**TL;DR version**

Are women underrepresented as APS fellows? Yes. Is it anyone’s fault? It’s complicated. Is there anything simple that can be done? YES! Any member of APS can nominate a potential fellow starting early in the calendar year, with deadline varying by unit.

**Long version**

On October 12, APS members received an announcement of newly elected fellows. Fellows are nominated by APS members (anyone can nominate) to a particular unit, are reviewed by a unit selection committee. Those nominations considered deserving of fellowship are then forwarded to the Committee on Fellowship for further consideration, and then recommends the nominees to the APS Council for election. It is my understanding that much of the latter part is a formality; once you are nominated by your unit, you are likely to become a fellow. Units are allocated nominations based on their membership.

When the announcement was made, many were very disappointed about the numbers of women fellows. A large number of units had zero women fellows, and many had only one. In fact, by my count, there appears to only be one unit (DAP) with more than one (3).

As women in physics, we are used to being the minority, so the small numbers in themselves were not (any more) disheartening. What was disheartening was that for several units with (relatively) high women membership, there were zero women fellows. While we are sad and mad, an uncomfortable thought ensues, as we are also scientists:

**Is this just a result of small-number statistics? **

Think about it this way. You have a six-sided die. You roll the die 5 times. You note the number of times you got a 1. Let’s call this one trial. Do a bunch more trials (5 rolls). You’ll notice that there were many trials that yielded zero 1’s. Maybe more than you would have expected, since you get 5 rolls each time. But there it is.

In this analogy, rolling the die 5 times randomly selects the gender of 5 nominees. Women are #1, men are 2-6. Coincidentally, 1 of 6 is about right for the datasets we’ll consider. Repeat this a bunch of times (different units nominate different sets of 5), you’ll often end up with sets of no women nominees.

So zero women are just likely! Not our fault. ¯\_(ツ)_/¯

But here’s the double-reverse mathe-magic: In a set of 5 random nominees, you might get more zero women sets that you might expect, but you will get even more “enough”/”too many” women sets.

**But units are of different sizes and membership compositions…**

Indeed. We need to look into the details. I’ve gathered statistics for unit demographics as not all units are equal. (Insert pun about unity here.) I’ve also gathered the information for 2017 fellows by gender and nominating unit. In the case of ambiguous names, I have made sure I researched which gender they appear to present as. (As always, this kind of binary-based methodology ignores the gender spectrum.)

You’ll notice in the demographics that the %men and %women don’t add to 100%. This is because there is a fraction of membership who has left off their gender. This is a large enough fraction it appears to be the result of simply not checking an optional box. So I have assumed this fraction is represented in the same ratio as the %men and %women, to estimate the true percentages. The main issue with these percentages as they stand is that they are for the entire unit membership, and not just for members of the appropriate career stage who are not fellows yet. I don’t have a compelling reason to believe the numbers are all that different, though.

Armed with the percent women and the unit allocations, I proceeded to use the Conference Diversity Distribution Calculator, which I could have written my own code for, but why reinvent the wheel? This tool was developed to demonstrate that statistically speaking, in an unbiased selection, you are (typically) more likely to overrepresent women than have zero women. More on the math here, though if you’ve made it this far, you probably have done this before.

For an input of %women and #nominees, this tool gives me a few numbers. The most likely number of women nominated, the chances that women are overrepresented, exactly represented, and zero. It also provides a ratio of overrepresentation:zero, i.e. the odds of overrepresentation vs none at all.

My question is: in 2017, are there units that are underperforming? Is this larger than the number of units that are overperforming? How do we even define these metrics?

**Example calculation**

DAMOP has 13.4% women and 11 allocated nominees. They had 1 woman fellow. The most likely number of women fellows is 1 according to the calculator. But this only accounts for about 35% of the possible outcomes. About 20% of the time you get no women, but about 45% of the time you will get more than one woman! However, in terms of “scoring” you might say, DAMOP performed to expectation in 2017.

**Findings**

There were four general groupings that naturally rose once my numbers were in. 1) Larger units that are more likely to overrepresent women compared to zero (cutoff at 1.2). 2) Larger units that are about as likely to overrrepresent compared to zero. 3) Small units that used all of their nominations. 4) Small units that did not use their nominations.

Let’s start with the 3rd group. Basically, these units only had 1 or 2 nominees allocated. All in all 3 of 10 are women. This looks fine.

Let’s move to the 4th group. Basically, these units did not use all of their allocation. This could be an avenue to nominate more women. Generally, things look fine here, though certainly disturbing is the FIAP row (8 nominees, 0 women).

And now we can think a little more concretely, but for funsies, we’ll still go out of order. In group 2, we have about equal odds of overrepresentation vs zero. And yet, the only overrepresentation we see is the trivial one: when most likely = 0 and female fellows = 1. Never do we see most likely =1 and female fellows = 2, even though we should expect to see this fairly often.

I’ve also done a little metascoring. I highlighted the ones with zero women fellows. I also color-coded a bit. If the number of fellows was greater than most likely value = green, equal=blue, less=red. We get three units in the red: GSOFT, DPOLY, DCP. I’m not saying that they generally do bad, but in 2017, they underrepresented women. And it seems reasonable that at least one of those three would have done better, since zero should only happen about 30% of the time. The silver lining is that 4 other units overperformed, albeit trivially.

**Group 1 time! **

This is where the ugly stuff happens. These are all units with a larger likelihood of overrepresentation than zero representation.

One unit overrepresents women trivially (DPP) with one fellow. But while the most likely value is 0, the overall odds of nonzero are higher than the odds of zero. Only one other unit overrepresents women (DAP) with a most likely value of 2 and an actual value of 3. But even this has a caveat: 60% of the time women should be overrepresented in a sample like this.

DCMP has 1 female fellow of 22. In this case, I’ve lumped 1 or 2 fellows into the “expected” odds of about 43%. However, 52% of the time we should expect n = 3 or greater. A similar issue is seen in DMP.

DGRAV has zero women fellows, but the odds are pretty close to even with a most likely value of zero.

DBIO, DFD, and DNP all have zero, with most likely values of one. It’s unlikely that they would all have the same value, but the numbers tell us it is unlikely (20-25%) for any single one of them to be zero. For all of them to be zero seems especially unlikely.

**So what?**

In summary, while of course any given sample has a significant chance of underrepresenting women, the same sample often has at least an equal chance (if not greater) of OVERrepresenting women. Forget for a moment about the underrepresentation. **We should see more overrepresentation if the sampling is unbiased. **The pendulum always seems to swing the wrong way.

While I hesitate to suggest anything like quotas, it seems inexcusable that a unit of greater than 5 or so would have zero women fellows in a given year. It’s of course true that any given year there might be zero, but as a pattern over several years, certainly indefensible. But even more so, committees need to not be afraid of (gasp!) nominating more than one woman. Men are already overrepresented. It’s okay if women are overrepresented from time to time.

Who can fix the problem of not enough women nominees? You if you’re an APS member. Nominating committee chairs should also read this document, particularly the last paragraph. Sometimes getting a good pool requires beating the bushes a bit. **This is a small numbers game. Just one or two more nominees makes a big difference. **

Chad Topaz has a great resource for math (SIAM), I believe one is the works for physics, and will link to it when it happens.

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—-**A few updates / comments**—-

- The corollary: We are clearly not making unbiased selections, as we would do better just by rolling dice! So it’s not helpful to have the illusion that we aren’t biased. However, most of us believe that equitable representation amongst fellows is a worthy goal. The evidence suggests we have to work a little harder than we are to ensure a representative pool.
- Committees, especially those with large allocations, should not be satisfied with one token woman nominee. If for some reason that falls through, then you’re at zero.
- Departments and department chairs should consider nominating candidates from their department. While it might be ideal to have someone from your field nominate you, everyone has too much on their plate already, and can too easily forget about these things. Someone who sees you every day might be the better instigator. (Someone from your field can co-sponsor, as I understand it.)
- I’ve received some comments that the nomination process is burdensome for the nominators, and certainly not just a matter of suggesting a name. Taking a quick glance at it, I don’t disagree. Maybe there is a better system?