Eric Winsberg then jumped in, saying that the inequality at an eight-participant all-male conference that I did report on wasn't significant either. He is right about that. Let's say that the null hypothesis is 8 males and 0 females and that the alternative to the null is two females and six males. The alternative then predicts 25 percent women, only slightly more than we find in the profession as a whole. Chi-squared for the observed fact then is 2.7 and the two-tailored p-value is about 0.1. Significance normally requires a p-value smaller than 0.05. However, we define a trend as p = 0.05 - 0.1. So if we encounter an eight-participant all-male conference, then while the inequality is not significant we do have a trend. Trends are worth reporting on. Close-enough-to-a-trend is worth reporting on, too, in this context.
Winsberg doubted that we would have significant inequality at any conference. I provided some examples of conferences where the inequality was significant, given the suggested null and alternative hypotheses. And others have made some remarks about that as well.
A further question is whether this is always the right way to look at the situation. Suppose for argument's sake that all conferences have three or fewer invited speakers. Suppose further that women are never invited to these conferences. Assuming the alternative to the null hypothesis mentioned above, the inequality at each conference is neither significant nor "trendy". However, it would be wrong to conclude on these grounds that there is no inequality in philosophy, in the envisaged scenario. What we should do in here is add up the invited speakers and then use this number to calculate the chi-square and the p-value. After three or four such conferences, the inequality will turn out significant.
One might take the fact that we often need data from more than one conference in order to get significant inequality as demonstrating that we should not single out or reject invitations to individual conferences. But I don't see how this follows. Turning down an invitation to speak at a conference with one male keynote would be ridiculous, if it's done for that reason. But it can't be true in general that I ought to wait until I have seen, say, ten conference announcements (with women and/or males on the program) and then do the calculations. I don't see how this approach would make philosophers organizing all-male projects feel better. They are bound to feel "singled out" or "rejected," regardless of whether I single out only their project or mention it alongside nine other projects (some of which include some females).
Furthermore, if we single out each all-male conference and all-male volume that we encounter (and that meets a close-enough-to-trend inequality criterion) and/or turn down invitations to contribute to such events, then people who organize conferences or put together philosophy volumes will hopefully start to think about the ratio of females to males before going ahead with their projects.
Sometimes there may be a legit reason for having an all-male conference. At least I don't want to rule that out. If some all-male conferences or volumes are okay, then we sometimes single out or turn down invitations to contribute to conferences or volumes that are okay despite not being gender-inclusive, thereby indicating that they are not okay. That's no good. But I don't see how it can be avoided. If the singling-out and turning-down approaches are going to be effective, then we need to take action with respect to all male-only conferences and all male-only volumes that demonstrate gender-inequality in the way discussed in the first part of the post. Organizers can then tell us if we were wrong to single out their conference or turn down invitations to contribute.
Another thing organizers can do to avoid being "outed" is indicate on their website why their all-male conference or volume is okay. For example, conference organizers can make it clear on PHILOS-L (where our readers often see the announcements -- at least before PhilEvents) if women are invited as discussants. They can also add non-speaking female co-authors to the program (noting their absence).