Is Caster Semenya's testosterone level in terms of standard deviation the equivalent of a man being more than 22 feet tall?

College student wrote:

Yao Ming would be 22’6” tall to be 50 standard deviations from the mean height of males.

I think it's easier for LRC to understand in terms of fatties, not height.

Plus, the very notion of a "standard deviation" is being mis-used here vis-a-vis the distribution (why is it "normal" - Gaussian - for outliers??).

First let's get facts. The "average" value for women is more like 2 nmol/L than 0.5. See any of your LRC threads that repeat while you ad nauseam ignore it.

E,g, The mean (SD) T levels of (2019 Russian) athletes and controls were 1.65 (0.87) and 1.76 (0.6) nmol/L

Your first cited paper (1999) specifically mentions the most normal of the women, sampled at 0.51 pm 0.03 in SI units (14.9 pm 0.9), had "thryroid complaints" BTW.

But ignoring everything else, just look at the difference in ratios: the LRC-favored data has a 17:1 ratio of mean to standard error; the other data has a 2:1 or 3:1 ratio! The Michigan Bone Study (1992) is similar with about 10:1.

Even the commisioned IAAF data (with its miscalculated 0.67 mean) doesn't get anything this large. It is more circumspect and uses 25%-75% ranges rather than SDs in Table 1, but in Tables 3 and 4 it gives SDs which are quite substantial compared to the mean (eg, 800m is 1.47 pm 4.03). Again the IAAF data is more like a 2:1 or 3:1 ratio, not 17:1 or 10:1 from the study that LRC "suddenly" promotes.

Secondly, as others have pointed out, without knowing the distribution, it's sort of ridiculous to apply it to outlier theory. That's a separate branch of statistics.

If I understand what is being said, it's not even Semenya's T-level, but the IAAF 5.0 limit that is the comparator.

I've seen a Semenya-number like 14 be claimed (unsourced).

IAAF themselves said in a paper, when they introduced the 10nmol limit, that it was five standard deviations from the mean.

David S wrote:

And of course the height analogy isn't fair because she isn't able to make use of the testosterone in her system. Even if 8 feet tall seems crazy, remember that most of it doesn't actually help her "height" -- maybe she's like a really tall basketball player with really short arms.

Indeed she is able to make use of the testosterone in her system, hence why when she was taking medication to reduce it, she couldn't even break 2mins

This guy gets it.

Rojo obviously has an obsession with Caster, an unhealthy sexual obsession - that's clear.

At least 89% of that I'm sure. Our sample size of b-curious males are hovering at around 78%, whereas Rojo is almost at 3261%. I just love bad statistical analysis.

And Rojo just loves obessing over Caster. He loves her.

more bad math wrote:

I've seen a Semenya-number like 14 be claimed (unsourced).

which is the level of a 75-year-old man. The w800 record holders were jacked up on anabolic steroids well beyond that level. It's not the T that makes Caster nearly as fast as them, it's the yDNA.

We need to move on from this debate to one that moves us forward.

It is clear that intersex athletes have attributes that give them clear advantages whether it be T, genes on the Y, insensitivity to hormones or whatever. Given the number of dysfunctions that can lead to these, there will be many variations on this theme.

For me it's simple, get rid of Men/Women sports and have Open / Female.

Females should be specifically defined in the same way we class any other "less-abled" athletes like para-athletes and anyone - male, female, intersex, XY people that identify as XX, XX that identify as XY, and attack helicopters can then compete in the "Open" division so long as they don't commit a doping offense.

For those who want to, why not even have an "enhanced" division for all the dopers out there.

I'll let someone else more enlightened pull together the definition of what female is for this purpose. This doesn't take a rocket scientist to figure out, and in reality would change very little - almost everyone would be unaffected but would result in what we want: all the XX women out there would be able to compete on a level playing field with their peers.

There are no men, or women, who are 22 feet tall. The normal distribution is clearly not an appropriate approximation for the distribution of heights when you're talking about the tails of the distribution. The normal distribution has unbounded support, so it has positive mass everywhere even though we don't observe individuals who are 100 feet tall.

Maybe look at the percentile that Caster sits on the distribution of women's T, and then find that percentile on the distribution of men's heights. I don't know if that comparison is meaningful, but I think that's more appropriate than the one you've proposed.

Bad Wigins wrote:

more bad math wrote:

I've seen a Semenya-number like 14 be claimed (unsourced).

which is the level of a 75-year-old man. The w800 record holders were jacked up on anabolic steroids well beyond that level. It's not the T that makes Caster nearly as fast as them, it's the yDNA.

I bet it's much more.

When she had to drop it to 10 her times fell away considerably and she started developing a slightly more 'feminine' figure.

I doubt we'd see that profound a change from 14 to 10, even over a reasonably period of time.

Armstronglivs wrote:

Statman Caruthers wrote:

Yao Ming was already something like 7’ 6”. So she’s got maybe 3x the testosterone of an average woman. Big whoop.

So how does that compare with 22' tall?

The answer is in the post you quoted.

Statistic Prof 101 wrote:

College student wrote:

Yao Ming would be 22’6” tall to be 50 standard deviations from the mean height of males.

I think it's easier for LRC to understand in terms of fatties, not height.

Plus, the very notion of a "standard deviation" is being mis-used here vis-a-vis the distribution (why is it "normal" - Gaussian - for outliers??).

Rojo said a college kid emailed him with the data. Do you expect anything less from undergraduates? Although I did laugh at the suggestion of the friend to use a Poisson distribution so that was nice

Banana Bread wrote:

How can a guy be 22 feet? That is 4 times more taller than an average man. This thread hurts my brains now trying to get this.

that's because its awful statistics. I really hope the OP and guy who cam eup with this aren't trying to get PhDs.

AB2 wrote:

If she were XX, yeah. But she's just an average boy inside a girl's skin. The "over 22 feet tall!" is the difference between the sexes.

Not at all. Her testosterone has been measured over 1200. That's pushing the envelope for the majority of men, and many doping weightlifters.

Read harder wrote:

Armstronglivs wrote:

So how does that compare with 22' tall?

The answer is in the post you quoted.

Literal minds. Some struggle with metaphor.

Is this guy borderline?

Why make this so complicated with all the science? Semenya is physiologically a male who was born with female genitalia. If we started from that foundation, this would be a lot easier to grasp.

As many have said before, there is an important distinction between choosing to live as a woman (gender) and choosing to run as a female (sex). The former is a matter of choice and identity; the latter is matter of biology. Semenya doesn't really have a choice about her sex. She is not being denied the opportunity to compete, but she should be competing with other biological males.

David S wrote:

From the second reference he's using these numbers:

Total testosterone (pg/ml)

 Mean (SD*) 209 (20.6) 210 (19.2) 223 (20.7)

 Median (25th–75th percentiles) 199 (131–299) 209 (135–297) 221 (142–312)

Even though it says Mean (SD), I think it really means the standard error (or "standard deviation of the mean"). So the SD here is an uncertainty estimate of the mean, not the standard deviation.

Look at the percentiles -- 131 to 299. There's no way the standard deviation is 20 if the 25th and 75th percentiles are 80 away from the mean.

Sorry I think he just misinterpreted the references. You can calculate a 5 standard deviation basketball player :) Something like 8 feet tall?

Second reference:

https://academic.oup.com/aje/article/153/3/256/80402

Thank you. Besides, wouldn't "50 standard deviations" be something like a trillion trillion to one?

You really didn't read the IAAF study closely you clown.

It says the median T level in women in the study is .67. Not the mean.

And this study is literally the exact population we want to compare to. It is elite women who competed at the world championship. They report a median of .67 with 25th and 75 percentiles of (0.48–0.90).

IAAF paper for those interested: