Monday, December 27, 2010

Videos to catch

In the absence of anything to watch on TV over the holidays, I've been watching videos from the internet. Here are three that I've found particularly interesting:

'Why we have too few women leaders' by Sheryl Sandberg, Chief Operating Officer at Facebook (approx 15 min). While she acknowledges that changes in business practices are necessary, for example, flexible hours, in this talk she focuses on what individuals can do. Her three points are:
  • ‘Sit at the table’ – Women tend to underestimate their own abilities, they don't negotiate higher salaries and while men attribute success their abilities women tend cite external factors. One of the issues is that while successful men are perceived as likeable successful women are not.
  • ‘Make your partner a real partner’ – sharing the chores is good for your marriage.
  • ‘Don't leave before you leave’ – Don’t turn down that promotion or that new project because you are planning on having a child, especially not if you don’t even currently have a boyfriend.

Women need to watch this video. So do managers.
Margaret Wertheim on the beautiful math of coral in which Margaret Wertheim reveals the link between crochet, coral and hyperbolic geometry (approx 15min). She makes an interesting point about our tendency to value symbolic knowledge, marks on paper or on a computer screen, over embodied knowledge, things we can touch and feel.
The truth about denial by Naomi Oreskes, Professor of History and Science Studies at the University of California San Diego. This is a video of a talk given in 2007. The first part covers the history of  the science of global warming from Tyndall to the Fourth Assessment Report of the IPCC. The second part addresses the question, why, if the science is uncontroversial, do so many Americans think it is still doubtful? In 1992  US President George H. W. Bush signed the United Nations Framework Convention on Climate Change. Why in 2007 were we still arguing about whether global warming was even happening? (approx 1 hour)

Monday, December 13, 2010

Simpson's Paradox

Suppose there are 300 students doing a Maths exam, 180 men and 120 women, and another 200 students doing an English exam, 60 men and 140 women. Suppose 30% of the Maths students and 20% of the English students get an A. If the performance of male and female students is exactly the same then the results will be as shown in the Table:

Proportion of men getting an A
Proportion of women getting an A
Overall Proportion getting an A
54/180 = 0.3
36/120 = 0.3
90/300 = 0.3
12/60 = 0.2
28/140 = 0.2
40/200 = 0.2
66/240  = .2750
64/260 = 0.2462
130/500 = 0.2600

So, despite the fact that there is no difference in men's and women's performance on the individual exams, overall 27.5% of men got an A and only 24.62% of women got an A. This phenomenon in which the trend in amalgamated data is different from the trends in the individual groups is known as Simpson's Paradox. A famous example is graduate admissions at UC Berkeley in 1973: 44% of the 8442 male applicants were admitted compared with 35% of the 4321 female applicants, a difference that was too large to be due to chance. However, when the data were disaggregated by decision making unit a different picture emerged: few units showed a statistically significant difference between  the rates of male and female admissions and there were just as many units that appeared to favour women as to favour men. The reason for the discrepancy in the overall admission rates was that women were proportionately more likely to apply to units with low admission rates. In fact, when the data were pooled taking this into account there was a small but statistically significant bias in favour of women. [P.J.Bickel, E.A. Hammel and J.W.O'Connor Science, vol 187 pp 398-404 (1975)].

The Berkeley example dates from over thirty-five years ago. Do we still see this type of error in the analysis of gender statistics? Yes, we do.

I speculate that the reasons for this include:
  • A preference for results that confirm our existing beliefs. If we believe that women are hard done by we are less likely to question results that support that belief.
  • A fear that questioning specific results will be perceived as questioning the principle of equality or will be interpreted as a reason for failing to support an otherwise useful initiative.
  • Lack of knowledge of statistics and its pitfalls.

Additional Sources: I first came across the Berkeley example in a video of a lecture 'Lies, Damned Lies and Statistics: The misapplication of statistics in everyday life' by Dr Talithia D. Williams,  a lecture in the Distinctive Voices series of the US National Academy of Sciences. It's well worth watching.

Thursday, November 25, 2010

Equal Pay

This is, once again, a somewhat technical post. It highlights some of the shortcomings of focussing on gender pay gaps as a means of identifying biases in pay. It also raises the question: what is a practically important gap? I do not have a good answer to that question. It would be nice to see some discussion of what makes a pay gap important for practical purposes. A related question is: how much effort should employers put into addressing a pay gap that is in some sense ‘large’ but that has a high probability of being due to chance (i.e. is not statistically significant), bearing in mind that resources that are used for one activity are not available for other activities? Again, there is probably not a unique answer to this question but it would be nice to see it discussed.

The principle of equal pay is equal pay for:

•    Equal work – work that is the same or broadly similar.
•    Equivalent work – work that has been rated as equivalent by a job evaluation scheme.
•    Work of equal value – work that places similar demands on those performing it.

As noted by the Equality and Human Rights Commission (EHRC) the overall gender pay gap is not an indicator of unequal pay. They suggest that it should be seen as an ‘equal opportunity gap’. The analysis in my earlier post suggests that it is not a particularly useful measure of that either. Nevertheless, it is popular.

The tool to check for equal pay is an equal pay audit. Equal pay audits should be carried out for ethnicity and disability as well as gender but gender is often easier since the quality of the data is better. Basically the steps in an equal pay audit are:
1. Determine which people are doing equal work, equivalent work or work of equal value. An organisation that has a job evaluation scheme may assume that everyone with a job evaluated to be in the same grade is doing equivalent work or they may split people on the same grade into groups doing similar work. The latter procedure is preferable if there are enough employees since aggregating over all the employees in a grade could mask problems that were specific to one group.

2. Assess whether men and women are equally paid. There are two situations that might apply: there is systematic bias against women (or men) or a few individual women (or men) are disadvantaged, for example, the way in which starting salary is determined may disadvantage people returning from a career break which tends to disadvantage some, but not all, women. Although carrying out an equal pay audit may uncover instances of the latter it is more usual to concentrate on the former, though both are illegal. The EHRC suggests that the first step is to calculate the average basic pay for men and women and the average total pay for men and women. The EHRC recommends that if the difference between the average pay for men and the average pay for women is greater than 5% or if the difference between the average pay for men and the average pay for women is greater than 3% and there is a pattern of gaps favouring one sex over the other then further investigation is required. 

Most scientists asked to determine whether the difference of two means indicated the presence of systematic bias would probably start by trying a t-test. There are some problems with this approach, especially if the means are calculated from a small number of employees, because t-tests are based on the assumption that the estimate of the mean has a normal distribution. Tests of statistical significance, calculate the probability of observing a difference of at least the size you did observe on the assumption that there is no difference. The larger the value of this probability the more likely it is that the observed effect could have arisen just by chance even if, in fact, there is no difference.  It is not necessary to adopt the convention that a result is significant if the probability of getting a result at least that big is less than 0.05 and not otherwise. Depending on the cost it might be reasonable to take action even if the probability that the observed difference is due to chance is 0.3, or even more, depending on the circumstances. Note that observing an effect that is not statistically significant does not imply that there is no effect. It implies that there is not enough data to say whether or not there is an effect.

As noted by the EHRC, statistical significance should not be confused with effect size  (see Technical Note 3.5). A large difference can fail to be statistically significant if there are a small number of employees, or a small number of employees of one sex. A small difference can be statistically significant if there are a large number of employees. So, for example, an institution might be more worried about a 15% gender pay gap that had a 10% probability of being exceeded due to chance than about a 1% gender pay gap that had a 4% probability of being exceeded due to chance. In the latter case the institution is saying that they are willing to accept a low probability that the observed result is due to chance since they believe the bias to be too small to be of practical importance. What constitutes a large difference? What is practical importance?

The EHRC criteria are that if, on average, one sex earns more than 5% more than the other for doing particular equivalent jobs, or more than 3% more if there is a pattern, then there is a problem that needs investigating. These criteria could lead to anomalies depending on how pay is determined. Organizations that rely on negotiation by individuals to set pay or on pay schemes with a significant component dependent on performance evaluation are open to inadvertent discrimination leading to systematic discrepancies that would be evident in gender pay gaps. Other organizations use a system in which the person identifying the need for a position writes a job specification that is used by a professional job evaluator to assign a grade to the job with the person appointed to the position being assigned to a point within the grade on the basis of their qualifications and experience and then progressing by automatic annual increments to a point at which he or she needs to apply for promotion to discretionary or contribution points of the grade. Under this system there is much less scope for discrimination. Possible ways in which bias can occur are:
1.    There could be a tendency for women to be appointed at a lower point in the grade.
2.    Women could be less likely to apply for promotion to discretionary or contribution points.
3.    The job evaluation scheme could result in jobs predominantly done by men being graded higher than jobs predominantly done by women.
4.    Women could be less likely to receive, or receive lower amounts of, additional payments such as allowances, payment for additional responsibilities, recruitment incentives or market supplements.
5.    There could be differences in the contractual hours of different occupational groups in jobs evaluated to be at the same grade.
6.    There could be differences in pension entitlements or retirement ages between different groups with different representations of men and women.

Two factors which could influence gender pay gaps but which are not equal pay issues are:
1. Women might be more likely to leave giving a greater proportion of women on lower points in the grade or men might be more likely to leave, for example, for higher graded positions, leaving proportionately more women at the top of the grade.
2. Women may have been entering jobs at this level in increasing numbers in recent years leading to a clustering of women at lower points in the grade.

We thus have factors which are equal pay related that will be reflected in gender pay gaps, such as lower starting salaries, factors which are equal pay related that will not be reflected in equal pay gaps, such as biases in the job evaluation scheme, and factors that are not equal pay related but will affect the gender pay gap.

Figure 1 shows a distribution of women on a nine point scale, perhaps arising as a combination of women ending up with lower starting salaries, being less likely to apply for promotion and men leaving for better paid positions. The trend line has a slope of -0.0425, so the proportion of women falls by about 4 percentage points per scale point. If there are the same number of people on each salary point and each salary point is 2.5% higher than the one below then this distribution leads to a gender pay gap of 2.8% and no investigation is required. If, however, each salary point is 5% higher than the one below the gender pay gap is 5.7% and further investigation is required although the underlying biases that led to this situation would be the same in both cases. Both gaps are statistically significant if there are twenty or more people on each salary point.

Figure 2 shows a similar distribution on a fourteen point scale. The trend line has a slope of -0.0312. In this case the gender pay gap is 5.1% when the increment from one scale point to the next is 2.5%. This gap is highly statistically significant if there are at least twenty people on each scale point. Note that if this grade was split into two grades of seven scale points the gender pay gaps would be 1.6% for each grade though the men and women would be being paid the same salaries as before.

These examples show that the same underlying biases can give rise to gaps that may or may not be regarded as practically important depending on the particular salary structure.

As another example, suppose you have 100 men doing a particular job at a particular grade with an average salary of £25,000 and 100 women doing the same job at the same grade who would have the same average salary except that a policy of taking existing salary into account when determining the starting point in the grade has led to twenty women who returned from a career break being paid 6% less than similarly qualified men or women who had not taken a career break. The average salary for all the women is £24717, a gap of 1.2%. This is not likely to be statistically significant (on a ten point scale with an average of twenty people per scale point with a 3% increment there is a 15% chance of men’s average pay exceeding that of women by at least 1.2%) and nor is it large, though the twenty affected women might disagree.

This example shows that relying on the gender pay gap to identify anomalies could result in failing to detect substantial biases.

This still leaves the question: what is a practically important gap? There does not seem to be a good answer to this question. Is it acceptable for women to paid one scale point less than comparable men as long as the gap between scale points is less than 3% but not acceptable if the gap between scale points is greater than 3%? Is exactly the same bias acceptable if it occurs over two grades with a small number of steps but not if it occurs over one grade with a larger number of steps? Is it acceptable for 50% of women to be paid one scale point less than comparable men but not for 100% of women? What are the criteria for practical importance? Practically important to whom? The women earning 6% less than they might have been? The employer who might face an equal pay claim?

Does this mean carrying out an equal pay audit is a waste of time? No, it does not. An organization that measures its gender pay gaps for groups identified as doing the same or equivalent work or doing work of equal value is more likely to identify anomalies than one that does not. What it does mean is that organizations should examine their pay schemes and identify how anomalies could occur, for example, that people returning from career breaks tended to be placed on lower starting salaries thus tending to disadvantage women, and monitor those points directly regardless of whether or not they have observed substantial gaps.

An effective equal pay audit would:
•    Describe the way the institution sets pay or, at the very least, refer to another document that does so.
•    Identify the processes where bias could occur, e.g. setting starting salaries.
•    Monitor those processes.

 It could be that in a system where individuals negotiate their own pay or individuals’ line managers have a large say in setting performance pay that the best way of monitoring is to measure the gender pay gap. In institutions with job evaluation schemes and set pay scales it would be better to monitor starting salaries and progression directly to avoid potential bias being masked by other factors that affect the pay gap.

Processes that could introduce bias include the job evaluation scheme, if one is in place. The EHRC has pertinent advice on how to check that a job evaluation scheme does not itself inadvertently discriminate against women.

Has your institution carried out an equal pay audit? Does it meet the above criteria? Do you think it should? Is there anything you can do about it if it doesn’t?

Tuesday, November 23, 2010

Women's Networks

I have been involved in women's networks in science either passively or actively for about twenty-five years. These are my thoughts on women's networks.

Why do we need them? What are the benefits?
Women's networks can:
•    Provide a safe and supportive environment for women to exchange experiences.
•    Provide a means for women to exchange information.
•    Build women's skills by giving them the opportunity to take on various roles within the network.
•    Increase women's visibility.
•    Enable women to push for change more effectively.

How can they be effective?
•    Provide a regular programme of events to maintain momentum. It does not matter if attendance at some events is low. Just getting the email saying that something is happening reminds people that the network is active.
•    The best publicity is word of mouth. Women who have had a good experience tell their friends.
•    Maintain a positive focus.
There are many types of events that women's networks can run, for example, speaker events, career-focussed events and social events. Generally the types of events a network runs will depend on the interests and enthusiasms of its members. Although, in principle, women's networks provide a way for women to make their views on existing policies or proposed changes to policies known, in practice, whether or not this happens depends on whether an individual feels strongly enough about the issue, and has the time and energy, to do something about it.

In my experience members of women's networks are not interested in formal structures. They prefer informal arrangements to prescriptive specifications. It is better to make things happen and then worry about structures. Nevertheless, in my experience there are minimum requirements if the network is to be more than a handful of friends who happen to meet fairly regularly. There needs to be someone who is visibly responsible for the network. This person will often be known as the Chair of the network. There also needs to be a treasurer, someone to keep records and someone who is responsible for communicating with members, for example, via a newsletter. These responsibilities do not need to be held by different people but I think it helps if there are identifiable people taking responsibility for these areas. It gives people a point of contact if they have a query or suggestion or if they want to invite a representative of the network to an event. It is also important that the network does not become reliant on one or two people otherwise it can collapse if one of them gets a new job, has a baby or moves away. This means there has to be a way of ensuring new people take up positions of responsibility. Having an ‘incoming president’ or ‘incoming chair’ position is useful for ensuring continuity.

In order to function effectively a network needs some resources. Obviously the time and energy of those who organise events are essential. Women's networks within organisations need to be properly resourced either with money or with in-kind assistance such as free meeting rooms. The work that people put into such networks needs to be recognised as part of their job and not seen as an optional extra. A women's network can increase productivity, for example, by helping women find effective solutions to difficulties they may be experiencing. For women's networks operating outside of a single employer the situation is more difficult, although they play a very important role in broadening the range of experiences available to their members. Such networks have to have sufficient resources to pay for venue hire and refreshments as well as, in some cases, expenses for speakers. These resources have to found either from members, potentially deterring some women from participating, or through sponsorship, which can be time-consuming to find and is especially difficult for women with day jobs who do not necessarily have the time to contact and follow-up potential sponsors.

Exclusive or Inclusive
Every women's network I have been involved with has, at some point, discussed the issue: is it just for women or can men join too? This has usually been a question of principle rather than practice since men usually self-exclude anyway. One one hand  women's networks need to provide a safe and supportive environment for women. On the other many of the issues that constrain women's full participation in employment are never going to be resolved by groups of women talking among themselves. We need men to get involved. In my view a safe and supportive environment means one in which the discourse is set and shaped by women not one from which men are excluded.

What would help?
•    Money – of course. Ideally support would be aimed at helping the network achieve its objectives but inevitably a sponsor tends to want the network to help achieve the sponsor’s objectives.
•    Recognition - line managers making sure women know about opportunities to participate in women's networks and senior managers and influential members of the business community promoting the benefits of women's networks.
•    Capacity building in skills such as effective use of the web from on-line booking to running a discussion forum, running effective meetings, and fund-raising.

Wednesday, November 17, 2010

The Pace of Change

One of the indicators of the position of women in academic science is the proportion of women among academic staff in STEM departments. How fast can this indicator change?

The first constraint is the number of vacancies available for women to be appointed to. For example, if a department has a turnover of 5% per year and the number of academic staff is growing at 2% per year then the overall vacancy rate is 7% per year.

The next most important constraint is the proportion of women in the pool of potential applicants. If the pool of potential applicants is 50% women and no women leave the department then a department with a vacancy rate of 7% could achieve an increase in the proportion of women of 3.5 percentage points per year. In these circumstances a department could get from 25% to 50% women in 7-8 years. However, if turnover was around 3% and the number of academics was static then the best the department could achieve, if no women leave, is a growth in the proportion of women of 1.5 percentage points per year. At that rate it would take 17 years to get from 25% to 50%. Of course, this might well be an underestimate since it is unlikely that no women would leave over a seventeen year period.

There is an additional complication. Suppose a department is able to make six appointments over a three year period and it makes the appointments from a pool that is 50% women. If recruitment is fair with respect to gender then the probability distribution for the number of women appointed will be a binomial distribution with N=6 and p=0.5. This gives a probability of 0.31 of appointing exactly three women, a probability of 0.34 of appointing two or fewer women and a probability of 0.34 of appointing four or more women (probabilities do not add to one due to rounding). Hence for time periods in which a small number of appointments are made fair recruitment processes could easily result in apparent growth rates between 2/3 and 4/3 times the expected rate.

1.    There are limits to how fast the proportion of women among academic staff in STEM can increase. Growth rates of a few percentage points per year are not unreasonable.
2.    Estimating the long-term growth rate from measurements made over short periods is futile.

The second conclusion implies that simply collecting data on the proportion of women among new appointees is unlikely to reveal inadvertent bias in the recruitment process. While these data are necessary it is also necessary to assess the recruitment process against best practice established by large studies, such as that described in the US National Academies Report Gender Differences at Critical Transitions in the Careers of Science, Engineering and Mathematics Faculty. (A briefing on the report is available from the pages of the National Academies Committee on Women in Science, Engineering and Medicine.)

Monday, November 8, 2010


I have just read two very different books: Randy Olson's 'Don't be such a scientist' and 'Healing our History: the challenge of the Treaty of Waitangi ' by Robert and Joanna Consedine.

Olson's book is an easy read - short, breezy, anecdotal but making the very important point that if we want to engage non-scientists with science we need to have good stories while retaining factual accuracy. Anyone who is involved in science communication should read this book but for me it also sparked some thoughts about how we communicate about women in science. For example, much of our communication is directed to scientists, people to whom accuracy matters, the sort of people who feel the need to point out to an actor speaking enthusiastically about spotting whales that there are no gray whales in the Atlantic or who are worried by the fact that in James Cameron’s original version of Titanic the ship sinks under southern hemisphere stars. Are we careful to make accurate statements? Do we play to the strengths of academics or do we regard them as problems? A male participant in the University of Michigan’s STRIDE programme commented on its style saying it followed ‘pure academic principles of engagement … It was clear that they wanted you to study, work, read, form opinions, validate or invalidate current approaches … to become educated.’ (Reference 1) Are our efforts concerned with engaging scientists as scientists or are we uncomfortable with argument and dissent?

'Healing our History' was a difficult book for me as a Pakeha to read. Some background: in 1840 the British government signed a treaty with the Maori people of New Zealand. The representatives of the British government and successive New Zealand governments then spent the next 140 years ignoring the provisions of the treaty and exploiting the Crown’s position as the sole purchaser of Maori land, while promoting the view that if Maori were disadvantaged then it was their own fault and the solution was for them to become Europeans. Requests for restitution for the failure to abide by the treaty are still spun as ‘demands for handouts’.

I would hesitate to draw parallels between the situation of Maori in New Zealand and women in science. I think the histories and consequences are quite different. Nevertheless, I believe there are lessons from the Consedines’ book that can be applied to thinking about women in science.

Firstly, I now understand the attraction of ‘wilful ignorance’. If you take no steps to understand the facts then you can comfortably deny that there is a problem. Those who refuse to collect data on the grounds that they already know that their workplace is fair may fall into this camp. Knowing that there is a problem demands a response, even if that response is to decide to do nothing.

Secondly, Robert Consedine runs workshops on Treaty issues. The initial workshops are run in parallel: one for Maori with a Maori facilitator and one for Pakeha with a Pakeha facilitator. Prior to attending a workshop, many people are uncomfortable with this arrangement, which they feel smacks of separatism. However, experience has shown that it is useful for Pakeha to be able to express their fears and misconceptions in a safe environment and it is useful for Maori to be able to explore their identity as Maori without being regarded as representative of all Maori. Before attending a parallel workshop only 16% of participants believed they were needed. After attending a workshop 90% thought they were needed. The need for women to have a safe environment in which to express their concerns has long been recognized. What about men? Do they have a safe space in which to express their concerns and fears?

A common reaction to the workshops was puzzlement that a group of Pakeha were teaching the Treaty of Waitangi. The idea that Pakeha would take responsibility for learning and teaching Treaty commitments was mystifying. How many men are willing to take responsibility for promoting gender equality? How often is it seen as a women’s issue? What does ‘take responsibility’ mean? The Consedines quote Jorge Rosner: ‘Responsibility literally means “the ability to respond”. You only respond when you are fully aware of you behaviour and your choices, then, on the basis of your awareness, you can freely choose what to do.’ (Reference 2) Taking responsibility does not mean accepting guilt for what has happened in the past. It means looking at the current situation, asking what needs to be done, and doing it.

Robert Consedine also writes ‘I encourage people to live with the questions, as a ‘solution focus’ is often a barrier to change in this arena.’ This is a difficult concept for those of us in a ‘What’s the question? Here’s the answer. Move on’ culture, especially those of us trained in using reductionist techniques to solve problems.

So, two very different, but challenging and thought-provoking books.

Thursday, November 4, 2010


Men do not let anyone seize their estates, and if there is the slightest dispute about their boundaries they rush to stones and arms; but they allow others to encroach on their lives - why, they themselves even invite in those willing to take over their lives. You will find no one willing to share out his money; but to how many does each of us divide up his life!

De Brevitate Vitae (On the Shortness of Life) Lucius Annaeus Seneca (c. 3 BC - 65 AD) Roman philosopher, statesman and dramatist Translated by C. D. N. Costa (1997), Penguin Books - Great Ideas

How good are you at setting boundaries on other people's access to your time?

The picture shows two kereru (New Zealand wood pigeons) in a tree. It was taken from our living-room window. If you want a link to the subject of the post I guess it is a reminder to look out the window from time to time.

Friday, October 29, 2010

Earlier this month there was a furore here in New Zealand that resulted in one of the hosts of a popular television breakfast programme resigning after firstly suggesting in an interview with the Prime Minister that the next Governor-General of New Zealand should look more like a New Zealander than the current Governor-General, Sir Anand Satyanand, who was born in New Zealand and is of Indian ethnic origin, and secondly creating a diplomatic incident by making jokes about the Delhi Chief Minister Sheila Dikshit’s name.

Among the many opinion pieces that appeared was one by Karlo Mila, who is a New Zealander of Tongan/Pakeha (European) descent. She recounts the story of how she was welcomed into the coolest group of girls in the class at secondary school only to have one of its ringleaders say ‘I’m so glad there are no Maoris in our class’, then turn to her and add, ‘Sorry, Karlo, if I offended you? I didn’t mean you, of course.’ Karlo describes how quickly her thirteen year old self responded ‘I don’t mind. Why would I care? I’m not Maori.’

It reminded me of a quote from Elizabeth Blackburn :
"Someone once asked me how I did it as a woman," Blackburn recalls. "I said something that surprised even me at the time: 'I disguised myself as a man.' I had not really realized until that conversation that that's what I was doing. At the time, I didn't think of it as a sad thing, but it is sad."

Elizabeth Blackburn, UCSF
DISCOVER Vol. 23 No. 11 (November 2002)
And, indeed of my own response on being asked how I had coped with a predominantly male work environment: ‘Once I had been accepted as a good bloke there were no problems.’

Clearly, this is not as straightforward as denying that you are a woman, although one may hear the occasional approving comment ‘But you are not one of those women.’ I believe it has more to do with a tacit acceptance of male as norm, for example, an uncritical acceptance of the proposition that you have to stay late to do science, a proposition described by Blackburn in the same article as ‘the biggest pile of crap’.

I suspect that some of the antipathy that some women express towards organizations or events with the word ‘women’ in the title stems from having gone to considerable effort to fit in their male dominated workplace and not wanting to blow their cover.

I do not see a problem with adopting a more masculine style if that is more effective. I do not see that as being any different from saying ‘S’il vous plaĆ®t’ and ‘Merci’ when in France. I think it is more about having to behave in ways that are not comfortable. As one of the post-docs quoted in the Discover article put it "It's just, you've got to be this person that I don't want to be in order to be successful as a scientist."

This is why programmes such as Springboard and, at a different level, Suzanne Doyle-Morris’s “Beyond the Boys’ Club” are so important: they are about being successful and a woman rather than being successful despite being a woman.

We also need to articulate what needs to change and engage men in conversations about how to bring change about.

Monday, September 27, 2010

Gender Pay Gaps - Myths

Myths about the Gender Pay Gap

Warning: this post contains mathematics. I apologise to those of you who find this intimidating but I make statements that follow mathematically from the definition of the gender pay gap and it is important that I give my reasoning so that those who are not put off by a bit of straightforward algebra can check it. If you can not read the equations and want to, try this link.

The important conclusion is that an institutional gender pay gap is an incomplete and ambiguous measure of inequality. It is incomplete because the gender pay gap can be small or zero even when the overall proportion of women in the workplace is low. We therefore need to know the proportion of women in the workplace as well as the gender pay gap. It is ambiguous because while if the proportion of women in each salary interval falls as the salary increases then the pay gap is non-zero it is possible for the pay gap to be small or zero and the proportion of women by salary interval to still have undesirable features such as a lack of women at the highest levels. In addition, because the gender pay gap compounds structural factors that are common to both men and women, namely, the salary scale and the number of people in each salary interval, with an inequality factor, namely, how the proportion of women varies with salary, it is difficult to compare different workplaces unless the structural factors are similar.

For these reasons the minimum information required to make sense of a gender pay gap is

  • the number of women and the number of men (number rather than proportion since the proportion can be calculated from the numbers and the numbers give an idea of whether the measured gap reflects underlying inequality or just a fluctuation or contingency)
  • the average salary for women
  • the average salary for men
  • the proportion of women by grade or salary

Myth 1: The gender pay gap measures the extent to which women are paid less than men for doing the same job.

There are three contributions to the gender pay gap:
1. Occupational segregation: there are more women in low paid occupations and occupations in which women predominate attract lower pay.
2. Vertical segregation: within an occupation there are more women at lower levels.
3. In some cases women are paid less than men for doing the same job or for work of equivalent value, which is illegal.

There are numerous causes of the gender pay gap, for example, research commissioned by the Government Equalities Office in the UK identifies several factors including differences in years of full time work and the negative effect on wages of having worked part time or taken time out of the labour market to care for a family.

Myth 2: The gender pay gap is a useful indicator of inequality.

The gender pay gap is defined by:

gap = (average pay for men - average pay for women)/(average pay for men)

The average pay for women can be written as:

S_A^W = \frac{\sum_{i=1}^{n}{p_iN_iS_i} }{\sum_{i=1}^{n}{p_iN_i} }

and the average pay for men as

S_A^M = \frac{\sum_{i=1}^{n}{(1-p_i)N_iS_i} }{\sum_{i=1}^{n}{(1-p_i)N_i}}

where N_i is the number of people with salary S_i and p_i is the proportion of them who are women. The number of different salaries (or salary categories) is n. The symbol \sum_{i=1}^{n}{} means add all the terms from 1 to n together. These formulas work when people are paid on a salary scale or when there are enough people that it makes sense to make a histogram of the number of people in each salary interval.
The total number of people is N_T = \sum_{i=1}^{n}{N_i} . The total number of women is N_W = \sum_{i=1}^{n}{p_iN_i} , the total number of men is N_M = \sum_{i=1}^{n}{(1-p_i)N_i} and the overall proportion of women is p=\frac{N_W}{N_T} . This implies that the difference between the average pay for men and the average pay for women can be written as

S_A^M-S_A^W=\frac{1}{p(1-p)} \sum_{i=1}^{n}{(p-p_i)(\frac{N_i}{N_T})S_i }

and the gender pay gap as

g = \frac{S_A^M-S_A^W}{S_A^M} =\frac{\sum_{i=1}^{n}{(1-p_i/p)N_iS_i} }{\sum_{i=1}^{n}{(1-p_i)N_iS_i} } .

So, the difference between average pay for men and average pay for women depends on two structural factors, namely, the salary scale and the proportion of jobs at each salary scale point, and an inequality factor, namely, the way in which the proportion of women at each scale point varies with scale point. One implication is that the pay gap will be zero whenever the proportion of women is constant with scale point regardless of what that proportion is. Hence, the pay gap is an incomplete measure of inequality. A workplace with a zero pay gap that has only 10% women is hardly a shining example of gender equality.

From a mathematical point of view we have two equations

p=\frac{\sum_{i=1}^{n}{p_iN_i} }{\sum_{i=1}^{n}{N_i} } , which defines p, and

g = \frac{S_A^M-S_A^W}{S_A^M} =\frac{\sum_{i=1}^{n}{(1-p_i/p)N_iS_i} }{\sum_{i=1}^{n}{(1-p_i)N_iS_i} }

which defines the gap. If we want g=0 then we have two equations in n unknowns. This is an under-determined system, unless there are only two steps on the salary scale, so there is the possibility of finding other solutions that give a zero gap besides p_i=p for all i. This means that while if p_i is constant then the gap is zero and if p_i falls systematically as i increases then the gap will be non-zero there could be solutions which have a small or zero gap that nevertheless have undesirable features such as a lack of women at the highest salary levels. The figure below shows an example, which has 220 men and 180 women (45% women among a staff of 400) on an eleven point scale where each point is has a salary 5% greater than the one below starting from £20,000. The average salary for men is £24,923.41 and the average salary for women is £24,901.72, which is a gap of 0.09%. Nevertheless, only 35% of the posts in the top three grades are held by women and only 20% of the posts in the highest grade are held by women. Click here to view the spreadsheet I used to create this figure. The spreadsheet itself is available at this link.

So, as a measure of inequality the gender pay gap is both incomplete and ambiguous.

Myth 3: The overall national pay gap will be eliminated if each workplace eliminates its own pay gap.

Suppose Employer A has a largely female, largely relatively unskilled workforce while Employer B has a largely male, largely skilled or professional workforce. Both employers could eliminate their pay gaps but Employer A would still be paying their predominantly female workforce less on average than Employer B was paying their predominantly male workforce.

Myth 4: The gender pay gap provides a means of comparing inequality across workplaces

As noted in under Myth 2, the gender pay gap depends on two structural factors and an inequality factor. Unless the workplaces have the same salary scale and the same proportion of jobs at each salary scale point it is very difficult to draw conclusions about differences in equality in different workplaces. It would also be helpful if there was agreement on whether to divide by the average salary for men or the average salary for women in the expression for the pay gap. It could also be the case that in the example discussed under Myth 3 that Employer B has a gender pay gap that is hard to eliminate due to a shortage of women with the necessary professional qualifications, for example, in engineering, while Employer A is able to eliminate their gap despite the fact that women working for Employer B have higher average salaries than women working for employer B.

Thursday, September 23, 2010

Uk Equality Legislation: Specific Duties Consultation

In a previous post I wrote about different approaches to equality under Teresa Rees’s headings: Tinkering, Tailoring, Transforming. Recent equality legislation in the UK has the potential to be a framework for transforming both workplaces and service delivery to incorporate genuine equality. It also has the potential to create self-sustaining bureaucracies that achieve very little. Which happens depends not on the competence of organisations’ equality and diversity personnel but on the extent to which women, and other groups, avail themselves of the opportunities presented. The consultation on the specific duties is one such opportunity. While responding to consultations can seem like a waste of time, if you do not even attempt to make your views known your voice certainly will not be heard. So, if you live in the UK, download the consultation document from the Government Equalities Office website and respond.

The Equality Act 2010 integrates the former general equality duties that applied to disability, race and sex and extends them to apply to other characteristics such as sexual orientation. The general equality duty requires public authorities, which include universities and research councils, to eliminate discrimination and harassment, advance equality of opportunity and foster good relations between members of different groups. In the context of gender, the Act makes it explicit that advancing equality of opportunity includes removing or minimising disadvantages experienced by women (or men) but not by men (or women), taking steps to meet the needs of women (or men) that are different from those of men (or women), and encouraging women (or men) to participate in public life or any other activity in which participation by women (or men) is disproportionately low. (Note: the Act frames these duties in a way that applies to all characteristics. I have used gender as an example to avoid using the jargon that is required for a more general formulation.)

The specific duties are set by regulation and are intended to provide a framework that ensures that something actually happens. Under previous legislation the specific duties varied. For example, the Race Equality Duty had a detailed prescription for data collection in Higher Education. The Gender Equality Duty required public authorities to gather and use information but had no specific requirements for data collection, other than that the requirement ‘to consider the need to include objectives to address the causes of any gender pay gap’ implies that you actually know what your pay gap is.

The previous specific duties for gender were:
  •      To prepare and publish a gender equality scheme, showing how it will meet its general and specific duties and setting out its gender equality objectives.
  •       In formulating its overall objectives, to consider the need to include objectives to address the causes of any gender pay gap. 
  •       To gather and use information on how the public authority's policies and practices affect gender equality in the workforce and in the delivery of services.
  •       To consult stakeholders (i.e. employees, service users and others, including trade unions) and take account of relevant information in order to determine its gender equality objectives.
  •       To assess the impact of its current and proposed policies and practices on gender equality.
  •       To implement the actions set out in its scheme within three years, unless it is unreasonable or impracticable to do so.
  •       To report against the scheme every year and review the scheme at least every three years.
[Source: Gender Equality Duty Code of Practice Gender Equality Duty Code of Practice England and Wales EOC 2006]. It was the responsibility of the Equality and Human Rights Commission (EHRC) to enforce the legislation by issuing guidance and, if necessary, through compliance orders or court orders.

The focus of the proposed new specific duties is on accountability through transparency. Public authorities will be required to publish data that will enable citizens and concerned groups to hold public authorities to account. The EHRC will determine what data should be published though the consultation document mentions the gender pay gap, the proportion of staff from ethnic minority communities and the distribution of disabled employees throughout an organisation’s structure.

Differences from the old specific duty for gender are
  • Public authorities will no longer be required to have an equality scheme. Consequently there will no longer be requirements to implement the scheme, to report against the scheme or to review the scheme.
  • There will no longer be a specific requirement for consultation but public bodies will be expected to be open about how they have engaged with people.
  • There will not be a specific duty requiring equality impact assessments as it is expected that equality impact assessment would form part of normal decision-making. However, the annual publication of equality information will include impact assessments.
  • Equality objectives should be reviewed every four years.

Differences from the proposals put forward under the previous government are:
  • There will be no national priorities set by the Secretary of State.
  • There will be no special focus on procurement as the general and specific duties already apply to all the functions of a public body.
  • Public bodies will no longer be required to set out the steps they propose to take in order to achieve equality objectives.

The proposed specific duties are
  • Workforce Transparency: Public bodies with 150 or more employees will be required to publish data, to be specified by the EHRC, on equality in their workforces. This is expected to include data on their gender pay gap, the proportion of staff from ethnic minorities and the distribution of disabled employees throughout the organisation’s structure. The data will have to be published at least annually.
  • Service Provision: Public bodies will be required to publish data, at least annually, that will enable people to judge how effectively they are eliminating discrimination, advancing equality and fostering good relations through the services they provide.
  • Setting objectives: Public bodies will be required, as part of their normal business planning process to set equality outcome objectives that are informed by evidence and that are specific, relevant and measurable. This will enable meaningful scrutiny by citizens and other interested groups. The objectives should be reviewed at least every four years.

The focus on outcomes is welcome. Far too much time and effort has gone into producing plans and then writing reports against those plans in which whatever did happen is presented as though it were what was planned. Trying to minimise the work involved in demonstrating compliance is also welcome. Partly because resources should be directed to achieving aims not demonstrating compliance and partly because equality should be embedded within normal procedures and practices not treated as an optional or externally imposed extra.

My concerns are:
  1. Will this ‘meaningful scrutiny by citizens and other interested groups’ actually occur? Are there enough people with the time and resources to carry out this scrutiny? How is it envisaged that such people will hold an institution such as a large, research-intensive university accountable?
  2. What data will be required? From a mathematical point of view the institutional gender pay gap is a flawed measure of inequality. However, a lot of people have invested a lot of time and effort into promoting it as a measure of inequality so we are probably stuck with it. The minimum amount of information required to make sense of a gender pay gap is the number of men, the number of women, the average salary of the men, the average salary of the women, and the proportion of women by salary band. It would also be helpful to know if women are disproportionately represented in some occupational groups and, in the context of research and academic staff in universities, whether there are differences by discipline. For workplaces that are large enough for such an exercise to be meaningful, it would be useful to know the proportion of women by salary band and age. This would help distinguish between situations where women are hard done by and something should be done and situations where women were hard done by and something has been done. There is no point in devoting time and resources to fixing something that is not broken. The Equality Challenge Unit, which provides guidance on equality for the higher education sector, has suggestions for the data that higher education institutions should use to inform setting equality objectives in their briefing ‘Revising Gender Equality Schemes’  (January 2010) and the ECU Gender Equality Scheme Self-Assessment Tool.
  3. If there is a conflict between presenting data and maintaining the privacy of individuals then privacy should be paramount.
  4. Objectives should be realistic and achievable as well as measurable. There is no point aiming for some arbitrary percentage of women among some particular group if that cannot be attained within a reasonable timeframe. It is often forgotten that the most important constraint on how fast the proportion of women among academics can change is the rate at which vacancies occur for them to be appointed to, unless new positions are created. Similarly there is no point aiming to train some proportion of your staff in something-or-other if the resources to deliver the training are not available.
  5. What do we mean by measurable? For example, in 2004 women made up 49% of acceptances to Natural Sciences at Cambridge. Five years later in 2009 women made up 40% of acceptances to Natural Sciences at Cambridge (Source: Cambridge University Reporter Undergraduate Admissions Statistics Special Issue, No. 15 2009-2010 and 21 February 2005). Is this a worrying decline or a random fluctuation? Having looked at the numbers, I am inclined to the latter view, though the former is tenable depending on how much the data are tortured. It could also reflect a change in the proportion of acceptances to biological Natural Sciences. Suppose the numbers had been the other way around (i.e. 49% in 2009 and 40% in 2004). Would this be evidence that the University was meeting equality objectives?
  6. It is hard to see how an institution could set or achieve equality objectives without consulting with relevant groups. It is very important that institutions should be required to state with whom and how they consulted.
  7. Institutions should also be required to state what steps they took to achieve their equality objectives. This would aid the ‘citizens and other interested groups’ to assess whether an institution is building a genuinely equal environment or whether it is just managing the numbers. For example, suppose an institution has reduced its gender pay gap. It would be of interest to know if this had been achieved by making lots of catering assistants and clerical workers redundant or by waiting for other institutions to develop the careers of their female staff and then poaching them. In addition it would be useful to other institutions to help them assess what actions are effective.

The proposed specific duties should enable institutions to embed equality within their organisations. If you have a view on whether or not the proposed specific duties make it more or less likely that this will happen then you should respond to the consultation.

Sunday, September 19, 2010

Christchurch Earthquake 2

More on the Christchurch earthquake, also known as the Canterbury earthquake or  the Darfield earthquake...

After much emailing on my husband's part, he and I travelled to Christchurch on Wednesday 8 September to help install sensors to measure accelerations caused by earthquakes in the aftershock sequence following the 7.1 earthquake on 4 September. The project is part of the Quake Catcher Network run from Stanford ( the Rapid Aftershock Mobilization Program in New Zealand ( A Ph.D. Student from Stanford had arrived in Christchurch that morning with 200 sensors in her luggage.

People volunteer to have a sensor in their home for a period of 4-6 weeks. The picture shows one of the sensors. It is secured to the floor using duct tape and glue for a hard floor and duct tape and Velcro for carpet. The cable plugs into a USB port on a computer which has to have BOINC (Berkeley Open Infrastructure for Network Computing)  installed to manage data transfers to the server. Between 8 September and 14 September up to five teams of people from GNS Science, Stanford and the Universities of Auckland and Wellington installed nearly all of the 200 sensors around Christchurch and the surrounding region.

Different parts of the city were affected differently by the shaking. Driving in from the south, we saw very little damage until we reached the central city area where a number of older brick or masonry buildings had been badly damaged. In fact, the three main types of damage were chimneys that either collapsed or became unsafe, older brick or masonry buildings that partially collapsed and problems due to soil liquefaction. When we arrived on 8 September many streets in the central city area were cordoned off. In fact, the serviced apartments where we were staying were inside a cordoned area and we had to be escorted to reception by a soldier. By the time we arrived, water and power had been restored over most of the affected area, though not in some of the most badly affected neighbourhoods and in rural areas. The biggest inconveniences for us were that for the first few days we were not allowed to use the lifts and the internet connections to the rooms were not working properly, possibly because aftershocks were loosening the ethernet cables. By Monday 13 September much of the city was  functioning normally, though a few streets were still closed due to unsafe buildings or continuing demolition.

The response of Christchurch residents to the call for volunteers to host a sensor was amazing. Even those whose houses were undamaged had still had an extraordinarily stressful experience, plus the additional stress of on-going aftershocks, including one of magnitude 5.1 on the morning of 8 September (before we arrived) that caused additional damage.

The GeoNet website has more information about the earthquake, including a video montage of the fault trace reconnaissance and some more on aftershocks. The GNS Science website has more information as well. There is an animation of the aftershock sequence at

We also recommend the Nobanno Bengali restaurant on the corner of Armagh and Colombo Streets in Christchurch. The food is excellent.