Rationality Rules is an Abusive Transphobe

Abuse comes in more forms than many people realize. Take financial abuse, where someone uses economic leverage to control you, or reproductive coercion, or this behaviour.

Gaslighting is a form of emotional abuse where the abuser intentionally manipulates the physical environment or mental state of the abusee, and then deflects responsibility by provoking the abusee to think that the changes reside in their imagination, thus constituting a weakened perception of reality (Akhtar, 2009; Barton & Whitehead, 1969; Dorpat, 1996; Smith & Sinanan, 1972). By repeatedly and convincingly offering explanations that depict the victim as unstable, the abuser can control the victim’s perception of reality while maintaining a position of truth-holder and authority.

Roberts, Tuesda, and Dorinda J. Carter Andrews. “A Critical Race Analysis of the Gaslighting against African American Teachers.” Contesting the Myth of a” Post Racial Era”: The Continued Significance of Race in US Education, 2013, 69–94.

A small but growing amount of the scientific literature considers gaslighting a form of abuse. It’s also worth knowing about a close cousin of gaslighting known as “DARVO.”

DARVO refers to a reaction perpetrators of wrong doing, particularly sexual offenders, may display in response to being held accountable for their behavior. DARVO stands for “Deny, Attack, and Reverse Victim and Offender.” The perpetrator or offender may Deny the behavior, Attack the individual doing the confronting, and Reverse the roles of Victim and Offender such that the perpetrator assumes the victim role and turns the true victim — or the whistle blower — into an alleged offender. This occurs, for instance, when an actually guilty perpetrator assumes the role of “falsely accused” and attacks the accuser’s credibility and blames the accuser of being the perpetrator of a false accusation. […]

In a 2017 peer-reviewed open-access research study, Perpetrator Responses to Victim Confrontation: DARVO and Victim Self-Blame, Harsey, Zurbriggen, & Freyd reported that: “(1) DARVO was commonly used by individuals who were confronted; (2) women were more likely to be exposed to DARVO than men during confrontations; (3) the three components of DARVO were positively correlated, supporting the theoretical construction of DARVO; and (4) higher levels of exposure to DARVO during a confrontation were associated with increased perceptions of self-blame among the confronters. These results provide evidence for the existence of DARVO as a perpetrator strategy and establish a relationship between DARVO exposure and feelings of self-blame.

If DARVO seems vaguely familiar, that’s because it’s a popular tactic in the far-Right. Brett Kavanaugh used it during his Congressional hearing, this YouTuber encountered it quite a bit among the Proud Boys, and even RationalWiki’s explanation of it invokes the Christian far-Right. DARVO may be common among sexual abusers, but it’s important to stress that it’s not exclusive to them. It’s best to think of this solely as an abusive tactic to evade scrutiny, without that extra baggage. [Read more…]

The Crisis of the Mediocre Man

I was browsing YouTube videos on PyMC3, as one naturally does, when I happened to stumble on this gem.

Tech has spent millions of dollars in efforts to diversify workplaces. Despite this, it seems after each spell of progress, a series of retrograde events ensue. Anti-diversity manifestos, backlash to assertive hiring, and sexual misconduct scandals crop up every few months, sucking the air from every board room. This will be a digest of research, recent events, and pointers on women in STEM.

Lorena A. Barba really knows her stuff; the entire talk is a rapid-fire accounting of claims and counterclaims, aimed to directly appeal to the male techbros who need to hear it. There was a lot of new material in there, for me at least. I thought the only well-described matriarchies came from the African continent, but it turns out the Algonquin also fit that bill. Some digging turns up a rich mix of gender roles within First Nations peoples, most notably the Iroquois and Hopi. I was also depressed to hear that the R data analysis community is better at dealing with sexual harassment than the skeptic/atheist community.

But what really grabbed my ears was the section on gender quotas. I’ve long been a fan of them on logical grounds: if we truly believe the sexes are equal, then if we see unequal representation we know discrimination is happening. By forcing equality, we greatly reduce network effects where one gender can team up against the other. Worried about an increase in mediocrity? At worst that’s a temporary thing that disappears once the disadvantaged sex gets more experience, and at best the overall quality will actually go up. The research on quotas has advanced quite a bit since that old Skepchick post. Emphasis mine.

In 1993, Sweden’s Social Democratic Party centrally adopted a gender quota and imposed it on all the local branches of that party (…). Although their primary aim was to improve the representation of women, proponents of the quota observed that the reform had an impact on the competence of men. Inger Segelström (the chair of Social Democratic Women in Sweden (S-Kvinnor), 1995–2003) made this point succinctly in a personal communication:

At the time, our party’s quota policy of mandatory alternation of male and female names on all party lists became informally known as the crisis of the mediocre man

We study the selection of municipal politicians in Sweden with regard to their competence, both theoretically and empirically. Moreover, we exploit the Social Democratic quota as a shock to municipal politics and ask how it altered the competence of that party’s elected politicians, men as well as women, and leaders as well as followers.

Besley, Timothy. “Gender Quotas and the Crisis of the Mediocre Man: Theory and Evidence from Sweden.” THE AMERICAN ECONOMIC REVIEW 107, no. 8 (2017): 39.

We can explain this with the benefit of hindsight: if men can rely on the “old boy’s network” to keep them in power, they can afford to slack off. If other sexes cannot, they have to fight to earn their place. These are all social effects, though; if no sex holds a monopoly on operational competence in reality, the net result is a handful of brilliant women among a sea of iffy men. Gender quotas severely limit the social effects, effectively kicking out the mediocre men to make way for average women, and thus increase the average competence.

As tidy as that picture is, it’s wrong in one crucial detail. Emphasis again mine.

These estimates show that the overall effect mainly reflects an improvement in the selection of men. The coefficient in column 4 means that a 10-percentage-point larger quota bite (just below the cross-sectional average for all municipalities) raised the proportion of competent men by 4.4 percentage points. Given an average of 50 percent competent politicians in the average municipality (by definition, from the normalization), this corresponds to a 9 percent increase in the share of competent men.

For women, we obtain a negative coefficient in the regression specification without municipality trends, but a positive coefficient with trends. In neither case, however, is the estimate significantly different from zero, suggesting that the quota neither raised nor cut the share of competent women. This is interesting in view of the meritocratic critique of gender quotas, namely that raising the share of women through a quota must necessarily come at the price of lower competence among women.

Increasing the number of women does not also increase the number of incompetent women. When you introduce a quota, apparently, everyone works harder to justify being there. The only people truly hurt by gender quotas are mediocre men who rely on the Peter Principle.

The like ratio for said talk. 47 likes, 55 dislikes, FYI.Alas, if that YouTube like ratio is any indication, there’s a lot of them out there.

Rationality Rules DESTROYS Women’s Sport!!1!

I still can’t believe this post exists, given its humble beginnings.

The “women’s category” is, in my opinion, poorly named given our current climate, and so I’d elect a name more along the lines of the “Under 5 nmol/l category” (as in, under 5 nanomoles of testosterone per litre), but make no mistake about it, the “woman’s category” is not based on gender or identity, or even genitalia or chromosomes… it’s based on hormone levels and the absence of male puberty.

The above comment wasn’t in Rationality Rules’ latest transphobic video, it was just a casual aside by RR himself in the YouTube comment section. He’s obiquely doubled-down via Twitter (hat tip to Essence of Thought):

Of course, just as I support trans men competing in all “men’s categories” (poorly named), women who have not experienced male puberty competing in all women’s sport (also poorly named) and trans women who have experienced male puberty competing in long-distance running.

To further clarify, I think that we must rename our categories according to what they’re actually based on. It’s not right to have a “women’s category” and yet say to some trans women (who are women!) that they can’t compete within it; it should be renamed.

The proposal itched away at me, though, because I knew it was testable.

There is a need to clarify hormone profiles that may be expected to occur after competition when antidoping tests are usually made. In this study, we report on the hormonal profile of 693 elite athletes, sampled within 2 h of a national or international competitive event. These elite athletes are a subset of the cross-sectional study that was a component of the GH-2000 research project aimed at developing a test to detect abuse with growth hormone.

Healy, Marie-Louise, et al. “Endocrine profiles in 693 elite athletes in the postcompetition setting.” Clinical endocrinology 81.2 (2014): 294-305.

The GH-2000 project had already done the hard work of collecting and analyzing blood samples from athletes, so checking RR’s proposal was no tougher than running some numbers. There’s all sorts of ethical guidelines around sharing medical info, but fortunately there’s an easy shortcut: ask one of the scientists involved to run the numbers for me, and report back the results. Aggregate data is much more resistant to de-anonymization, so the ethical concerns are greatly reduced. The catch, of course, is that I’d have to find a friendly researcher with access to that dataset. About a month ago, I fired off some emails and hoped for the best.

I wound up much, much better than the best. I got full access to the dataset!! You don’t get handed an incredible gift like this and merely use it for a blog post. In my spare time, I’m flexing my Bayesian muscles to do a re-analysis of the above paper, while also looking for observations the original authors may have missed. Alas, that means my slow posting schedule is about to crawl.

But in the meantime, we have a question to answer.

What Do We Have Here?

(Click here to show the code)
Total Assigned-female Athletes = 239
  Height, Mean           = 171.61 cm
  Height, Std.Dev        = 7.12 cm
  Weight, Mean           = 64.27 kg
  Weight, Std.Dev        = 9.12 kg
  Body Fat, Mean         = 13.19 kg
  Body Fat, Std.Dev      = 3.85 kg
  Testosterone, Mean     = 2.68 nmol/L
  Testosterone, Std.Dev  = 4.33 nmol/L
  Testosterone, Max      = 31.90 nmol/L
  Testosterone, Min      = 0.00 nmol/L

Total Assigned-male Athletes = 454
  Height, Mean           = 182.72 cm
  Height, Std.Dev        = 8.48 cm
  Weight, Mean           = 80.65 kg
  Weight, Std.Dev        = 12.62 kg
  Body Fat, Mean         = 8.89 kg
  Body Fat, Std.Dev      = 7.20 kg
  Testosterone, Mean     = 14.59 nmol/L
  Testosterone, Std.Dev  = 6.66 nmol/L
  Testosterone, Max      = 41.00 nmol/L
  Testosterone, Min      = 0.80 nmol/L

The first step is to get a basic grasp on what’s there, via some crude descriptive statistics. It’s also useful to compare these with the original paper, to make sure I’m interpreting the data correctly. Excusing some minor differences in rounding, the above numbers match the paper.

The only thing that stands out from the above, to me, is the serum levels of testosterone. At least one source says the mean of these assigned-female athletes is higher than the normal range for their non-athletic cohorts. Part of that may simply be because we don’t have a good idea of what the normal range is, so it’s not uncommon for each lab to have their own definition of “normal.” This is even worse for those assigned female, since their testosterone levels are poorly studied; note that my previous link collected the data of over a million “men,” but doesn’t mention “women” once. Factor in inaccurate test results and other complicating factors, and “normal” is quite poorly-defined.

Still, Rationality Rules is either convinced those complications are irrelevant, or ignorant of them. And, to be fair, that 5nmol/L line implicitly sweeps a lot of them under the rug. Let’s carry on, then, and look for invalid data. “Invalid” covers everything from missing data, to impossible data, and maybe even data we think might be made inaccurate due to measurement error. I consider a concentration of zero testosterone as invalid, even though it may technically be possible.

(Click here to show the code)
Total Assigned-male Athletes w/ T levels >= 0        = 446
                             w/ T levels <= 0.5      = 0
                             w/ T levels == 0        = 0
                             w/ missing T levels     = 8
                             that I consider valid   = 446

Total Assigned-female Athletes w/ T levels >= 0      = 234
                               w/ T levels <= 0.5    = 5
                               w/ T levels == 0      = 1
                               w/ missing T levels   = 5
                               that I consider valid = 229

Fortunately for us, the losses are pretty small. 229 datapoints is a healthy sample size, so we can afford to be liberal about what we toss out. Next up, it would be handy to see the data in chart form.

(Click here to show the code)

Testosterone, elite athletes

I've put vertical lines at both the 0.5 and 5 nmol/L cutoffs. There's a big difference between categories, but we can see clouds on the horizon: a substantial number of assigned-female athletes have greater than 5 nmol/L of testosterone in their bloodstream, while a decent number of assigned-male athletes have less. How many?

(Click here to show the code)
Segregating Athletes by Testosterone
Concentration  aFab  aMab
   > 5nmol/L    19   417
   < 5nmol/L   210    26
   = 5nmol/L     0     3

8.3% of assigned-female athletes have > 5nmol/L
5.8% of assigned-male athletes have < 5nmol/L
4.4% of athletes with > 5nmol/L are assigned-female
11.0% of athletes with < 5nmol/L are assigned-male

Looks like anywhere from 6-8% of athletes have testosterone levels that cross Rationality Rules' line. For comparison, maybe 1-2% of the general public has some level of gender dysphoria, though estimating exact figures is hard in the face of widespread discrimination and poor sex-ed in schools. Even that number is misleading, as the number of transgender athletes is substantially lower than 1-2% of the athletic population. The share of transgender athletes is irrelevant to this dataset anyway, as it was collected between 1996 and 1999, when no sporting agency had policies that allowed transgender athletes to openly compete.

That 6-8%, in other words, is entirely cisgender. This echoes one of Essence Of Thought's arguments: RR's 5nmol/L policy has far more impact on cis athletes than trans athletes, which could have catastrophic side-effects. Could is the operative word, though, because as of now we don't know anything about these athletes. Do >5nmol/L assigned-female athletes have bodies more like >5nmol/L assigned-male athletes than <5nmol/L assigned-female athletes? If so, then there's no problem. Equivalent body types are competing against each other, and outcomes are as fair as could be reasonably expected.

What, then, counts as an "equivalent" body type when it comes to sport?

Newton's First Law of Athletics

One reasonable measure of equivalence is height. It's one of the stronger sex differences, and height is also correlated with longer limbs and greater leverage. Whether that's relevant to sports is debatable, but height and correlated attributes dominate Rationality Rules' list.

[19:07] In some events - such as long-distance running, in which hemoglobin and slow-twitch muscle fibers are vital - I think there's a strong argument to say no, [transgender women who transitioned after puberty] don't have an unfair advantage, as the primary attributes are sufficiently mitigated. But in most events, and especially those in which height, width, hip size, limb length, muscle mass, and muscle fiber type are the primary attributes - such as weightlifting, sprinting, hammer throw, javelin, netball, boxing, karate, basketball, rugby, judo, rowing, hockey, and many more - my answer is yes, most do have an unfair advantage.

Fortunately for both of us, most athletes in the dataset have a "valid" height, which I define as being at least 30cm tall.

(Click here to show the code)
Out of 693 athletes, 678 have valid height data.

Height, elite athletes

The faint vertical lines are for the mean adult height of Germans born in 1976, which should be a reasonable cohort to European athletes that were active between 1996 and 1999, while the darker lines are each category's mean. Athletes seem slightly taller than the reference average, but only by 2-5cm. The amount of overlap is also surprising, given that height is supposed to be a major sex difference. We actually saw less overlap with testosterone! Finally, the height distribution isn't quite Gaussian, there's a subtle bias towards the taller end of the spectrum.

Height is a pretty crude metric, though. You could pair any athlete with a non-athlete of the same height, and there's no way the latter would perform as well as the former. A better measure of sporting ability would be muscle mass. We shouldn't use the absolute mass, though: bigger bodies have more mass and need more force to accelerate as smaller bodies do, so height and muscle mass are correlated. We need some sort of dimensionless scaling factor which compensates.

And we have one! It's called the Body Mass Index, or BMI.

$$ BMI = \frac w {h^2}, $$

where \(w\) is a person's mass in kilograms, and \(h\) is a person's height in metres. Unfortunately, BMI is quite problematic. Partly that's because it is a crude measure of obesity. But part of that is because there are two types of tissue which can greatly vary, body fat and muscle, yet both contribute equally towards BMI.

That's all fixable. For one, some of the athletes in this dataset had their body fat measured. We can subtract that mass off, so their weight consists of tissues that are strongly correlated with height plus one that is fudgable: muscle mass. For two, we're not assessing these individual's health, we only want a dimensionless measure of muscle mass relative to height. For three, we're not comparing these individuals to the general public, so we're not restricted to using the general BMI formula. We can use something more accurate.

The oddity is the appearance of that exponent 2, though our world is three-dimensional. You might think that the exponent should simply be 3, but that doesn't match the data at all. It has been known for a long time that people don't scale in a perfectly linear fashion as they grow. I propose that a better approximation to the actual sizes and shapes of healthy bodies might be given by an exponent of 2.5. So here is the formula I think is worth considering as an alternative to the standard BMI:

$$ BMI' = 1.3 \frac w {h^{2.5}} $$

I can easily pop body fat into Nick Trefethen's formula, and get a better measure of relative muscle mass,

$$ \overline{BMI} = 1.3 \frac{ w - bf }{h^{2.5}}, $$

where \(bf\) is total body fat in kilograms. Individuals with excess muscle mass, relative to what we expect for their height, will have a high \(\overline{BMI}\), and vice-versa. And as we saw earlier, muscle mass is another of Rationality Rules' determinants of sporting performance.

Time for more number crunching.

(Click here to show the code)
Out of 693 athletes, 227 have valid adjusted BMIs.
                     663 have valid weights.
                     241 have valid body fat percentages.

Total Assigned-female Athletes = 239
 total with valid adjusted BMI = 86
  adjusted BMI, Mean     = 16.98
  adjusted BMI, Std.Dev  = 1.21
  adjusted BMI, Median   = 16.96

Total Assigned-male Athletes = 454
 total with valid adjusted BMI = 141
  adjusted BMI, Mean     = 20.56
  adjusted BMI, Std.Dev  = 1.88
  adjusted BMI, Median   = 20.28

The bad news is that most of this dataset lacks any information on body fat, which really cuts into our sample size. The good news is that we've still got enough to carry on. It also looks like there's a strong sex difference, and the distribution is pretty clustered. Still, a chart would help clarify the latter point.

(Click here to show the code)

Adjusted BMI, elite athletes

Whoops! There's more overlap and skew than I thought. Even in logspace, the results don't look Gaussian. We'll have to remember that for the next step.

A Man Without a Plan is Not a Man

Just looking at charts isn't going to solve this question, we need to do some sort of hypothesis testing. Fortunately, all the pieces I need are here. We've got our hypothesis, for instance:

Athletes with exceptional testosterone levels are more like athletes of the same sex but with typical testosterone levels, than they are of other athletes with a different sex but similar testosterone levels.

If you know me, you know that I'm all about the Bayes, and that gives us our methodology.

  1. Fit a model to a specific metric for assigned-female athletes with less than 5nmol/L of serum testosterone.
  2. Fit a model to a specific metric for assigned-male athletes with more than 5nmol/L of serum testosterone.
  3. Apply the first model to the test group, calculating the overall likelihood.
  4. Apply the second model to the test group, calculating the overall likelihood.
  5. Sample the probability distribution of the Bayes Factor.

"Metric" is one of height or \(\overline{BMI}\), while "test group" is one of assigned-female athletes with >5nmol/L of serum testosterone or assigned-male athletes with <5nmol/L of serum testosterone. The Bayes Factor is simply

$$ \text{Bayes Factor} = \frac{ p(E \mid H_1) \cdot p(H_1) }{ p(E \mid H_2) \cdot p(H_2) } = \frac{ p(H_1 \mid E) }{ p(H_2 \mid E) }, $$

which means we need two hypotheses, not one. Fortunately, I've phrased the hypothesis to make it easy to negate: athletes with exceptional testosterone levels are less like athletes of the same sex but with typical testosterone levels, than they are of other athletes with a different sex but similar testosterone levels. We'll call this new hypothesis \(H_2\), and the original \(H_1\). Bayes factors greater than 1 mean \(H_1\) is more likely than \(H_2\), and vice-versa.

Calculating all that would be easy if I was using Stan or PyMC3, but I ran into problems translating the former's probability distributions into charts, and I don't have any experience with the latter. My next choice, emcee, forces me to manually convolve two posterior distributions. Annoying, but not difficult.

I'm a Model, If You Know What I Mean

That just leaves one thing left: what models are we going to use? The obvious choice for height is the Gaussian distribution, as from previous research we know it's a great model.

(Click here to show the code)
Fitting the height of lT aFab athletes to a Gaussian distribution ...
     0: (-980.322471) mu=150.000819, sigma=15.000177
    64: (-710.417497) mu=169.639051, sigma=8.579088
   128: (-700.539260) mu=171.107358, sigma=7.138832
   192: (-700.535241) mu=171.154151, sigma=7.133279
   256: (-700.540692) mu=171.152701, sigma=7.145515
   320: (-700.552831) mu=171.139668, sigma=7.166857
   384: (-700.530969) mu=171.086422, sigma=7.094077
    ML: (-700.525284) mu=171.155240, sigma=7.085777
median: (-700.525487) mu=171.134614, sigma=7.070993

Alas, emcee also lacks a good way to assess model fitness. One crude metric is look at the progression of the mean fitness; if it grows and then stabilizes around a specific value, as it does here, we've converged on something. Another is to compare the mean, median, and maximal likelihood of the posterior; if they're about equally likely, we've got a fuzzy caterpillar. Again, that's also true here.

As we just saw, though, charts are a better judge of fitness than a handful of numbers.

(Click here to show the code)

Height, elite athletes (now with a model).

If you were wondering why I didn't make much of a fuss out of the asymmetry in the height distribution, it's because I've already seen this graph. A good fit isn't necessarily the best though, and I might be able to get a closer match by incorporating the sport each athlete played.

(Click here to show the code)
            Assigned-female Athletes            
         sport              below/above 171cm   
           Power lifting:  1 / 0
              Basketball:  2 /12
                Football:  0 / 0
                Swimming: 41 /49
                Marathon:  0 / 1
                Canoeing:  1 / 0
                  Rowing:  9 /13
    Cross-country skiing:  8 / 1
           Alpine skiing: 11 / 1
          Weight lifting:  7 / 0
                    Judo:  0 / 0
                   Bandy:  0 / 0
              Ice Hockey:  0 / 0
                Handball: 12 /17
         Track and field: 22 /27

Basketball attracts tall people, unsurprisingly, while skiing seems to attract shorter people. This could be the cause of that asymmetry. It's no guarantee that I'll actually get a better fit, though, as I'm also dramatically cutting the number of datapoints to fit to. The model's uncertainty must increase as a result, and that may be enough to dilute out any increase in fitness. I'll run those numbers for the paper, but for now the Gaussian model I have is plenty good.

(Click here to show the code)
Fitting the height of hT aMab athletes to a Gaussian distribution ...
     0: (-2503.079578) mu=150.000061, sigma=15.001179
    64: (-1482.315571) mu=179.740851, sigma=10.506003
   128: (-1451.789027) mu=182.615810, sigma=8.620333
   192: (-1451.748336) mu=182.587979, sigma=8.550535
   256: (-1451.759883) mu=182.676004, sigma=8.546410
   320: (-1451.746697) mu=182.626918, sigma=8.538055
   384: (-1451.747266) mu=182.580692, sigma=8.534070
    ML: (-1451.746074) mu=182.591047, sigma=8.534584
median: (-1451.759295) mu=182.603231, sigma=8.481894

We get the same results when fitting the model to >5 nmol/L assigned-male athletes. The log likelihood, that number in brackets, is a lot lower for these athletes, but that number is roughly proportional to the number of samples. If we had the same degree of model fitness but doubled the number of samples, we'd expect the log likelihood to double. And, sure enough, this dataset has roughly twice as many assigned-male athletes as it does assigned-female athletes.

(Click here to show the code)

Height, elite athletes (now with both models)

The updated charts are more of the same.

Unfortunately, adjusted BMI isn't nearly as tidy. I don't have any prior knowledge that would favour a particular model, so I wound up testing five candidates: the Gaussian, Log-Gaussian, Gamma, Weibull, and Rayleigh distributions. All but the first needed an offset parameter to get the best results, which has the same interpretation as last time.

(Click here to show the code)
Fitting the adjusted BMI of hT aMab athletes to a Gaussian distribution ...
     0: (-410.901047) mu=14.999563, sigma=5.000388
   384: (-256.474147) mu=20.443497, sigma=1.783979
    ML: (-256.461460) mu=20.452817, sigma=1.771653
median: (-256.477475) mu=20.427138, sigma=1.781139
(Click here to show the code)
Fitting the adjusted BMI of hT aMab athletes to a Log-Gaussian distribution ...
     0: (-629.141577) mu=6.999492, sigma=2.001107, off=10.000768
   384: (-290.910651) mu=3.812746, sigma=1.789607, off=16.633741
   ML: (-277.119315) mu=3.848383, sigma=1.818429, off=16.637382
median: (-288.278918) mu=3.795675, sigma=1.778238, off=16.637076
(Click here to show the code)
Fitting the adjusted BMI of hT aMab athletes to a Gamma distribution ...
    0: (-564.227696) alpha=19.998389, beta=3.001330, off=9.999839
   384: (-256.999252) alpha=15.951361, beta=2.194827, off=13.795466
ML    : (-248.056301) alpha=8.610936, beta=1.673886, off=15.343436
median: (-249.115483) alpha=12.411010, beta=2.005287, off=14.410945
(Click here to show the code)
Fitting the adjusted BMI of hT aMab athletes to a Weibull distribution ...
    0: (-48865.772268) k=7.999859, beta=0.099877, off=0.999138
  384: (-271.350390) k=9.937527, beta=0.046958, off=0.019000
   ML: (-270.340284) k=9.914647, beta=0.046903, off=0.000871
median: (-270.974131) k=9.833793, beta=0.046947, off=0.011727
(Click here to show the code)
Fitting the adjusted BMI of hT aMab athletes to a Rayleigh distribution ...
    0: (-3378.099000) tau=0.499136, off=9.999193
  384: (-254.717778) tau=0.107962, off=16.378780
   ML: (-253.012418) tau=0.110751, off=16.574934
median: (-253.092584) tau=0.108740, off=16.532576
(Click here to show the code)

Adjusted BMI, elite athletes (now with a LOT of models).

Looks like the Gamma distribution is the best of the bunch, though only if you use the median or maximal likelihood of the posterior. There must be some outliers in there that are tugging the mean around. Visually, there isn't too much difference between the Gaussian and Gamma fits, but the Rayleigh seems artificially sharp on the low end. It's a bit of a shame, the Gamma distribution is usually related to rates and variance so we don't have a good reason for applying it here, other than "it fits the best." We might be able to do better with a per-sport Gaussian distribution fit, but for now I'm happy with the Gamma.

Time to fit the other pool of athletes, and chart it all.

(Click here to show the code)
Fitting the adjusted BMI of lT aFab athletes to a Gamma distribution ...
    0: (-127.467934) alpha=20.000007, beta=3.000116, off=9.999921
   384: (-128.564564) alpha=15.481265, beta=3.161022, off=12.654149
ML    : (-117.582454) alpha=2.927721, beta=1.294851, off=14.713479
median: (-120.689425) alpha=11.961847, beta=2.836153, off=13.008723
(Click here to show the code)

Adjusted BMI, elite athletes (now with two Gamma models superimposed)

Those models look pretty reasonable, though the upper end of the assigned-female distribution could be improved on. It's a good enough fit to get some answers, at least.

The Nitty Gritty

It's easier to combine step 3, applying the model, with step 5, calculating the Bayes Factor, when writing the code. The resulting Bayes Factor has a probability distribution, as the uncertainty contained in the posterior contaminates it.

(Click here to show the code)
Summary of the BF distribution, for the height of >5nmol/L aFab athletes
         n       mean   geo.mean         5%        16%        50%        84%        95%
        19      10.64       5.44       0.75       1.76       5.66      17.33      35.42

Percentage of BF's that favoured the primary hypothesis: 92.42%
Percentage of BF's that were 'decisive': 14.17%

Bayes factor, height, >5nmol/L aFab athletes

That looks a lot like a log-Gaussian distribution. The arthithmetic mean fails us here, thanks to the huge range of values, so the geometric mean and median are better measures of central tendency.

The best way I can interpret this result is via an eight-sided die: our credence in the hypothesis that >5nmol/L aFab athletes are more like their >5nmol/L aMab peers than their <5nmol/L aFab ones is similar to the credence we'd place on rolling a one via that die, while our credence on the primary hypothesis is similar to rolling any other number except one. About 92% of the calculated Bayes Factors were favourable to the primary hypothesis, and about 16% of them crossed the 19:1 threshold, a close match for the asserted evidential bar in science.

That's strong evidence for a mere 19 athletes, though not quite conclusive. How about the Bayes Factor for the height of <5nmol/L aMab athletes?

(Click here to show the code)
Summary of the BF distribution, for the height of <5nmol/L aMab athletes
         n       mean   geo.mean         5%        16%        50%        84%        95%
        26   4.67e+21   3.49e+18   5.67e+14   2.41e+16   5.35e+18   4.16e+20   4.61e+21

Percentage of BF's that favoured the primary hypothesis: 100.00%
Percentage of BF's that were 'decisive': 100.00%

Bayes factor, height, <5nmol/L aMab athletes

Wow! Even with 26 data points, our primary hypothesis was extremely well supported. Betting against that hypothesis is like betting a particular person in the US will be hit by lightning three times in a single year!

That seems a little too favourable to my view, though. Did something go wrong with the mathematics? The simplest check is to graph the models against the data they're evaluating.

(Click here to show the code)

Height, elite athletes, <5nmol/L aMab athletes

Nope, the underlying data genuinely is a better fit for the high-testosterone aMab model. But that good of a fit? In linear space, we multiply each of the individual probabilities to arrive at the Bayes factor. That's equivalent to raising the geometric mean to the nth power, where n is the number of athletes. Since n = 26 here, even a geometric mean barely above one can generate a big Bayes factor.

(Click here to show the code)
26th root of the median Bayes factor of the high-T aMab model applied to low-T aMab athletes: 5.2519
26th root of the Bayes factor for the median marginal: 3.6010

Note that the Bayes factor we generate by using the median of the marginal for each parameter isn't as strong as the median Bayes factor in the above convolution. That's simply because I'm using a small sample from the posterior distribution. Keeping more samples would have brought those two values closer together, but also greatly increased the amount of computation I needed to do to generate all those Bayes factors.

With that check out of the way, we can move on to \(\overline{BMI}\).

(Click here to show the code)
Summary of the BF distribution, for the adjusted BMI of >5nmol/L aFab athletes
         n       mean   geo.mean         5%        16%        50%        84%        95%
         4   1.70e+12   1.06e+05   2.31e+02   1.60e+03   4.40e+04   3.66e+06   3.99e+09

Percentage of BF's that favoured the primary hypothesis: 100.00%
Percentage of BF's that were 'decisive': 99.53%
Percentage of non-finite probabilities, when applying the low-T aFab model to high-T aFab athletes: 0.00%
Percentage of non-finite probabilities, when applying the high-T aMab model to high-T aFab athletes: 10.94%

Bayes factor, BMI, >5nmol/L aFab athletes

This distribution is much stranger, with a number of extremely high BF's that badly skew the mean. The offset contributes to this, with 7-12% of the model posteriors for high-T aMab athletes assigning a zero percent likelihood to an adjusted BMI. Those are excluded from the analysis, but they suggest the high-T aMab model poorly describes high-T aFab athletes.

Our credence in the primary hypothesis here is similar to our credence that an elite golfer will not land a hole-in-one on their next shot. That's surprisingly strong, given we're only dealing with four datapoints. More data may water that down, but it's unlikely to overcome that extreme level of credence.

(Click here to show the code)
Summary of the BF distribution, for the adjusted BMI of <5nmol/L aMab athletes
         n       mean   geo.mean         5%        16%        50%        84%        95%
         9   6.64e+35   2.07e+22   4.05e+12   4.55e+16   6.31e+21   7.72e+27   9.81e+32

Percentage of BF's that favoured the primary hypothesis: 100.00%
Percentage of BF's that were 'decisive': 100.00%
Percentage of non-finite probabilities, when applying the high-T aMab model to low-T aMab athletes: 0.00%
Percentage of non-finite probabilities, when applying the low-T aFab model to low-T aMab athletes: 0.00%

Bayes factor, BMI, <5nmol/L aMab athletes

The hypotheses' Bayes factor for the adjusted BMI of low-testosterone aMab athletes is much better behaved. Even here, the credence is above three-lightning-strikes territory, pretty decisively favouring the hypothesis.

Our final step would normally be to combine all these individual Bayes factors into a single one. That involves multiplying them all together, however, and a small number multiplied by a very large one is an even larger one. It isn't worth the effort, the conclusion is pretty obvious.

Truth and Consequences

Our primary hypothesis is on quite solid ground: Athletes with exceptional testosterone levels are more like athletes of the same sex but with typical testosterone levels, than they are of other athletes with a different sex but similar testosterone levels. If we divide up sports by testosterone level, then, roughly 6-8% of assigned-male athletes will wind up in the <5 nmol/L group, and about the same share of assigned-female athletes will be in the >5 nmol/L group. Note, however, that it doesn't follow that 6-8% of those in the <5 nmol/L group will be assigned-male. About 41% of the athletes at the 2018 Olymics were assigned-female, for instance. If we fix the rate of exceptional testosterone levels at 7%, and assume PyeongChang's rate is typical, a quick application of Bayes' theorem reveals

$$ \begin{align} p( \text{aMab} \mid \text{<5nmol/L} ) &= \frac{ p( \text{<5nmol/L} \mid \text{aMab} ) p( \text{aMab} ) }{ p( \text{<5nmol/L} \mid \text{aMab} ) p( \text{aMab} ) + p( \text{<5nmol/L} \mid \text{aFab} ) p( \text{aFab} ) } \\ {} &= \frac{ 0.07 \cdot 0.59 }{ 0.07 \cdot 0.59 + 0.93 \cdot 0.41 } \\ {} &\approx 9.8\% \end{align} $$

If all those assumptions are accurate, about 10% of <5 nmol/L athletes will be assigned-male, more-or-less matching the number I calculated way back at the start. In sports where performance is heavily correlated with height or \(\overline{BMI}\), then, the 10% of assigned-male athletes in the <5 nmol group will heavily dominate the rankings. The odds of a woman earning recognition in this sport are negligible, leading many of them to drop out. This increases the proportion of men in that sport, leading to more domination of the rankings, more women dropping out, and a nasty feedback loop.

Conversely, about 5% of >5nmol/L athletes will be assigned-female. In a heavily-correlated sport, those women will be outclassed by the men and have little chance of earning recognition for their achievements. They have no incentive to compete, so they'll likely drop out or avoid these sports as well.

In events where physicality has less or no correlation with sporting performance, these effects will be less pronounced or non-existent, of course. But this still translates into fewer assigned-female athletes competing than in the current system.

But it gets worse! We'd also expect an uptick in the number of assigned-female athletes doping, primarily with testosterone inhibitors to bring themselves just below the 5nmol/L line. Alternatively, high-testosterone aFab athletes may inject large doses of testosterone to bulk up and remain competitive with their assigned-male competitors.

By dividing up testosterone levels into only two categories, sporting authorities are implicitly stating that everyone within those categories is identical. A number of athletes would likely go to court to argue that boosting or inhibiting testosterone should be legal, provided they do not cross the 5nmol/L line. If they're successful, then either the rules around testosterone usage would be relaxed, or sporting authorities would be forced to subdivide these groups further. This would lead to an uptick in testosterone doping among all athletes, not just those assigned female.

Notice that assigned-male athletes don't have the same incentives to drop out, and in fact the low-testosterone subgroup may even be encouraged to compete as they have an easier path to sporting fame and glory. Sports where performance is heavily correlated with height or \(\overline{BMI}\) will come to be dominated by men.

Let's Put a Bow On This One

[1:15] In a nutshell, I find the arguments and logic that currently permit transgender women to compete against biological women to be remarkably flawed, and I’m convinced that unless quickly rectified, this will KILL women’s sports.

[14:00] I don’t want to see the day when women’s athletics is dominated by Y chromosomes, but without a change in policy, that is precisely what’s going to happen.

It's rather astounding. Transgender athletes are a not a problem, on several levels; as I've pointed out before, they've been allowed to compete in the category they identify for over a decade in some places, and yet no transgender athlete has come to dominate any sport. The Olympics has held the door open since 2004, and not a single transgender athlete has ever openly competed as a transgender athlete. Rationality Rules, like other transphobes, is forced to cherry-pick and commit lies of omission among a handful of examples, inflating them to seem more significant than they actually are.

In response to this non-existent problem, Rationality Rules' proposed solution would accomplish the very thing he wants to avoid! You don't get that turned around if you're a rational person with a firm grasp on the science.

No, this level of self-sabotage is only possible if you're a clueless bigot who's ignorant of the relevant science, and so frightened of transgender people that your critical thinking skills abandon you. The vast difference between what Rationality Rules claims the science says, and what his own citations say, must be because he knows that if he puts on a good enough act nobody will check his work. Everyone will walk away assuming he's rational, rather than a scared, dishonest loon.

It's hard to fit any other conclusion to the data.

Cherry Picking

With the benefit of hindsight, I can see another omission from Rationality Rules’ latest transphobic video. In his citations, he cites two sporting bodies: the International Association of Athletics Federations and the Australian Sports Anti-Doping Authority. He relies heavily on the former, which is strange. The World Medical Association has condemned the IAAF’s policies on intersex and transgender athletes as “contrary to international medical ethics and human rights standards.” The IAAF has defended itself, in part, by arguing this:

The IAAF is not a public authority, exercising state powers, but rather a private body exercising private (contractual) powers. Therefore, it is not subject to human rights instruments such as the Universal Declaration of Human Rights or the European Convention on Human Rights.

Which is A) not a good look, and B) false. If you won’t take my word on that last one, maybe you’ll take the UN’s? [Read more…]

Rationality Rules Is Delusional

I glossed past something in my last post. Emphasis mine:

[9:18] You see, I absolutely understand why we have and still do categorize sports based upon sex, as it’s simply the case that the vast majority of males have significant athletic advantages over females, but strictly speaking it’s not due to their sex. It’s due to factors that heavily correlate with their sex, such as height, width, heart size, lung size, bone density, muscle mass, muscle fiber type, hemoglobin, and so on. Or, in other words, sports are not segregated due to chromosomes, they’re segregated due to morphology.

I think it’s time we had a look at his science on this. Of the eleven scientific studies I counted in RR’s citations, only two dealt with muscle fibre composition:

Oertel, Gisela. “Morphometric Analysis of Normal Skeletal Muscles in Infancy, Childhood and Adolescence: An Autopsy Study.” Journal of the Neurological Sciences 88, no. 1 (December 1, 1988): 303–13. https://doi.org/10.1016/0022-510X(88)90227-4.

Staron, Robert S., Fredrick C. Hagerman, Robert S. Hikida, Thomas F. Murray, David P. Hostler, Mathew T. Crill, Kerry E. Ragg, and Kumika Toma. “Fiber Type Composition of the Vastus Lateralis Muscle of Young Men and Women.” Journal of Histochemistry & Cytochemistry 48, no. 5 (May 2000): 623–29. https://doi.org/10.1177/002215540004800506.

From that, we can extract the key charts on fibre composition. I’ll dim the irrelevant sections. [Read more…]

And the Beat Goes On

Essence of Thought has published a timeline of the Rationality Rules affair. If you’re missed any of the last five months, it’ll bring you up to speed.

Cripes, has it been that long already?! I had a look through my archives, and all but two of my posts over the last two months have been focused on Rationality Rules, and even those two were about transphobia. I know, I know, the constant drumbeat is getting a bit repetitive and boring. But there’s a reason for it.

[11:31] Now, some of the walkouts had formed a support group, which I was later added to, and reading through their accounts is truly horrifying. Many discussed the abuse they suffered thanks to Woodford and his audience. There are numerous discussions on how their sleep was impacted, about how they’re having to see psychiatrists and other specialists. I’ve even seen [a post?] discussing suicide in relation to what had occurred. That’s the level of severity we are talking about with this issue: people discussing suicide. That’s the damage Woodford and his supporters have caused this one group, this one organization.

I don’t have any way to verify this part, but some of it tracks with comments I’ve read elsewhere, the claims have remained consistent over time, and it would explain why ACA members seem willing to talk to Essence of Thought despite the ocean between them.

One thing I do know: the odds of anyone holding Rationality Rules responsible are basically zero. Some big names in the atheo-skeptic sphere, such as Matt Dillahunty and AronRa, either agree with RR or don’t care enough to do their homework. The ACA tried to do the right thing, but it appears RR supporters elected themselves into a majority on the ACA’s board, possibly breaking the rules in the process, and promptly started kissing their abuser’s ass.

In order to remove any ambiguity in the following statement, I wish to make clear that the ACA earnestly and sincerely apologizes to Stephen Woodford (Rationality Rules) for vilifying his character and insinuating that he is opposed to the LGBTQIA+ community. The Board of Directors has officially retracted our original statement.

Rationality Rules was so confident nobody would take him to task, his “improved” video contains the same arguments as his “flawed” one. And honestly, he was right; I’ve seen this scenario play out often enough within this community to know that we try to bury our skeletons, that we treat our minorities like shit, that we “skeptics” are just as prone to being blind followers as the religious/woo crowds we critique. And just like all those other times, I cope by writing words until I get sick of the topic. Sometimes, that takes a while.

This is one of those “a while” times. If it helps, I’m actively trying to avoid covering topics other people already have, and elevating the voices of others to break up the monotony.

Rationality Rules is a “Lying” Transphobe

There’s a reason why Rationality Rules keeps referencing EssenceOfThought; on YouTube, they‘re by far his highest-profile critic, and have done the most comprehensive critique. Other YouTubers haven’t been silent, though, and today I’d like to highlight one of them. Rhetoric&Discourse do an excellent job of summing up one specific example of dishonest behavior. I’ll only quote their conclusion here:

[11:18] Stephen comes to this conclusion in the same way that he did the last time: comparing cis men to cis women, and by ignoring the actual literature that compares trans women to cis women. To make matters worse, Stephen lies about the content of the studies in order to push his anti-trans agenda. Stephen claimed that he understood what his biggest mistake was – comparing cis men to cis women, and concluding that this comparison applied to trans women who had undergone HRT – but this new video only shows that he either didn’t understand or he cares more about bashing on trans individuals than he cares about intellectual honesty.

Ouch. Go and watch the video to get the full argument. In the meantime, I’ll point out that out of RR’s nearly forty sources used for his latest video, only two were scientific studies of transgender athletes, and only one of those actually evaluated their performance!

Gooren, Lj, and Mc Bunck. “Transsexuals and Competitive Sports.” European Journal of Endocrinology, October 1, 2004, 425–29. https://doi.org/10.1530/eje.0.1510425.

Harper, J. “Race Times for Transgender Athletes.” Journal of Sporting Cultures and Identities 6, no. 1 (2015): 1–9.

Their conclusions?

The pivotal question is this: can reassigned transsexuals compete fairly with others of their new sex? Our data are limited and do not provide insight into all pertinent aspects. In competitive sports, in all likelihood, small differences may be critical for winning or losing. Our analysis is not refined enough to detect these small differences, allowing only an approximation. As far as our data allow conclusions, the answer for F –M is probably yes, provided the administration of testosterone has not generated and does not generate supraphysiological testosterone levels, as these levels and exercise induce a surplus in muscle mass over exercise alone (…). For M –F, there is an element of arbitrariness. There is no conclusive evidence pro or con that the prenatal/perinatal testosterone exposure of men has an impact on future physical traits. […] In real life, there will always be an element of arbitrariness in the drawing of competitive lines. Different individuals are born with and develop postnatally different potentials. The caprices of genetics and postnatal development will make any form of competition intrinsically unfair at some level. In the studies of Bhasin and colleagues (…), changes in muscle size correlated with testosterone dose and concentration. These correlations were established in groups of men receiving graded doses of testosterone. Nevertheless, there was considerable heterogeneity in response to testosterone administration within each group of men receiving the same amount of testosterone. These individual differences in response to androgen administration might reflect differences in activity level, testosterone metabolism and nutrition, or polymorphisms in androgen receptor, myostatin, 5a-reductase or other muscle growth regulators, all genetically determined and inherently personal. The implication is that all men and women are not born equally endowed for competition in sports.

(Gooren 2004)

Despite the fact that transgender women have been allowed to compete against cisgender ones since 2004, there has been no study used to justify this decision beyond the original work of Gooren and Bunck. It bears repeating that this original study was not undertaken on athletes, nor did it directly measure any aspect of athleticism. In fact, this is the first time a study has been developed to measure the performance of transgender athletes. […]

The author chose to use the standard age-grading methodology which is commonly used in master’s (over forty) track meets worldwide, to evaluate the performance of eight distance runners who had undergone gender transition from male to female. As a group, the eight study participants had remarkably similar age grade scores in both male and female gender, making it possible to state that transgender women run distance races at approximately the same level, for their respective gender, both before and after gender transition.

It should be noted that this conclusion only applies to distance running and the author makes no claims as to the equality of performances, pre and post gender transition, in any other sport. As such, the study cannot, unequivocally, state that it is fair to allow to transgender women to compete against 46,XX women in all sports, although the study does make a powerful statement in favor of such a position.

(Harper 2015)

Compare this with what Rationality Rules concludes.

[19:07] In some events – such as long-distance running, in which hemoglobin and slow-twitch muscle fibers are vital – I think there’s a strong argument to say no, [transgender women who transitioned after puberty] don’t have an unfair advantage, as the primary attributes are sufficiently mitigated. But in most events, and especially those in which height, width, hip size, limb length, muscle mass, and muscle fiber type are the primary attributes – such as weightlifting, sprinting, hammer throw, javelin, netball, boxing, karate, basketball, rugby, judo, rowing, hockey, and many more – my answer is yes, most do have an unfair advantage. There are exceptions, of course, just as there are exceptions to everything, but far more often than not their TUE in such events does not bring them down to anywhere near the 100% mark. […]

[20:09] I am opposed [to these athlete’s inclusion] because the attributes which are granted from male puberty that play a vital role in some events have not been shown to be sufficiently mitigated by HRT.

I dunno about you, but I find it comforting that the only way you can justify excluding transgender athletes is to misrepresent the relevant science.