although I wonder how many male dominated professions that applies to.
I couldn’t think of a single profession it would apply to. But I look forward to you arguing that a far higher percentage of women should become leaders of engineering companies (or cabinet ministers) in a way that is disproportionate to their numbers in the lower ranks.
Isn’t it already the case for Cabinet ministers,or are there more women on the Tory backbenches than I’d realised?
Look, he “can’t think of one”. Isn’t that enough evidence for you?
Do we need more female head teachers or fewer? The answer to this depends entirely upon your definition of equality.
If we want strict equality (i.e. 50% male and female across all levels of teaching) then we might draw one conclusion. If we want seniority to be representative of the population of teachers, then we might draw another. I thought I’d have some fun with the numbers:
According to the 2014 data there were 440,000 teachers (I assume this is England and Wales). In total, 117,500 (26.7%) were male and 322,500 (73.3%) were female. There were 19,600 (4.45% of total population) head teachers. 6,700 head teachers were male (1.52% of total population; 34.2% of head teachers). 12,900 head teachers were female (2.93% of total population; 65.8% of head teachers).
If we wanted strict equality in gender representation within teaching (i.e. 50% male, 50% female), then we need 10,250 more male teachers (and 10,250 fewer female teachers). We would also need 3,100 more male head teachers (and 3,100 fewer female head teachers).
On the other hand, if we want seniority to reflect the disparity of gender representation within teaching, then we need 1,467 more female head teachers (and 1,467 fewer male head teachers).
In primary schools the pattern is the same – because the vast majority of head teachers are in the primary sector.
225,400 teachers worked in primary. 35,100 (15.6%) were male and 190300 (84.4%) were female. There were 16300 (7.23% of total) head teachers in primary. 4600 head teachers were male (2.04% of total primary; 28.2% of primary heads). 11700 head teachers were female (5.19% of total primary; 71.8% of primary heads).
If we want strict equality, then we need 77,600 more male primary teachers (and 77,600 fewer female teachers). We would also need 3550 more male primary head teachers (and 3550 fewer female primary heads).
On the other hand, if we want seniority to reflect the disparity of gender representation within primary teaching, then we need 2,057 more female primary head teachers (and 2,057 fewer male primary heads).
In secondary schools, the numbers of head teachers is much lower than in primary. Here though, both equality and representative models suggest a need for more female secondary heads.
214,600 teachers worked in secondary. 82,400 (38.4%) were male and 132,200 (61.6%) were female. There were only 3300 (1.5% of total) head teachers in secondary. 2100 (0.98% of total secondary; 63.6% of secondary heads) were male. 1200 (0.56% of total secondary; 36.4% of secondary heads) were female.
If we want strict equality, then we need 24,900 more male secondary teachers (and 24,900 fewer female secondary teachers). However, we would also want 450 more female secondary heads (and 450 fewer male secondary heads).
If we want seniority to reflect the disparity of gender representation within secondary teaching, then we need 833 more female secondary heads (and 833 fewer male secondary heads).
So – that’s the disagreement in a nutshell. If you believe equality means roughly 50:50 gender proportion across all levels of teaching you’ll draw one conclusion. If you believe equality means seniority should be proportionate to the gender split across the profession you’ll draw another.
*If we wanted strict equality in gender representation within teaching (i.e. 50% male, 50% female), then we need 102,500 more male teachers (and 102,500 fewer female teachers).
What if you think it requires equality of opportunity?
How would you measure that?
Without an operationalised definition, I’m not sure it necessarily helps your thesis – as some people would argue that ‘equality of opportunity’ would be reflected in the proportion of teachers becoming head teachers (i.e. Jude’s point about the ‘chances’ of becoming a head).
We may need more data in order to measure it. But if you don’t get a job you didn’t want and didn’t apply for common sense would suggest you have not been treated unequally.
Yes – perhaps you could look at the proportion of successful vs unsuccessful applications. If equally qualified males and females were both applying successfully for 1:5 head teacher positions (for example) then you might argue that there was equality of opportunity and that the disparity was not due to bias in promotion.
Still, I suspect you’d still fail to convince others. For example, some would counter that the lack of motivation for women to apply for head teacher posts was itself symptomatic of inequality in the system.
True, but at least we’d be able to clear governors of systematic bias.
Education would be a fantastic inspiration to people in other sectors, if state education was a place of real intellectual development for all students and teachers. Personally, I’m inspired by the #WomenED movement and those behind it. Why not create a community where conversations on ‘equality’ are nurtured rather than stifled? Why not create safe spaces so those who feel under pressure can say ‘I’m struggling’ and find companionship? I personally don’t care about campaigning, not really. Stats are abstract and we can all do clever things with them. I care only about connection, and creating spaces to freely offer and opt in for support, both of which are happening in abundance within the #WomenED community.
Great satire is always a hair’s breadth from the truth. I laughed so much it hurt.
But women, as a group, aren’t struggling in Education.
Women individually might be, but then so are men.
The problem with promoting the #WomenED line is that in a primary sector where men are in desperately short supply, promoting the idea that women are struggling is likely to put even more men off.
The “Stats is abstract” is an argument I would hope no-one interested in the truth, rather than the feelz would use. It means “I’m right” and don’t you go finding evidence I’m not.
This whole discussion mystifies me. Why would anyone want to send their child to a school where heads, or teachers, were selected on the basis of their reproductive organs rather than their ability to educate children?
I have never worked in a school where the staff room was divided along ‘gender’ lines. As a researcher, on every controversial issue I can think of there is a random distribution of sexes on either side of the argument.
The notion that we should try to create equality of outcomes is profoundly at odds with equality of opportunity. WomenEd should be ignored, not confronted.
I’m just interested in establishing the facts of the matter rather than confronting anybody. That said, it is always useful to know who is willing to deny the facts when it suits them.
I agree with you. Within the field of education, I don’t have strong opinions about gender equality because I don’t find it important. As a teacher, I have worked in schools with male and female administrators and never seen that their gender affects how the school is operated. I have also never worked in a school that divided by gender.
It should be the best quality person for the job gets the job.
Reblogged this on The Echo Chamber.
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