## Wednesday, June 24, 2009

### SAT Math Scores Reveal HUGE Gender Differences

On a previous post, I documented the statistically significant male-female test score gap for the 2008 SAT math exam, and the graph above shows that this statistically significant difference of more than 30 points has persisted over time. Could the male-female SAT math test score gap be explained by: a) males taking more math classes than females in high school, or b) males demonstrating higher performance in high school math classes than females, or c) male high school students having higher GPAs than female students? The answers appear to be NO, using data from the 2008 SAT report.

Table 13 below (click to enlarge) shows that female high school students dominate male students at the highest GPA levels (A+, A and A-) by wide margins, and male students dominate female students at the lowest GPA levels (C, D, E or F). For example, there are 150 female students earning GPAs at the highest A+ level for every 100 male students, and there are 160 male students earning GPAs at the lowest D/E/F level for every 100 female students. Further, the overall GPA for all female students (3.38) is higher than the overall GPA for male students (3.23).

Table 14 below (click to enlarge) shows that there is essentially no male-female difference for average years of math study (3.9 years for males vs. 3.8 years for females) or math GPA (3.12 for both male and female students).

Table 15 below (click to enlarge) shows no male-female differences for: a) years of math study or b) highest level of math achieved, and shows that the 54% of students taking AP/Honors math classes are female vs. 46% male. That is, there are 117 female students taking AP/Honors math classes for every 100 male students.

Bottom Line: Female high school students are better students on average compared to male high school students, and they are equally or better prepared than males for the math SAT exam based on the number and level of math classes taken in high school. And yet, male students score significantly higher on the SAT math test than females, and the statistically significant male-female test score gap of more than 30 points persists over time.

Based on the statistical evidence, is there any other conclusion than this obvious one: In general and on average, male high school students in the U.S. are just plain better at math than female high school students? If there are other reasonable conclusions, please share them.

And yet, we hear statements like this: "There just aren't gender differences anymore in math performance,"
says University of Wisconsin-Madison psychology professor Janet Hyde. Stereotypes are very, very resistant to change," she says, "but as a scientist I have to challenge them with data."

Do those data include publicly available SAT score data showing statistically significant gender differences in math scores that persist over time? Apparently not.

At 6/24/2009 8:40 AM,  Don Harrison said...

"Is there any other conclusion than this obvious one: In general and on average, male high school students in the U.S. are just plain better at math than female high school students?" Of course there is, for those who believe that there are no inherent cognitive differences between the sexes: the SAT tests are in some mysterious way gender-biased. High school grades reflect "real" ability, while SAT scores are the result of a probably unconscious rigging of the tests to favor males. The answer is to continually tinker with the tests until boys and girls have the same outcomes.

At 6/24/2009 8:42 AM,  Anonymous said...

Isn't it possible that the teachers are inflating the grades of the females more than the males? Therefore, they look equally prepared according to the teachers grades but fall short in the standardized test.

At 6/24/2009 8:55 AM,  Paintsmh said...

I think part of it, personal experience here, is that a lot of us girls get panicked before things like the SATs. I think some of us over prepare, and end up so mentally bogged that it ends up being like an overloaded circuit. And as far as Anonymous' does that mean that you could look at jocks and say the same thing? I was a straight A student, and I worked my butt off for my grades. My brother is a B and C student because he doesn't hand in his papers or remember to do his homework. But we could walk in and take the same math test, and he would likely out score me by at least 3 or 4 points every time. It is a difference in learning styles, and ability to conform to the standardization in my personal opinion.

At 6/24/2009 8:58 AM,  C Ward said...

I am not sure whether to cry or be ill. It seems as if males ON THE WHOLE have higher mathematical skills. These skills/ ability are critical for engineering and technology advancement that will move society forward. Yet couple this with the fact that females outnumber males in higher education/ college, and ask yourself about the implications. Those very things that are necessary are being systematically devalued (best spin)/ squashed.

Full disclosure - I am a female who (thirty plus years ago) won a state wide math/ calculus prize in high school. That does not change the fact that males ON THE WHOLE have higher math ability than females. I was the only girl in the class.

At 6/24/2009 9:08 AM,  Anonymous said...

What is interesting about the graph is how steady the gap is, despite what I could guess has been a tremendous effort to encourage girls into math and science over the last 30 years.

At 6/24/2009 9:16 AM,  Junkyard_hawg1985 said...

"Is there any other conclusion than this obvious one: In general and on average, male high school students in the U.S. are just plain better at math than female high school students?"

Statistically, there is one other possibility. If you look at the number of male and female students taking the SAT, you see more females took the test (813,0000 vs. 704,000). Since the SAT is a selective test instead of a universal test, the brighter students take the test. If the 813,000 brightest females took the test and the 704,000 brightest males took the test, you had some skew in the data because the male dataset was missing 109,000 less bright males that was included in the female dataset.

While I personally believe males are better at math, this data alone does not prove it.

At 6/24/2009 9:24 AM,  Anonymous said...

I think that a big part of stronger female performance in non-math subjects has to do with the feminization of the curriculum.

Sure, there are more females at college, but they are pursuing mostly non-technical degrees. Marxist theory may prepare them to support every liberal cause under the sun, but it contributes very little to the progress of society.

Men like math because the answers are not subjective. They need not depend on the good will of some radicalized teaching school grad to succeed.

At 6/24/2009 9:59 AM,  Anonymous said...

I believe in the innate gender difference, but a couple of related notes:

1. More girls take the SAT. Even if males and females had identical distributions of math talent, if you assume that those at the top of the distribution take the test, and more females take it, their mean will obviously be lower. [IE, two boys get 800, and two girls get 800, and a third girl gets 750. Girls will have the lower average because the male who would have scored lower did not take the test.][Just saw that Junkyard said the same. Oops.]

2. Selection bias. Those at the top of the distribution of math talent [for each gender] are more likely to take the test. If men have a higher variance [and we do], the male sample will get all the high performers but will omit the worst of the worst that would have made the mean about the same as the female mean. We're not talking about a random sample here.

At 6/24/2009 10:11 AM,  Mark J. Perry said...

A few comments have discussed the greater number of females taking the test, which could affect the mean test score. However, this
previous CD post shows that for SAT math scores above 750, boys outnumber girls by a factor of almost 2:1, which wouldn't necessarily be explained by the greater number of girls taking the SAT.

At 6/24/2009 10:28 AM,  Anonymous said...

Mark,

Second, see my second point above: given that men have higher variance, many more of them will perform fantastically [750+], but we'd also have many more that would do terribly. It's just that those who would do terribly don't take the test.

I'm not arguing in the innate difference in variance, which this data demonstrates. But I don't think you can use this data to support an innate difference in the mean, simply because given a difference in variance, the non-random male sample will have a higher mean than the non-random female sample. We can't actually say whether a random male sample would have a higher mean than a random female sample.

At 6/24/2009 10:33 AM,  Junkyard_hawg1985 said...

Mark,

Thanks for your reply, however, your data still fails to prove that men are smarter ON AVERAGE at math than women. Because men and women have the same average IQ, but men have a higher standard deviation, one would expect men to have a higher % of the very best math scores. The data are consistent with this observation.

Many people blame discrimination on the differences in outcomes due to the shape of the bell curve for IQ between men and women. Some men blame discrimination on the fact that more women get college degrees than men even though 62% of high school seniors go to college. Based on the bell curve, the top 62% of IQ's should be disporportionately high in women. Likewise, some women complain about a glass ceiling in corporations because men dominate corporate boardrooms in America. If it takes someone with the top 0.1% of IQ's to run a company, the CEO's should be disporportionately males.

I do believe that on average men are better at math, but SAT data is the wrong set of data to prove it because it is not a universal test.

At 6/24/2009 10:52 AM,  Anonymous said...

As a team trainer, we see this all the time. We have to plan our training by not letting teams self-select.

When given a problem to solve, women will naturally get together in a group and try to solve the problem--they need assurance from others that they have the right answer even when they are right. They need to orally work through problems.

Men, on the other hand, tend to work by themselves to solve problems. They believe they are right even if they are wrong. In fact, they have to be forced to talk and work together.

Which gender sounds like they would do better on a standardized test? I guess that depends--team dynamics are complicated. But you can't expect to get the same outcomes (SAT scores) with different inputs (people). Try orally asking men and women the same mathematical questions and let each group work to their respective strengths. Then compare the results to the written test to see if there is any statistically significant difference between the genders. I don't believe the SATs can be a viable testing method for both genders unless the delivery system is challenged.

At 6/24/2009 10:59 AM,  Benny Crap Pants said...

Back when I was in junior high school (see "Eisenhower years"), we were told flat out that the scores on a mechanical reasoning test were "adjusted" by gender. These tests involved images of belts rounding pulleys, and being asked to determine the direction of the belt at various points, or other reasoning skills.
To this day, I have never had a woman correctly answer this question: If you have a two-volume dictionary, on the shelf in proper order, and a bookworm eats from the first "A" page to the last "Z" page, then how many pages were eaten through?

-Benjamin

At 6/24/2009 11:28 AM,  Marko said...

Walt G has an interesting observation. And Paintsmh points out something I saw on the bar exam as well.

My first thought on seeing the chart was that the test score results mean that males are better on the SAT math portion. Whether that is an accurate reflection of what is separate question.

At 6/24/2009 12:29 PM,  Anonymous said...

In many cases high school grades are more weighted to homework than to tests. I received C's throughout high school due to my allergic reaction to homework, but scored in the 98th percentile the year I took my SAT and ACT.
As teacher now, I can tell you girls are far more likely to complete their homework assignments than equally talented boys.

At 6/24/2009 1:49 PM,  thomasblair said...

Benny Crap Pants,

Sitting on a shelf as:

[xxx][xxx][A-L][M-Z][xxx][xxx]
______________________________

The bookworm, starting on the first page of the letter A (on the right side of the left volume as looking at the shelf) and eating continuously through to the last page of letter Z (on the left side of the right volume as looking at the shelf) would encounter (theoretically) two pages. This is not true in practice because it does not account for the variables of counting the covers or any title pages at the front of the A-L volume or any "note-taking" pages that result from the typesetting process at the end of the M-Z volume.

At 6/24/2009 1:57 PM,  silvermine said...

Okay, just as long as people don't think it in any way applies to individuals.

I'm one of those weird women who hate committees and consensus. I'd rather just do it on my own and get it done. Math was my favorite class. I won math competitions. Oh, and I kicked butt on the SAT Math section. I barely missed 800.

I went to grad school for biophysics for a year, then realized I actually had respect for myself and got a job that paid money. ;D

At 6/24/2009 2:49 PM,  Anonymous said...

Men are simply inherently better at math, and this is especially true if we limit ourselves to the top half of the distribution (men are also more variable).

However, women work harder, and school teaching style is geared toward women since no one really cares if men do well or not, they are on there own. This is true across the board, just look at the books students read! I hated reading relationship books, but I was a huge military history buff, yet there was no class I could take where this was encouraged. There are also countless support groups for women (women in science, etc.), and nothing for men.

Anecdotally, I was a mediocre student in HS and in College despite scoring always scoring on the top 1% of every standardized test, because I found the material boring. All the smart women I knew did very well in school. We are really killing ourselves by ignoring (the male) half of our country, and it is a great injustice.

At 6/24/2009 7:43 PM,  Anonymous said...

Perhaps 30 points should be added the the math scores of each female. That way, the average results for women and for men would be about equal.

At 6/24/2009 8:01 PM,  Anonymous said...

for SAT math scores above 750, boys outnumber girls by a factor of almost 2:1

Which in itself is an artifact of the scoring system. The SAT used to have a more linear scoring system, and the gap used to be much larger than 2:1. That was politically unacceptable, so the scoring system was changed to make it much easier to get a 750, while 800 (obviously) remained just as hard. Viola, suddenly many more girls were scoring 750. For political purposes, pundits were able to proclaim how much better girls were doing at math, when in fact nothing had changed. The switch in scoring from 1600 to 2400 was another politically motivated scheme to artificially increase girl's scores by manipulating the scoring system.

At 6/24/2009 9:15 PM,  Anonymous said...

What is interesting is that the gap persists despite the commitment of the education establishment to destroy boys. They have succeeded in sharply reducing the number of boys going to and graduate from college.

At 6/25/2009 6:49 AM,  Anonymous said...

I'll give it my best shot:

Dan Ariely reported on a study conducted by a couple of female Asian-American researchers involving Asian-American women students.

The students were given a math test, but before the test began, they were briefly interviewed.

Group 1 was asked questions that reminded them they were female (e.g., What are your feelings on abortion?).

Group 2 was asked questions that reminded them they were Asian (e.g., How do you feel about Hong Kong reverting to Chinese control?).

The students in group 2 scored much higher on the subsequent math test.

Stereotypes have an impact on self-image, and undoubtedly explain SOME of the difference, IMHO.

At 6/25/2009 10:29 AM,  ExtremeHobo said...

Men and women are inherently different. If you don't believe this, then you are a moron, end of story.

Men could be better at math, women can be better at human to human interactions, it doesn't matter. Unless someone begins genetically engineering some sort of hermaphradite race, its the way things are going to be.

Estrogen and testosterone (in addition to different levels of MANY different chemicals) affect brain development from the womb. These changes affect the way data is processed from the outside.

I guess you could say they are like Macs and PCs, they both do the same things, they just have their own strengths and weaknesses.

At 6/26/2009 11:47 AM,  Anonymous said...

I teach math at college level and these numbers do not say anything. They are more an artifact and bad statistics rather than anything to account for. Many of those who scored too high in SAT exams, when go to college, in must cases, fail the first exams and it happens statistically even, irrespective of gender...I had students scoring close to 700 in SAT who were not able to solve a quadratic equation resulting from a word problem...I personally do not pay too much attention to either SAT or ACT scores...In summary, I have not seen yet any reliable data supporting gender differences in math performance...

At 6/27/2009 11:01 AM,  Anonymous said...

Dan's reported study is nonsense. I will bet that it was run more than once to get the reported results. As a graduate student in a top ten program I saw how frequently these BDT studies were rerun to getthe desired results. Until they propose a real mechanism and demonstrate how they can manage the effect I will assert that they have no internal, contrsuct, or external validity. One may also question statistical validity.

At 6/27/2009 12:21 PM,  Al said...

"
Group 1 was asked questions that reminded them they were female (e.g., What are your feelings on abortion?).

Group 2 was asked questions that reminded them they were Asian (e.g., How do you feel about Hong Kong reverting to Chinese control?)."

Source? And, I don't see how asking a question on abortion is reminding you of your gender, it's more of a depressing question.

At 6/27/2009 7:03 PM,  Anonymous said...

The original Harvard study of Asian-American female performance on math tests after attempts were made to focus them on either their ethnic or gender identity was Margaret Shih et. al. in 1999. Here is a link to the pdf of the first article:

http://www.wjh.harvard.edu/~na/Identity.pdf

Subsequently, there have been followup studies, and searching the research pages of Shih, Pittinsky, or Ambady will provide other studies that presumably responded to challenges of this original. Those who really are interested should have no trouble locating most of it online. I won't bore those who don't care.

Dan Ariely wasn't involved in these studies: he simply reported them in chapter 9 of Predictably Irrational. Since I purchased the Audible version, I couldn't conveniently find the examples of questions they asked to manipulate the students: I'm sorry I used the abortion example, since it is distracting, but that's the only question I could remember off the top of my head, having listened to the book a year ago. The gender angle was more obvious in other questions.

I thought these studies were a reasonable response to Mark's question of whether there was ANY possible explanation for the gender differences other than boys simply being better at math than girls. As long as we remember that we are dealing with averages, I'm of the opinion that the variability of male results can't be explained away, and as long as I'm willing to accept gender-based variability, why not gender-based averages? I don't find it more offensive than arguing that boys are, on average, physically stronger than girls.

ON AVERAGE is the key to avoiding stereotypes.

At 10/20/2009 7:02 PM,  Anonymous said...

stereotype threat can explain this.

At 5/24/2010 7:08 AM,  Zacster said...

Ok. I am actually in high school, and am in an advanced math class. I can tell you that throughout high school, boys are the better students in the class. Girls may be better at non-math/science classes, and may occasionally do better in math because of hard work. But boys drastically overepresent at the top when it comes to natural mathmatical ability.

At 3/30/2011 10:51 AM,  Unknown said...

I'm a female that scored 800 on the math SAT, who was consistently at the top of all her math classes (through PhD), and who is now an applied mathematician. Yes, we can talk all we want about AVERAGES not applying to individuals, but what I've observed is that these stereotypes get applied to all women---and somehow it gets lost that there are many women who are better at math than most every guy they meet. One key personality difference I've observed is that many more guys (applied mathematicians) are absolutely convinced they are right, even when they are wrong, and you have to beat it into them to prove that they are wrong. That lack of self-doubt is a huge advantage---I have this trait myself and I realize it gives me an edge, but I have definitely observed that it is much rarer among women. This trait does not make one more capable or competent, however.

At 9/15/2012 11:10 PM,  Oddur said...

Ehm... the SAT tests are standardized, proven tests. That last comment, and some others here, bear signs of wishful thinking, at best.
Boys are better in some, girls in some. Deal with it.