William M. Briggs

Statistician to the Stars!

Statistics “Proves” Men And Women Are The Same

Science Quiz. The male is on the: A) right, B) left, C) there is no way to tell because gender is a social construct

Science Quiz. The male is on the: A) right, B) left, C) there is no way to tell because gender is a social construct

There are just as many women in prison as men. So too are there equal numbers of male and female ob/gyn patients: this is because the sexual aparatuses on both is identical. New measurements have determined men and women are similarly shaped, being equally tall, broad, and heavy. Facial hair grows at the same rate for both sexes.

When given the opportunity and when in groups, individuals of each sex will co-mingle and not preferentially segregate, which is not surprising given the last two findings (they cannot tell each other apart). A reexamination of history has proved just as many women as men were famous generals and mathematicians.

Perhaps the most fascinating discovering is that men and women have always treated members of the opposite sex in just the same way as members of the same sex; this includes all behaviors, like one sex denying voting rights to the other sex.

If you understood that last paragraph (and most won’t) then you will know that the modern fascination of “proving” men and women are the same, given the historical evidence, is based on a fallacy. If men and women were the same then we could never have the argument that men and women should be or are the same.

Consider the list (the internet loves lists), “Top 100 Mathematicians of All Time!” married to the proposition, “the sexes have equal mathematical talent.” Now you may earnestly believe and cherish that proposition, but you must then ignore the evidence of the list. Or you may believe the list, which forces you to abandon the proposition. If the two are held simultaneously, there is a fallacy.

Incidentally, the statistical evidence “boys and girls have equal mean scores on many but not all tests” is not inconsistent with either the list or the proposition, it supports both equally. The problem is the statistical evidence is incomplete: comparing only means ignores the variability and distribution of ability. Examining only means is statistically foolish.

Enter Bobbi Carothers, a psychologist featured in Popular Science‘s “Science Confirms The Obvious: Men And Women Aren’t That Different”. Everything wrong with that title is everything wrong with modern thinking. “Science” has not done what is claimed; “science” cannot do anything, only people can. And all that’s obvious is that Popular Science doesn’t want to be screamed at for denying the subtitle, which itself is obviously false.

Carothers fixated on the idea that other people (not her) thought that if men and women are different, they should be categorically so. Men are tall, women therefore cannot be. But sexual differences in heights are distributional: there are many tall women, but there are more tall men. Height, like most other traits, is therefore not categorically different.

Since Carothers set out to prove paucity of categorical differences, it therefore comes as no surprise she succeeded. “Men and women consistently overlapped in attitudes and traits like empathy, fear of success and mate selection, indicating that sex differences are not categorical, but more a matter of degree.”

Like an inveterate gambler, she did it the hard way. No plain observation for her, no sir. Instead, unnecessarily complicated statistical assays like “taxometric methods of mean above minus below a cut, maximum eigenvalue, and latent mode”. And while she gave a cursory look at obvious differences, she concentrated on academic constructs like “openness, conscientiousness, extraversion, agreeableness and neuroticism”, each trait defined via officially approved psychological “instruments” (i.e. questionnaires; the faith academics have in these is absolute; nobody ever lies to an academic).

In one sub-study she asked 30 WEIRD boys and girls to record five activities they and the opposite sex enjoyed doing. This produced 129 items, which were re-rated by other WEIRD people. “28 items that revealed significant sex differences for both ratings and no order effects were retained.” A third panel whittled those 28 down to 10. The overly complicated statistics finally proved that men liked boxing and construction and women scrapbooking and applying cosmetics. Tax dollars at work.

She went on and on and then on some more like this, asking questions to see where and if men and women answered differently. The closer the scale came to academic constructs, the more similar were the sexes; likewise, the closer the scale matched real-life activities, the more distinct the sexes.

Her sense of triumph was obvious as she stated a conclusion which nobody ever questioned, that all differences between the sexes do not have “sharp boundaries”, but often are a matter of degree. Which is to say, the differences are real and not apparent, a corollary she neglected to mention.

20 Comments

  1. The photo and caption would make a great blog post alone.

  2. Fallacies.

    Fallacies everywhere.

    For instance:

    If men and women were the same then we could never have the argument that men and women should be or are the same

    Nonsensical rubbish. Well of course men and women “are not the same”, but that fact does not deter me to call the above complete rubbish. People are known to create myths and differentiate what is not different and so on. Errare humanum est. And so the modus ponens above is clearly false.

    “Top 100 Mathematicians of All Time!” married to the proposition, “the sexes have equal mathematical talent.” Now you may earnestly believe and cherish that proposition, but you must then ignore the evidence of the list. Or you may believe the list, which forces you to abandon the proposition. If the two are held simultaneously, there is a fallacy.

    This is worse. Clearly false, since the list is about the “top 100 mathematicians” and the proposition is about *talent*, not success. I have no idea if women are worse, better or equal to men in maths, but the two propositions are *not*, I repeat, *not* contradicting. It’s like arguing in the 19th century that women are perfectly *able* to be leaders and presidents, and then say that this contradicts history that (mainly) only shows men in such places.

    For the rest of your rant, I have nothing in disagreement. But you did boil my blood there.

  3. Briggs

    14 February 2013 at 10:49 am

    Luis, brother, you are out of your mind.

    If men and women were the same, then we couldn’t tell them apart, we wouldn’t even have separate words, there would be no way to argue what is the same is seen to be different and is therefore the same.

    I’m also glad it was you who made the second mistake, which is to see things categorically, as Bobbi-with-an-I did not. Best you could say is that men are “more successful at math and at suppressing throughout all history equally mathematically talented women”, which is just another behavior men are better at (the “and” is logical).

    How about this proposition, “Men are better at keeping women down than women keeping men down”? Agree to it, as you seem anxious to, then you have discovered something which differentiates the sexes, and even discovered something men are better at, hence they are the different. Disagree, then the observed differences in mathematical ability must be real, and therefore the sexes are different. Either way, they’re different.

    How did you do on the quiz?

  4. “each trait defined via officially approved psychological “instruments” (i.e. questionnaires; the faith academics have in these is absolute; nobody ever lies to an academic).”

    Every so often in the UK we have a journalistic *Children in Danger* panic about sex and drugs etc. Generally virginity is lost younger, the number of sexual partners is vast, whole fields of weed and coca are smoked and snorted and whole lakes of alcohol consumed nightly. When you pick one of these apart it normally boils down to an acedemic survey by questionaire of, well schoolboys basically. Because no young post pubescent male is ever going to be dishonest about sex drugs and booze are they?

  5. a conclusion which nobody ever questioned, that all differences between the sexes do not have “sharp boundaries”. “All … do not” – vile phrase. If you meant “some … do not” or even “some … do” why not say it? If you meant “No … have” you didn’t say it.

    I do not have a womb. This is not a matter of degree so I take it to be a difference with a “sharp boundary.” Sadly, this characteristic seems to be valued according to its commonness and not according to the fact that it underpins our entire civilization.

  6. Something about this post put into my mind the debate:

    Do female dwarfs have beards?
    Of course, they do.
    Really?
    All dwarfs have beards. Have you ever seen a dwarf without a beard?
    I have never seen a female dwarf.
    Sure you have, you just can’t tell them apart from the men. Very few non-dwarfs can. Probably half the dwarfs you have seen are in fact female, but you assumed that they were male because they carried and axe and had a beard.
    Female dwarfs carry axes?

  7. Of course women are just as mathematically talented as men. I know that because the feminists say so. Women do have a little problem with the Putnam competition. It’s obviously sexist. Luis Dias should find the list of Putnam fellows interesting.
    http://en.wikipedia.org/wiki/William_Lowell_Putnam_Mathematical_Competition

  8. There are interesting studies from Stanford that look at the psychology of performance in the classroom. The authors suggest that normal hardships or failures may be interpreted as confirmation of a limiting stereotype (females can’t do math) instead of a more benign interpretation (math is hard).

  9. An interesting read. I can’t help but wonder: “Why would we want them to be alike?”

  10. Consider the list (the internet loves lists), “Top 100 Mathematicians of All Time!” married to the proposition, “the sexes have equal mathematical talent.” Now you may earnestly believe and cherish that proposition, but you must then ignore the evidence of the list. Or you may believe the list, which forces you to abandon the proposition. If the two are held simultaneously, there is a fallacy.

    Mr. Briggs,

    If I understand you correctly and if “equal mathematical talent” means “equal mathematical talent in general,” you believe the list can be used an evidence to conclude the proposition is incorrect.

    So, as a statistician, you would use the top 100 mathematicians as a valid representation of men’s mathematical talent. You also seem to suggest that having talent and being successful are the same thing.

    If the report in Popular Science is accurate, Carothers doesn’t deny there are physically differences between men and women. It doesn’t really matter to me whether men are more talented in mathematics, but I think it’s rather silly to repeatedly imply that some people actually think there are no physical differences between sexes.

    I’d like to know how “the Big Five” personality traits of psychology” are defined and measured. What does “not very different between sexes in those traits” mean? I am always interested in learning how something is quantified! Also I wish the original paper were cited, as I don’t trust journalists as much as you do.

    I love Marilyn Monroe.

  11. Oh, I wouldn’t use the top 100 mathematicians as a valid representation of men’s mathematical talent. Having talent and being successful are the not same thing. Those top 100 mathematicians might indeed have mathematics talent, but the fact that Briggs is not in the list doesn’t mean he has no such talent. Life!

  12. It seems to me that the same exact type examination of categories could be done on the differences between the young, say pre puberty, and the old, 60 and above, to prove that there were no differences between the young and old.

  13. Noblesse Oblige

    14 February 2013 at 9:36 pm

    Here’s another one.

    Popular Science and Science magazine are not that different. Both are super market tabloids of science. The main difference is that one of them has pretensions.

  14. Sander van der Wal

    15 February 2013 at 12:46 am

    Almost all men and almost all women are very bad at maths. There are a couple of men and a couple of women rather good at it, but that is the exception.

    Saying that all men are different from all women because a few men are better at maths than even less women, yeah, right.

  15. Science seems to have a self-image problem. It wants to be affirmed, respected, loved. It wants to be Popular…like the Arts. Everybody loves the Arts with all that color and flare. But Science is complicated and scary…it can’t be the Arts. We surveyed some WEIRD kids about their college majors and found that Chemists definitely were not Theater majors, even if they were forced into taking a Theater elective. We excluded that one weird WEIRD kid who double majored in Biology and Music as a outlier just because it was so unusual. That made the p-value better, of course, but that wasn’t the reason we did it. He was just weird…a drummer, and you know what they’re like. So pity poor Science — caught it that unfulfillable dream of wanting to be Popular when all the kids know that it’s really just a dork and can’t be cool no matter how much it tries.

    /sarc (just in case)

  16. Either you can say: “I believe men and women are the same, and therefore any lists or studied that prefer men to women are sexist and cannot be trusted.”

    Or you can say: “I believe men and women might be the same or might be different, but I would need to see lists or studies to confirm either way.”

    I don’t know how anyone, short of revelation or force, could ever leave the first category, as any contrary evidence will have to be ignored.

    I personally fall under: “I believe that men and women are different is a self-evident fact and I expect this to have practical effects that do not always support feminism.”

  17. Gary–Where would double majoring in psychology and chemistry, with a minor in philosophy lie? (Assume the holder is not just weird, though that could be the case).

  18. Sheri, a “far out”-lier at the Timothy Leary School of Mind Expansion, UC Berkeley. ;-)

  19. I did not say that I agreed with the notion that men and women are equal, mr Briggs, so I’m afraid that the retort you made was in vain.

  20. Hey Ray, from the same kind of moronic argument you put forward I could conclude that whites are also becoming completely stupid and orientals are just getting better and better genes the later years.

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