# Disrespecting Women in Science: Crunching the Numbers

One of the themes Occupy Math has been following is that, if you know math, you can provide hard evidence of discrimination. A wonderful example of this just blew up all over the interwebs. The topic is the (non)participation of women in scientific panels. A blog by Lauren Bacon describes a mathematical model used by mathematician Greg Martin to demonstrate the chance that the observed lack of women in these panels is cosmically unlikely to be the result of random chance. This, in turn, suggests bias, discrimination, and institutional failure to permit women to participate.

What do scientific panels do? These panels are convened at major conferences, or as parts of online presentations, to permit the audience to ask questions of a panel of leading experts and to listen to their discussion. These panels have enormous power because they:

• Set the agenda for research and, in some cases, research funding.
• They model for the audience, particularly students, what an “expert” looks like.
• They highlight the difference between what is known and what is a good place to focus your own research effort.

The pervasiveness of all-male panels is so great that they merit a Tumblr to mock them.

What Dr. Martin noticed was large numbers of panels with no women. The goal is to figure out, given the probability that a randomly sampled scientist is a woman, what is the probability of randomly choosing an all-male panel, or possibly one with only a small number of women.

#### Very unlikely: five women and only three loons.

Occupy Math wants to look at the probability model that Dr. Martin used to prove bias. Many of the popular media sources demonstrate their appalling ignorance of math by crediting Dr. Martin with devising this probability model. The model was devised by James Bernoulli centuries ago to describe the chance of getting a particular number of successes in an experiment with only two outcomes, success or failure. An example of this kind of experiment is flipping a coin with “heads” for success and “tails” for failure, like the picture above. The model is called the binomial distribution and what Dr. Martin did was apply it most effectively to demonstrate that women are not being asked to serve on prestigious panels.

If we know the fraction f of women in the general scientific population then, to find the chance of a panel with no women we compute the fraction of men 1-f and raise it to the power m where m is the number of panelists. Occupy Math has done this for some examples, computing the probability of an all-male panel, rounded to the nearest percent (or two digits when we drop below 1%).

 Size of Panel Pct. Women 3 5 10 15 10% 73% 59% 35% 21% 25% 42% 24% 6% 1.3% 50% 13% 3% 0.10% 0.0031% Chance of getting an all-male panel.

While it is a shame and an embarrassment, we know the fraction of women in the STEM disciplines is not 50%, and in fact Dr. Martin was using 25% for his exposition. That makes it seem like an all-male three-member panel is not that unlikely to happen.

But wait! The situation is much worse than you think!

Lets consider a conference with several panels, say, two of size three, one of size five, and one of size fifteen. Then the chance that all the panels are all male is obtained by multiplying the chances of the individual panels being all male. This means the chance of not seeing female panelists in the conference, as a whole is 0.056%. Since the standard in science is that a result is significant if there is only a 5% or smaller chance it happened by random chance, this probability is the scientific equivalent of an iron-clad result. If you want to check Occupy Math’s results, there are several good binomial calculator apps on the web.

What Dr. Martin showed was that we are either not asking women to serve on panels or they are turning down the invitations. I ran the IEEE Conference on Computational Intelligence in games in 2013 and invited two women and one man to speak. The women accepted, the man turned me down, then another man volunteered and sent in a really good outline. The first speaker was Dr. Jennifer Jensen. Occupy Math thought she gave an excellent, eye-opening talk. Her title and abstract follow.

It’s Not All Fun and Games: Gender, Misogyny and Videogames

In this talk, I will detail the conditions of precarity that women face as marginal subjects in the video games industry and as sexualized objects in its creative and cultural projects. I will do so through the documentation of recent examples of violent, vitriolic, and hate-filled speech that has been targeted at women who have either spoken out from those margins, or who have been made the object of ridicule from within the industry’s ranks. These examples demonstrate a form of extreme gender norm reinforcement that is being challenged both from within the industry’s ranks, and through feminist activist work from the margins. Some of that work is being done right here in Canada, and I will show how a few grassroots projects are working hard to change those conditions. I conclude with an accounting of the governing social and political order that ontologically re-inscribes women and their potential, actual creative capital and labour as first and foremost peripheral, when it might well be mobilized for innovation and change.

This is exactly the kind of situation that Occupy Math wants to see improved. The question period after the talk was hyperactive.

The bottom line is that we cannot possibly be asking women to serve on panels based solely on their qualifications. There is obvious, massive bias. Occupy Math calls on the community of scientific researchers to cut it out and start inviting the many interesting, qualified speakers and panelists that happen to be women.

I also ask my colleagues to abandon the tired, impossible justifications.

When someone says they asked women to participate and were turned down, it usually means they asked one woman and eleven men and two of the potential panelists accepted. While women do still have disproportional responsibility for family in our culture, this is not actually a barrier to female panelists. Some women have no family, or an adult family, and many now share their responsibilities with a partner. I know from observing dozens of colleagues that someone with a family and a scientific career works out ways to accept prestigious invitations. If you are concerned about these issues, or have a story to share, feel free to comment or tweet.

I hope to see you here again,
Daniel Ashlock,
University of Guelph,
Department of Mathematics and Statistics