## Gender bias in academic science

Many a male scientist would have you believe that, when it comes to pursuing an academic career in a scientific field, female candidates at various levels enjoy a preferential treatment, often being chosen over equally or better qualified male applicants. This is allegedly due to a concerted effort taking place in many countries in the western world, aimed at increasing academic female representation in fields of science and engineering where women have traditionally been vastly outnumbered by men.
On the other hand, many if not most female scientists take issue with the above contention. They maintain that such actions, if they occur at all, have little or no effect in an environment that is dominated by and strongly biased in favor of men, and where women attempting to establish a career routinely face more or less overt discrimination.

Aside from anecdotal evidence [0] (more or less accurately recollected and recounted), is there any way of assessing such a statement quantitatively ? In other words, is it possible to determine whether, say, a female postdoc in a scientific discipline is more likely to land a tenure-track assistant professorship than a male counterpart ? Or whether she is more or less likely to make it all the way to full professorship, once on the tenure track ?
At least as far as the North American academic science scene is concerned, data are rather easily available. The US National Science Foundation publishes annually the Science and Engineering indicators. Appendix table 5-19 of the 2008 edition offers a fairly detailed breakdown of the employment figures for male and female doctorate holders across the various disciplines.
With the aid of Bayesian statistics, one may seek to provide an answer to the above questions [1].

Bayesian statistics
The basic aspects of Bayesian statistics are quite intuitive. Elementary rules of probability assert that, given two independent events A and B, each one characterized by a well-defined probability of occurring (let us call them p(A) and p(B)), the probability p(A,B) that both of them will occur is given by
p(A,B)=p(A) p(B)
i.e., by the product of the individual probabilities.
For two events that are not independent, i.e., the occurrence of one is affected by that of the other, one introduces the conditional probability p(A|B) for event A to occur, given that event B is known to have taken place. An analogous definition is given for p(B|A).
A fundamental result known as Bayes’ Theorem asserts the following:
p(A,B) = p(A|B) p(B) = p(B|A) p(A)
Stated in common language, the above means that the probability of occurrence of two events, can be conceptually broken down into the product of the probability for either one of the two to occur (typically referred to as the prior probability), with the conditional probability that the second one take place if the first one has happened. It does not matter which one of the two events is considered “first”.
For example, the probability of being in a car accident can be regarded as the product of the prior probability for one to be in a car, multiplied by the conditional probability of being in an accident if inside a moving car.

First case: postdocs landing tenure-track faculty jobs
It is essentially the norm, nowadays, for newly hired tenure-track (TT) faculty in most scientific disciplines to have undergone a period of a few years of postdoctoral training. The probability for a postdoctoral researcher to be female and to land a TT faculty position can be expressed as
p(TT,F) = p(F) p(TT|F)
where p(F) is the prior probability that a postdoctoral researcher be female in the first place, and p(TT|F) is the conditional probability that the postdoctoral researcher make the transition to tenure-track faculty given that her gender is female. Analogously, for male researchers one can write
p(TT,M) = p(M) p(TT|M)
On taking the ratio of the above two expressions one obtains
g = [p(TT|F)/p(TT|M)] = [p(M)/p(F)] [p(TT,F)/p(TT,M)]
The quantity g can be regarded of a measure of hiring bias either in favor or against female researchers, as it expresses the relative probability that a female postdoc will land a a faculty job, compared to that of a male postdoc. A value of g equal to, or sufficiently close to one, indicates a substantially gender-blind hiring, whereas a value of g significantly greater (lower) than one indicates hiring bias in favor of (against) female postdocs.
Because data for the prior probabilities p(M) and p(F), as well as for the joint probabilities p(TT,M) and p(TT,F) can be inferred from the above mentioned NSF data, which keep track of the female fractions of the postdoctoral and tenure-track populations, one can estimate the “gender bias ratio” g [2].

Let us consider the most recent (2006) data in the above-mentioned table, pertaining to all fields of science. Men account for 56.3% of all postdocs and 55.2% of all junior faculty. This means that the value of g across all sciences is
gAS = [56.3/43.7][44.8/55.2] = 1.05
It is easy to obtain estimates for individual fields as well:
gPS = [2.9/1.0][1.9/5.6] = 0.98 (physical sciences)
gLS = [6.7/6.1][9.8/11.2] = 0.96 (life sciences)
gMTH = [0.8/0.2][1.1/2.4] = 1.83 (mathematics)
gENG = [2.4/0.6][1.3/4.8] = 1.08 (engineering)
gPSY = [0.6/1.1][4.8/2.9] = 0.90 (psychology)
gSS = [0.4/0.5][5.2/4.8] = 0.87 (social sciences)

The above numbers would appear to indicate remarkably gender-blind hiring at the tenure-track level. For, the values of g for the various scientific disciplines and engineering, are less than 10% away from unity (which corresponds to lack of gender bias). The only case where some noticeable bias seems to exist (in favor of women) is Mathematics. Perhaps surprisingly, the sciences and engineering seem to be in fact overall friendlier to women at TT hiring time, than psychology and the social sciences, albeit not by a large amount.

Second case: from the TT to full professorship
The same analysis can be carried out to investigate the relative probability that a female tenure-track faculty will eventually become a tenured full professor (FP), with respect to the same probability for a male colleague. Using the same notation as above, we define
p(FP,F) = p(FP,F|TT,F) p(TT,F)
p(FP,M) = p(FP,M|TT,M) p(TT,M)

and consider the “gender bias ratio” h = [p(FP,F|TT,F)/p(FP,M|TT,M)].
The values, computed as above using data from the same source, are the following:
hAF = [33.7/89.8][28.6/23.2] = 0.46 (all sciences)
hPS = [2.7/17.6][5.6/1.9] = 0.45 (physical sciences)
hLS = [13.3/30.5][11.2/9.8]= 0.50 (life sciences)
hMTH = [1.4/9.2][2.4/1.1] = 0.33 (mathematics)
hENG = [1.2/15.1][4.8/1.3] = 0.29 (engineering)
hPSY = [7.0/9.1][2.9/4.8] = 0.46 (psychology)
hSS = [8.7/20.7][4.8/5.2] = 0.39 (social sciences)

The problem here is clear: women on the tenure track are significantly (between two and three times) less likely than men to make it all the way to full professorship. It is at this stage, not at TT hiring time, that problems begin for female academics, who ostensibly face an environment much more hostile to them than to their male counterparts.
It would be interesting to know at what level much of the “weeding out” occurs, i.e., whether it is along the TT, or at the time of applying for tenure, or later. The data provided by the NSF Science and Engineering Indicators are not broken down into further stages (e.g., tenured associate professors), and therefore it is not possible to make further statements.
It is interesting, however, to note how the social sciences and psychology are no better than science and engineering, from the standpoint of female academic advancement. In fact, social sciences are only better than mathematics and engineering (where women appear to have the hardest time), and worse than the physical and life sciences.
This suggests that this may not be so much an issue of women in academic science, as much as one of women in academia. If the above analysis is accurate (as usual I welcome comments and I shall publicly thank anyone who points out any flaw in my reasoning), then it would suggest that perhaps the bulk of the effort aimed at increasing female representation in academic science (or in academia) ought be directed at providing effective mentoring and support on the tenure track and afterwards, rather than ensuring fairness at hiring time.

Notes

[0] I have personally witnessed some half-hearted attempts, on the part of various university administrations, to increase the fraction of female faculty in fields where their under-representation is most severe (e.g., my own, physics). In my experience, such efforts never really go beyond some recommendations, e.g., that search committees pay particular attention to qualified female candidates.

[1] It must be emphasized that the issue addressed here is only possible bias against women who are already in the science career track. There exists, of course, a much broader (and arguably more important) issue, namely why so few women choose science as a career path in the first place, but that issue is not discussed here.

[2] The assumption is made that the numbers do not change significantly over the average duration of a postdoctoral stage (which varies across the fields but is roughly between three and four years).

### 15 Responses to “Gender bias in academic science”

1. Devin Says:

You have proven that women are less likely to make full professorship from tenure track, not that there is a bias against them. There are external factors to be considered as well, such as:

If women are more likely to decide to stop working and start a family.
If women are more likely to accept positions offered (or more likely to be offered positions) outside of academia.
etc.

Note that I’m not saying there is no bias, just that we can’t conclude it from these statistics alone.

Also, it seems you missed a step in the reasoning here
g = [p(TT|F)/p(TT|M)] = [p(M)/p(F)] [p(TT,F)/p(TT,M)]
In order to use 44.8/55.2, which is p(F|TT)/p(M|TT), you must first use that p(TT,F) = P(F|TT)P(TT), and P(TT,M) = P(M|TT)P(TT). It doesn’t change the result at all, since the P(TT) cancels, but then at least you would be using the numbers that the symbols actually represent.

2. Massimo (formerly known as Okham) Says:

Note that I’m not saying there is no bias, just that we can’t conclude it from these statistics alone.

I think that there is bias against women on the part of the academic environment, and it is shown by the numbers. It may not be deliberate, but that is a different issue.

Also, it seems you missed a step in the reasoning here
Oh-kay….

3. Schlupp Says:

Hi Massimo,

Some of the outside factors that Devin mentions might be of a similar category as the ones you mention in footnote [1], i.e., while they are a form of bias, they may not be directly under a university’s control. However, the universities might hopefully be in a better position to do something about them, because they at least know their TT faculty as opposed to middle- and high school kids.

4. Steven O Says:

One possible factor that may contribute to the disparity between TT and FP is departmental service. (This is not my idea (I might have even read it here), although it makes sense, and matches my observations….limited as they may be). Female faculty members can end up on many more committees than men, since departments may want a female prospective. Since there are much less women in many departments this means that a few, or the same faculty member will get stuck on many committees, which in turn takes away from their time to conduct research, which then effects their chance at tenure.

I am not sure how much this happens else where, but at seems like one factor that is quite reasonable.

• Massimo (formerly known as Okham) Says:

Steve,

I would be surprised if that were a factor but, hey, you may be right. Committee work is supposed to be assigned equitably, and if anything probationary faculty are routinely reminded by senior colleagues (both in the department as well as in the Faculty/College) not to spend too much time with service (I was told that flat out when I was an assistant professor).

5. Cherish Says:

1) I find it interesting that, with the exception of mathematics, even with the “leg up” of affirmative action (which most universities still claim to opt into), women are hired at about the same rate as men.

2) I wish I could figure out a way to test a notion: if, in general, it is perceived that women have a better (and hence, unfair) opportunity of landing a TT position, does that cause a bias against them that can be gauged in a meaningful way? I’m thinking that perhaps there is a perception that because they have all this extra help via affirmative action (or they wouldn’t be there in the first place, after all) that they don’t need additional faculty support (or perhaps any, creating a situation where men are supported and women aren’t) which, in turn, makes it more likely that they will not be able to get tenure. I do honestly think this is the case (in part, not totality) because of how much I hear that women have much better chances of getting faculty positions when it appears, from the statistics you site, that there really isn’t much difference.

It’s like when one sees a bicyclist with a helmet and drives closer as they pass them than they would if they didn’t have the helmet, making helmets an actual liability. In the case of hiring, there is the perception of bias in favor of women, whether or not it really exists, leading to the removal of support structures and a greater chance of failure.

6. rumor monger Says:

anecdotal evidence, from this year’s statistics alone:

a physicist with h-index of 25 was just elected to National Academy of Sciences. Normally the h-index on the order of at least 55 or 60 is in line with Academy membership.

a grad student – who didn’t even get a PhD yet, no postdoc experience with 5 (yes five) publications total (and none first author) got offered a faculty position – over many candidates with record x3-4 that – at least on paper.

a physicist with h-index of 4 was offered a faculty position, and another with h-index of 6 was tenured this year – at top 20 physics department.

I didn’t mention it up front, but all examples above involve women. Whenever I hear blatant examples of unfair hiring it seems to be always involving a woman.

Now, these may be outliers, and there are in fact many others that I don’t hear about, but I doubt it. If anyone knows an example of under-qualified male candidate being hired/promoted, that can beat the examples posted above, post them in comments.

• Massimo (formerly known as Okham) Says:

RM, I tend not to trust anecdotal evidence for a number of reasons. I think none of us are ever 100% fair and objective when discussing these things, especially when we ourselves are competing for jobs (which you are, aren’t you ?). Problem is, your anecdotal evidence is not mine, and the way we interpret it is also biased.
I have witnessed myself hires of male candidates who, in my opinion, were not as qualified as others (including women), and could tell you about dozens of others I have followed through the rumor mill over the past decade (yes, there used to be an informal rumor mill even before it started being published on the web).
This is why i prefer to look at stats, large samples, and so on. And if you agree with my analysis (if not, please tell me where I am getting things wrong), there does not seem to be any bias whatsoever in favor of women at hiring time.

• Schlupp Says:

rumor monger, I guess your plea for examples is a rhetorical question, right? Because some of them are so easy to find that you might have seen them yourself….

Anecdotal “evidence” like yours tends to be biased even for well meaning observers if they involve majority and minority members: Suppose the very lucky hire with h-index 4 is male. (I chose this among your examples, because I know of a few cases, it’s not that rare.) In this case, the argument “He got it just because he is a man” would not fly. Since there are many male candidates, his gender did not set him apart from the competition and can not possibly explain the different outcome. Consequently, people would offer alternative explanations, e.g. “he just got it because his adviser is a big bully” or “he must be good after all” or “perhaps he is blackmailing the chair of the search committee with compromising snap shots taken at the last APS March Meeting” or whatever. The story would either not be repeated at all, or it would be told with a very different angle. Only when the lucky hire is female (or from a minority) does “she got it because of being a woman” even make sense enough as an explanation to get the story told at all.

The same effect can be at work in the opposite camp: “She didn’t get whatever just because she is a woman” might sound plausible if there was just one woman, so someone is going to say it even if there are other possible reasons. “He didn’t get whatever just because he is a man” is unlikely to be said if the other 9 men involved did not have similar problems.

7. Steven O Says:

All of the data looked at is from 2006 correct? Could it not be possible that the hiring biases could have been much different for the current crop of FP when they were applying for TT positions? What would happen if, say, you looked at the data from X years before 2006 (X being the average number of years for a TT to become FP). Would the g be the same as it was for the 2006 data? Maybe the current bias against female FP is from a hiring bias from X number of years ago, but it stayed constant from TT to FP? I don’t think we can eliminate that possibility at this point in the game.

• Massimo (formerly known as Okham) Says:

Steven, yes, if you read my note [2] that is exactly the assumption that I am making. I understand that there may be a “retardation” effect, but… how big can it be ? Anyway, if you want you can always do the check yourself — you know where all the data are 😉

8. Cherish Says:

If anyone knows an example of under-qualified male candidate being hired/promoted, that can beat the examples posted above, post them in comments.

I’d rather not go into specifics, but I have seen it happen…very, very recently.

9. Anon Says:

A big assumption is that the situation has reached equilibrium, which is not correct, I think. As of ~ 20 years ago it was very clear that there was gender discrimination, which explains the relatively small number of female tenured professors. I think that gender discrimination has lessened now, which is why the number of tenure track female hires is reasonably proportional to the postdocs available. Wait for another 20 years and run the numbers again.

• Massimo (formerly known as Okham) Says:

A big assumption is that the situation has reached equilibrium, which is not correct, I think.

I agree, which is why I am not making it, nor am I mentioning anything like that in the post — I do not see what relevance it would have anyway.

Wait for another 20 years and run the numbers again.

You mean, if it is solved in twenty years it is not a problem now ? Man, I’d hate to be your mortgage lender…