Sunday, 30 September 2012

Distributions, SAT scores, the Cult of Equality

I tell you one and one makes three
I’m the cult of equality

Based on the statistical shenanigans used in Lewontin's fallacy, there are two ways an argument of equality is put forward:

1)The differences between the groups are much smaller than the differences amongst the groups themselves.
2)There is more overlap between two groups than non-overlap.

The first one is less disingenuous than the second, so lets start with the second one.

To do so, we first require to lay down some groundwork about statistics.

With an average male height of 5'10'' it's much easier to find men 6' or 5'8'' inches tall, than 6'10'' or 4'10''.  Note that the average of both sets is 5'10''. It's an example of the common observations that more people are closer to the average than extremes when considering various human traits.

The graphic representation of this fact is the bell curve/normal distribution.

The mean(μ) being the average, and the standard deviation(σ) a measure of how spread out the distribution is. A higher mean means taller people, a higher standard deviation means more taller and shorter people than the mean.(higher SD - flatter curve, lower SD - more peaking curve)

Note that for the same difference, namely of 1 SD, there are very different proportions of people between the bounds of mean and one SD, one SD from the mean and two SD from the mean, and 2SD from the mean and 3SD from the mean, viz. 68.2%, 27.2% and 4.2% respectively.

Coming back to the argument, "there is more overlap than there is non-overlap", consider two populations whose means are separated by a difference of 2SD, but have the same number of individuals and standard deviation. They do overlap, the right half of one overlaps almost completely the left half of the other.

Using the numbers from above bell curve, there is about 52% of overlap in both the distributions.
So there is more overlap among the two groups than the their non-overlapping parts. However now consider how many of people in group 2 are above the average of the people in group 1.
While the average of group 1 is at 50th percentile, the corresponding person in the other group has to be almost at 98th percentile to make the cut.
The ratio of those making the cut from the different groups is thus almost 50:2 or 25:1.

If you increase the criteria to one SD above M1, then the ratios go to about 16:0.1 or 160:1.

This is not a proof of equality, but humongous inequality.

A difference expressed in terms of SD is therefore a big fucking deal.


Regarding SAT scores and how the boy-girl ratio has been falling(written here before):

The 2005 repetition found that there were 2.8 boys for each girl in the group which scored over seven hundred. Remember that the numbers were 13 boys to one girl in the early 1980s.  

The thing to realize about SAT distributions being the the jump in ratios when one goes farther at the ends of distributions. The ratio for one more SD increase, jumped from 25:1 to 160:1, i.e. a more than five-fold increase, even though the absolute numbers themselves are falling.(50% and 2.1% in the former, while 16% and 0.1% in the latter).

So while the ratio of 2.42 to 2.1 is close to 1, the ratio of 0.42 to 0.1 is more than 4.(not actual numbers). Secondly, it's easier to smother the difference when the numbers make up less than 1% of the distribution. Or even less than 0.1% (1 in 1000)
An easier test can go a long way at making the sex-differences disappear since the distributions are much closer together(the means are almost equal) and the small difference in the SD of the two distributions(men are more variable) only makes a big difference at the ends.

Irwing and Lynn (2005) found that men outnumber women 2-to-1 at the 125 IQ level, and 5.5-to-1 at 155.

Wednesday, 26 September 2012

On the inequality of SATs

The original thread of discusison.

"Conversely, there are feminists who don’t understand distributions either,"

Never attribute to stupidity what which can be attributed to malice when the people in question have an obligation to not be stupid.

"Britain’s GCSE has girls outperforming boys across the board. "

Boys have been outperforming girls in maths since the coursework was taken off, viz. 2010. From wikipedia:

'Pirie also observes that the GCSE focus on coursework has disadvantaged boys reversing the gender gap in attainment, to the degree where in all subjects girls outperform boys, including traditionally male subjects such as sciences and physical education.'

Also interesting, the grade inflation in the said exams (and the A-levels) and the recent Michael Gove's crusade against the dumbed-down GSCEs.

"Interestingly, girls flat out WHOMP boys in Chinese and English. Just sayin’."

How's that whomping in the top percentile? or even top ten percentile?

"Interestingly, the trend reverses for the relatively newer “Writing” portion of the test."

It was included precisely because of that, making the test less sexist. PSAT's writing portion has earned many more girls scholarships than doubling the weight of the verbal scores.(which funnily did nothing for the top percentile)

"However, give the large numbers, there are more than enough girls and boys to fill the positions requiring these skills."

That sheen is taken off when you consider:

"1990 In this year, ten students out of 1.2 million test takers (roughly one in 120,000 students) get perfect scores of 1600 on the SAT. "

"In 1994, 25 students got perfect scores out of about 1.25 million (about 1 in 50,000 students). The first recentered SAT in April has 137 perfect scores out of about 200,000 test takers (about 1 in 1,400 students). "

"Out of 1.38 million seniors taking the SAT, 238 (roughly 1 in 5,000 students) receive a perfect score of 2400. In 2004, approximately the same number of seniors took the SAT, and 939 (about 1 in 1,500 students) received a perfect score of 1600. " 

and look at this graph of SAT scores over time.

The people who are in the no-maths-gap-and-due-to-sexism camp, use the fact that the boy-girl ratio used to be 13 to 1 in SAT for >700 scores and is now around 2 to 1 as proof that it can be whittled down to nothing.

"Interestingly, one could also look at post-admissions data for anti-boy bias (if admitted boys have higher scores, then perhaps they faced a higher admissions hurdle). "

That would be so if the rejected boys didn't have higher scores than rejected girls.

7608 males applied, 10% admitted: 758. Number DENIED: 6850
2832 females applied, 26% admitteD: 736. Number DENIED: 2096

It's interesting to view these figures in the context of Simpson's Paradox(look for the Berkeley gender bias case at wikipedia). And that the almost-puking lady in Larry Summers's brouhaha came from MIT and Christina Sommers has written something about her past work in bringing about gender equality at MIT. And that the Dean of Admissions mentioned in above link was recruited for gender-equality, got some awards and MIT folks had a party for accomplishing this feat.

"the tendency for boys to be more likely, when down to two choices, guess and move on rather than dither"

and girls can't be taught this? For all the great steps they have taken in girl education, all that schooling changes and hard work they put in while the boys twiddle their thumbs on video games, and they can't be taught how to beat some sexist multiple-choice test!

Sunday, 23 September 2012

Flipping the narrative

What feminists say

 What you should say

They are compensating for their lack of manhood.

They are compensating for their lack of beauty, inner beauty included.

Patriarchy hurts men too.

Feminism causes women-hatred too.

You, good sir, are a misogynist.

You, dear madam, are a misandrist.

You, you, you, misogynist!

You, you, you, philogynist!

Testosterone is the hormone of violence!

Estrogen is the hormone of corpulence.

Women were property.

Men are property.

Male ego is fragile, can't take a few jokes.

Female ego is fragile, starts crying at jokes.

You have mommy issues, little boy.

You have daddy issues, little girl.

Women and children the majority of dead.

Men and children the majority of dead.

Tuesday, 18 September 2012

Lewontin's Fallacy on Gender

Lewontin's infamous argument stated in a not so strictly accurate analogy boils down to this:

Since the height differences amongst the groups men and women are much more than the difference between them(4-5 inches) the groups themselves don't exist.

Lewontin's conclusion stated for gender would be:

“Human sexual classification is of no social value and is positively destructive of social and human relations. Since such sexual classification is now seen to be of virtually no genetic or taxonomic significance either, no justification can be offered for its continuance.” 

The first sentence being implemented since the 60s culture revolution to an unsurprisingly devastating effect, the second however losing its meaning since genetic difference of sex chromosomes is not as easy to refute(and a big part of why this analogy is not 'strict').

Stated this way, one could easily see that the problem lies not with the grouping but the criteria that is being used and how it is being applied. A feminist rebuttal to the above can be that since it is gender that is socially constructed while sex is a biological fact, the fallacy should be written as :

Since the height differences amongst the groups human males and human females are  much more than the difference between them(4-5 inches) the groups themselves don't exist.

Gender classification still sounds wrong. For biological things like body-shape, hormone levels that are responsible for it, fat-content, muscle mass, etc., the term used should be sex and not gender.

So how does one show that genders don't exist? That gender is nothing but a social construct?

Ms. Hyde's monumental study of male-female differences in personality, with the Gender Similarities Hypothesis comes to the conclusion that:

males and females are similar on most, but not all, psychological variables

The work has been cited 924 times and has won Ms. Hyde not only media time but also awards in her field (her other paper regarding gender/sex differences in mathematics and science, or rather the lack thereof has been another feather in the bonnet). According to her award-winning, media-inflaming and androgynous gender warriors' go-to scientific literature when it comes to internet debates:

78% of gender differences are small or close to zero

and 22% aren't? mmkay!

Her hypothesis is recently argued against much in the same way the Lewontin's argument was criticized in the paper Lewontin's Fallacy by A. W. F. Edwards in 2003. That is, instead of taking single criteria(univariate modeling) on which there is considerable overlap between groups, they make use of multiple criterion to differentiate between two groups(multivariate modelling). From the 2012 paper 'The Distance Between Mars and Venus: Measuring Global Sex Differences in Personality', the authors come to the conclusion that:

....we believe we made it clear that the true extent of sex differences in human personality has been consistently underestimated.

It's funny to note that what Ms. Hyde said in her paper with the above proclamation in mind:

The Gender Differences Model, which argues that males and females are vastly different psychologically, dominates the popular media

Curiously she also makes the statement that:

"self-esteem is roughly as much of a problem for adolescent boys as it is for adolescent girls"

So apparently AAUW study on how schools shortchange girls was wrong or a statistical outlier(they accidentally the whole data!) or maybe it has brought equality to this sphere in the space of mere 20 years!
Since feminists are never wrong and since patriarchy has been known to keep women in low spirits, the only reasonable explanation is that equality has succeeded. Girls have overcome the trauma of becoming women!
Progress, comrade! Human nature has been modified, estrogen shock has been minimized and testosterone has been reined in, Vive la révolution!

Or boys are now as neurotic as teenage girls, still who cares! Equality! Equality!


According to the American research, there has been a 67 per cent increase in [Narcissism] over the past two decades, mainly among women.

Monday, 17 September 2012


The title is a riff on Hana Rosin's 'End of Men' series. Not much about her or her theories is discussed though.
In her latest column she writes of women's 'adaptability', however, copying men's identity is more like it, and hence the end of women.