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Topic: Re: Women in Maths
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Doug Kuhlmann

Posts: 3,630
Registered: 12/6/04
Re: Women in Maths
Posted: Mar 7, 2002 11:04 AM
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Kaz cites the average math SAT score as 521 for boys with a standard
deviation of 100. (I assume those numbers are correct.) He then assumes
that the average math, science and engineering Ph.D. is three standard
deviations above the average. That would be 821. Not a bad average on a
test that has a maximim score of 800.

Of course on his previous post he assumed 4.5 standard deviations above the
mean. Those folks would have averaged 971 on the SAT.


On 03/07/2002 10:35:57 AM owner-calc-reform wrote:

>At 06:00 PM 3/6/02 -0800, Martin Flashman wrote:

>>But a discussion that plays with data and seems to be aimed at
>>"scoring debate points" is not useful to the list members and is a
>>distraction from positive attempts to have a constructive dialog.

>If I want to learn something, someone else must have something sensible to
>say. (Although we also learn from someone else's mistakes).
>Let me repeat/paraphrase what I said before with more exact data. In 1990,
>mean math SAT score for boys was 521, for girls 483, that is 0.38 standard
>deviation difference (st. dev.= 100).
>Let assume that average math, science, engineering Ph.D. is three standard
>deviation above average math SAT for boys (3.38 for girls). We can

>the expected proportion of girls at that level of ability. The normal
>probability density function formula is f(x) = e^(-x^2/2) (I skipped
>constants). So f(3) = e^(-4.5) and f (3.38) = e^(-5.7122).
>That means 3.66 boys for each girl, or 21.5% girls. Yes, this normal
>distribution tells us that in year 2000 about 21.5% of all new math

>engineering Ph.D.s should have gone to women (if math SAT ability was the
>only factor!). I don't know exact data but am positive that the *actual*
>proportion of women was roughly the same. This means there were NO BIASES
>other than simple mathematical abilities (or there were other biases but
>they mutually canceled each other). Understand that? The proportion of
>women among math/science /engineering Ph.D.s is exactly the proportion of
>women among the assumed level of math abilities (as measured by math SAT).
>Since some girls get pregnant or for other "womanly reason" drop out of

>pool, we can claim that there must actually be a pro-women bias in
>education between grade 12 and Ph.D. level.
>As one can see, some data are needed to draw conclusions. The 12 grade

>SAT scores and the assumption of normality of the distribution explain
>well the decreasing proportion of women. There is no need to involve
>cultural factors. Sorry, Martin, for this "politically incorrect"

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Doug Kuhlmann
Math Department
Phillips Academy
180 Main St.
Andover, MA 01810



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