## Bell Curves & Gaussian Distributions

### As if though the race and gender gap wasn't already huge enough, there was another huge but completely unreported [and as yet, unexplained] jump in the gap in the 2000-2001 tests

The gender gap in GRE Verbal of 0.32 SD is about the size of the gender gap in SAT math, where none the highest scoring girls, the ones who got A's in college math, demonstrated the math skills of the boys who got A's and B's, who were more than half the boys

At the 8th grade level, girls in the US score 0.31 standard deviations higher than boys in PISA reading (513 vs. 488). By 12th grade, as measured by SAT verbal, boys have a slight 0.18 standard deviation advantage over girls (420 vs. 438). But after college, the gender gap in verbal skills as measured by GRE verbal (512 vs 484) gives males a 0.28 standard deviation advantage over females, on par with their 0.35 standard deviation advantage on SAT math.

There are 5,940,000 female and 4,861,000 male students in our undergraduate schools, and if the math skills of these girls follows the pattern of the Howard Wainer study, then 2,678,940 girls have math skills equivalent to boys who flunk out of math, 1,799,820 have math skills equivalent to boys who get D's, and 1,455,300 have math skills equivalent to boys who get C's.

None of them have math skills which would qualify them to follow a career in STEMS, while more than half of the 5,940,000 boys who were rejected (or 2,970,000 of them) to make room for these girl students, WOULD have benefited from a career in STEMS.

Why would we as a society do this at a time when high tech careers are so valuable, and so profitable? It's like cutting our nose off to spite our face. f you ever wondered why we can't make our own shoes, much less our own semiconductors and electronics, and instead must go all the way to China to have them made for us, then now you know why.

Math tests simply present mathematical facts to students to measure how well they can solve problems, and cannot be designed to "discriminate against" women, Blacks, Hispanics, nor Asians (particularly Asian men who score higher than the so-called privileged White men). The fact that 51% of college boys can solve
problems ( and thus get A's and B's in college math) which no girls can solve, not even those who get A's in college math, means just that--no American girl can solve problems that at least half of American boys have proven on SAT math tests that they CAN solve. All math problems are representative of how well a citizen can solve problems at school, at work, in science, in politics, and in life.

What's the effect of this invidious discrimination against our boys?  If all of the 5,940,000 boys who had been denied admission to make room for this many girls, had instead been accepted, we would now have 10,801,000 boys in college, and at least half of them, or 5,400,500 boys who CAN solve math problems, would be in our undergraduate schools where they CAN benefit from an undergraduate education. This is 122% more than the current figure of 2,430,500 students who DO understand math.

### One Standard Deviation is 3.7 IQ Points

In 2007, in TIMSS math, 4,972 students from Hong Kong scored 584, with a Standard Deviation of 68, which is 9.5 SD higher than the 5,101 students from Ghana who scored 261.

http://timss.bc.edu/timss2007/intl_reports.html

According to Professor Lynn, Ghana has an IQ of 71, which is 35 IQ points lower than Hong Kong at 106.

Thus 35 IQ points = 9.5 SD, statistical proof that the actual SD for IQ scores is 1SD = 3.7 IQ points.

This means that the 106 - 64 = 42 point gap between Hong Kong and Senegal is 11.4 SD, whereas a Sengalese has one chance out of 506,797,346 of scoring only 5 standard deviations higher than the mean for Senegal of 64, which is an IQ of only 106, not 137.

For a Senegalese to have an IQ of 137, he would have to score TWENTY STANDARD DEVIATIONS higher than the average of 64 for Senegal.

This is pure math. We don't need to engage in character assassination against Senegal to make this point.﻿

Another way to look at this is Exhibit 2.2 on pg. 71 which shows that NONE of the students in Botswana or Ghana (nor even Northern Africa, in Algeria, and Morocco) scored higher than 550, compared to 71% in Taipei, Korea, or Singapore, 61% in Hong Kong and Japan, and half in Massachusetts:

http://timss.bc.edu/timss2007/PDF/TIMSS2007_InternationalMathematicsReport.pdf

Needless to say, none in Africa scored higher than 625 compared to almost half in Taipei, Korea, and Singapore, and one third in Japan and Hong Kong.

625 equals an IQ of 106 so any claim of a Senegalese to have an IQ of 137 is 4.2 SD higher than Japan, an IQ that NONE of the Japanese students exhibited.﻿

I went to school in Japan and know that the real serious education there starts AFTER the 8th Grade which is the grade tested by both PISA and TIMSS. No Asian country has participated in any of the 12th grade tests as we have. So we are very aware that both the race and gender gaps get much bigger between 8th and 12th grade.

American Blacks go BACKWARDS between 8th and 12th grade, and yet we already know that on IAEP at the 8th grade level, Blacks in D.C. score one standard deviation lower than Mozambique.﻿

### One Standard  Deviation = 3.0 IQ Points

On TIMSS Math in 2003, the Netherlands, with an average IQ of 103, scored 540, and South Africa, with an average IQ of 72, scored 264. Since the standard deviation for TIMSS  scores was 55, this 276 point gap is 10.0 standard deviations. And since this 10.0 standard deviations is equivalent to a 30 point gap in IQ scores, the standard deviation for IQ scores is 30 / 10 or 3.0 IQ points.

540 - 264 = 276

/ (55 /2) = 10.04

102 - 72 = 30

30 / 10.04 = 2.98804780876494 or rounded to 3.0

### 40 Years of GRE Verbal

Over 4 decades, the 264,501 American Black men who have taken the Graduate Record Exam Verbal test, the creme de la creme of American Blacks, scored an average of 399 with a standard deviation of 93. None have scored over 590, and only 8 scored higher than 585.

The 660,521 American Black women who took the test scored an average of 388, 11 points lower, with a standard deviation of 88, none have scored over 570, and only 21 scored over 564, the average for White protestant men.

The 203,880 Asian men who took the test scored 490 with a standard deviation of 121, which means that 32,3457 scored higher than 573 (higher than any Black woman and higher than all but 32 Black men). The 84,805 Mexican men who took the test scored an average of 449 with a standard deviation of 101, which means none of them scored higher than 650 and only 119 scored higher than 595. Ditto for the 84,Hispanic men who scored 472, none scored higher than 690, and only 108 scored higher than 634. Ditto for the 1,019,213 Catholic men who took the test who scored even lower than Mexicans (432 vs. 449), with a standard deviation of 101. This means none of them scored higher than 640 and only 1,427 scored higher than 584, about the average for White Protestant men.

Of the 2,038,427 Protestant men who've taken the test and scored 559 with a standard deviation of 99, 323,407 scored higher than 609, a score no Black man, no Black woman, and less than a thousand Hispanic men, Mexican men, and White Catholic men, combined, have ever achieved.

### Standard deviation, GRE quantitative

Within race
Indian = 0.47 sd
Asian = 0.58 sd
Black = 0.13 sd
Mexican = 0.59 sd
Puerto Rican = 0.50 sd
Hispanic = 0.64 sd
White = 0.68 sd
Other = 0.60 sd
Total = 0.62

Across race
Asian male to Black Female = 2.25 sd
White female to Black Male = 1.11 sd
White male to Black Female = 1.4 sd (verbal)

### TIMSS Math

Within country, by sex
Netherlands = 0.65 sd
Norway = 0.68
US = 0.1 sd
Switzerland = 0.41 sd
South Africa = 0.21
Denmark = 0.65 sd
Iceland = 0.68
Czech Republic = 0.65 (science)

### TIMSS Calculus

Within country, by sex
US AP calculus = 0.19 sd
US avg = 0.26
Denmark = 0.33 sd
Lithuania = 0.44 sd
Russia = 0.53
Switzerland = 0.63 sd
Czech Republic = 0.89
Austria = 0.93 sd

Women HATE to be reminded that their smaller brains DO have a significant negative effect on their IQ, across the world, across the races, across the country, from state to state, and from city to city.

1. Race/sex gap leaps from 234 to 267 points.
2. Ain't no black geniuses.
3. The top 97% of applicants to the University of Texas are WHITE men who are DENIED ADMISSION.
4. University of Texas applicants are representative of nationwide scores.
5. The distribution of GRE scores are equivalent to that for MCAT scores.
6. This pattern is identical with SAT, TIMSS, and all other standardized test scores.
7. Race and sex differences are 20 times greater than year to year variations in GRE test scores.
8. Converting GRE Verbal Scores to IQ.

Scoring of the GRE Quantitative test is similar to that for the SAT Math test which consists of one essay question which can be scored only by subjective means, opening it up to controversy about whether or not it's valid or accurate. The most objective part of the test are the 225 five part multiple choice questions which attempt to measure the probability of a student succeeding in college or graduate school. About 1/4th of these questions can be answered strictly from rote memorization. For simplicity we include the three quarters of the test which require some form of reasoning or calculation which can be measured objectively.

Both tests have a base score of 200 which is assigned when a student signs their name. Of the 600 points between 200 and 800, another 150 points can be gained by knowing the subjects but not exhibiting any reasoning or critical thinking skills, for a total score thus far of 350. If a person were to just guess on the balance of the five part multiple choice questions without evaluating the answers in any way whatsoever, he would on average get 20% of them correct just by chance, for another 90 points and a total score of 440.

This score of 440 is conservative. In TIMSS physics, which is scored similarly and which has questions of equal validity and depth, a score of 446 for American girls represents a score which is 30 points lower than if they'd just guessed on this part of the test.  A score of 446 is not indicative of any reasoning or critical thinking skills at all. These skills can be measured accurately only between 446 and 800.  And because many Asian students (more than 10% of them) score higher than 800, the SAT is not a very accurate IQ test, particularly when American blacks consistently score lower than 431 in both SAT Verbal and SAT Math, lower than 391 in GRE Verbal, and lower than 416 in GRE Quantitative.

While the College Board does provide the standard deviation for black students in both SAT and GRE, scores this low most likely do not follow a normal Gaussian Distribution. For the average to be 431, there can't be too many students who score higher than this, because it's almost impossible to score lower than this, so their estimate that the standard deviation, say for black women who took GRE Verbal, is 88, is the most optimistic estimate.

### GRE vs. IQ

The correlation of Graduate Record Exam quantitative scores with IQ's enables us to express the huge race and sex differences in terms that more people might understand or appreciate.  Where many people might not grasp what a 234 GRE point spread between Asian men and black women means, expressing it as a 61 point spread in IQ might make more sense.  This is a test that more than one quarter of a million students spend a lot of money to take very year, because they know that both graduate schools and employers depend heavily on the outcome of these scores in admissions and hiring decisions.  Whatever quantity is measured by this test is a desirable feature in both students and employees.  People who don't do well on this test aren't, or should not be, hired or admitted, even under affirmative action programs.

Year after year, from test to test, gaps between races and the sexes have been fairly consistent [other than the as-yet unexplained jump in the gap between 1997 and 2001].  Within each race, when expressed as IQ, the gap between black men and black women is the lowest, with black men scoring 10 points higher than black women.  The biggest gap is 19 points for "Other Hispanic", "White", and "Other".  The gap between Asian men and women, and Mexican men and women, is 17 points.  Puerto Ricans are at 16, and American Indians are at 13.

As seen in the graph above, within each sex, the IQ of Asian men is 116, which is 13 points higher than White men at 103, and 51 points higher than black men at 65; and the IQ of Asian women is 99, which is 15 points higher than White women at 84, and 44 points higher than black women at 55.

Across races and sexes, the most notable points are that the average IQ of White women is equal to Mexican men, 1 point higher than Indian and "Other" men, 2 points higher than Puerto Rican men, and 19 points higher than black men, whereas the IQ of black women is 28 points lower than Indian men and 61 points lower than Asian men.

Is it reasonable to believe that American black women have an average IQ of 55 rather than the 85 touted in the news media?  Could reality be 30 points lower than perception?  What other evidence is there to support it?

Without worrying too much about why females within each race score the equivalent of 13 to 19 IQ points lower than males within each race, and accepting point blank that whatever is being measured is of value to both industry and education, this 10 point gender gap is predicted, explainable, and completely reasonable.  Many different ways of measuring IQs in Africa have confirmed that two African nations have an average IQ of 59, and two dozen nations have an average IQ lower than 70.  It's reasonable to believe that those who had been taken as slaves were not selected from the intelligentsia, as the purpose of slavery was brawn, not brains.  It's not unreasonable to believe that the average IQ for slaves was from the lowest intellectual strata of Africa, or 55 for women and 65 for men.  And there's no reason to believe that this average increased during slavery, by miscegenation with Caucasoids, nor by the huge education expenditures which left them with the world's highest murder and violent crime rates.

 Group1 Mean GRE Quantitative Score Lynn IQ Adjusted American Indian 479 75 Men 511 83 Women 459 70 Asian/Pacific 598 106 Men 638 116 Women 572 99 Black/African 416 58 Men 446 65 Women 404 55 Mexican American 475 73 Men 517 84 Women 451 67 Puerto Rican 471 74 Men 504 82 Women 448 66 Other Hispanic 495 79 Men 543 91 Women 469 72 White 540 90 Men 586 103 Women 514 84 Other 541 90 Men 583 102 Women 509 83

### Race/sex Gap JUMPS From 234 to 267 Points

Why the news media blackout on this VITAL issue at a time when discussions about the quality of education had reached a crescendo?Why did the media convey the false impression that �the gender gap is decreasing�, at a time when it actually leapfrogged?For three years, the gender/race gap in GRE scores was fairly constant, but then suddenly on the Quantitative Scores of the 2000-2001 test:

The gap between Asian men and Black women jumped from 234 to 267 points.

The gap between White men and Black women jumped from 182 to 199 points.

The gap between Asian men and Asian women jumped from 66 to 72 points.

The gap between Indian men and Indian women jumped from 52 to 68 points.

The gap between Mexican men and Mexican women jumped from 66 to 71 points.

The gap between Black men and Black women jumped from 42 to 45 points.

The gap between �Other� men and �Other� women increased from 74 to 75 points.

The gap between all men and all women increased from 73 to 76 points.

At the very same time these gender and racial differences were WIDENING SIGNIFICANTLY, we also had IDIOT RACISTS and IDIOT SEXISTS proposing �solutions� like the following from the infamous FAME report:

The last issue I have been pondering has been what if there were no differences between white males and other groups, and, even, what if we developed a measure where white males were 80-100 points lower than other groups? What would the role of this measure be in the graduate admissions process?

Ironically, even punishing White men even more than they�ve already been punished still won�t solve your putative �problem�:� they�d STILL out perform every other race and every other sex by a MILE!It�s encouraging that, with such political or politically correct pressure on GRE to dumb down, water down, nullify, or even NEGATE the purpose of the test that the College Board stuck by its guns and published the TRUTH!

Except that another anomaly about the 2000-2001 test, the increase in the overall average score from 529 to 544, undermines that possibility.As this paralleled an increase in the number of test takers from 274,296 to 279,586, we cannot chalk it up merely to a more selective group of test takers.We thus must conclude it�s the result of intentionally re-centering or re-scaling the test in order to put rose colored glasses on students and teachers about the persistent and *permanent* race and sex differences which made this world and nation GREAT.

But why?What�s to be gained by conveying the FALSE impression that America�s scores are increasing when credible, solid, scientific international tests have PROVEN in spades that programs like NCLB have caused them to DECREASE, DRAMATICALLY?

People and organizations who LIE with statistics like that can never be trusted.

### NO BLACK Ever Scored Higher than 700

Since the Graduate Record Exam began in 1949, 2,038,427 Protestant men, 1,019,213 Catholic men, 76,920 Hispanic men, 84,800 Mexican men, 124,760 "other" men, and 203,880 Asian men have taken the test, and in total, the following scored higher than 700:

Protestant men = 323,407
Catholic men = 161,704
Hispanic men = 12
Mexican men = 211
Asian men = 6,636
"Other" men = 4,639

Conversely, of the 256,400 Black men and 660,520 Black women who've taken this premier test, NONE of them scored higher than 700, and:

Only 21 Black women scored higher than 612
Only 8 Black men scored higher than 696.

### GRE Scores Consistent With TIMSS Math Scores Broken Down by Race

GRE general test score information by ethnic group and sex: 1996-97

To accurately reflect the unannounced, unexpected, unpublicized, unknown, unexplainable, unpredictable INCREASE in the "gender gap" in the midst of all the media hoopla about the "narrowing of the gender gap", we must add that to the above charts, in red, as follows:

It seems GRE quit producing this study, and it seems the reason they did is that it revealed an alarming trend: while our mediots proclaim from the hilltops that the gender gap is narrowing, these studies instead showed an alarming INCREASE. As far as I know, the following is the last complete analysis of the GRE Verbal scores.

GRE Verbal scores from Table A.1 "GRE General Test Score Information by Ethnic Group and Sex: 2001-02

Total 279,856 students
98,763 Men = 500
181,093 Women = 471
gender gap = 29 points
Standard deviation = 105
Gender gap = 0.28 sd

Indian men = 473
Indian women = 443
Gender gap = 30 points

Asian men = 490
Asian women = 484
Gender gap = 6 points

Black men = 401
Black women = 391
Gender gap = 10 points

Mexican men = 442
Mexican women = 420
Gender gap = 22 points

Puerto Rican men = 419
Puerto Rican women = 403
Gender gap = 16 points

Hispanic men = 459
Hispanic women = 431
Gender gap = 28 points

White men = 512
White women = 484
Gender gap = 28 points

Note that this 29 GRE Point Gender Gap is very close to the 33 SAT Math Point gender gap which Howard Wainer proved actually conceals that what this means-- half the college boys scored in a range which NONE of the college girls scored in, which is most likely a very similar situation for GRE Verbal scores.

### A CERTIFIABLE LIE

"However, on average, higher scores are observed on Quantitative Reasoning for men than for women. Women performed better on Analytical Writing than men"

The ETS and NCES and most of our "educators" have bent over backwards to TRY to force the gender gap to narrow, and the only result has been to push the scores of both sexes DOWN, WAY DOWN.

But this statement even directly contradicts the GRE's very own Verbal reports which show that women of NO race score higher than the men of their race in Analytical Writing, Table 4 on your url.

Also note that even though this NEW scale shows a suspiciously small standard deviation, that the gap between Asian men and Black women on GRE quantitative of (156.3 - 142.3 = 14 points / sd of 6.4) is 2.18 sd, MUCH bigger than the 1.88 sd on the old scale [which is the only explanation for why they would make the old scale even more misleading, rather than being honest with us].

Base Score on new GRE test 2012 is 147

Indian men = 6.1
Indian women = 3.5
Gender gap = 2.6 points

Asian men = 6.5
Asian women = 4.7
Gender gap = 1.8 points

Black men = 0.6
Black women = - 0.6
Gender gap = 1.2 points

Mexican men = 2.7
Mexican women = 1.9
Gender gap = 22 points

Puerto Rican men = 2.4
Puerto Rican women = 1.2
Gender gap = 1.2 points

Hispanic men = 4.9
Hispanic women = 2.2
Gender gap = 2.7 points

White men = 8.6
White women = 6.1
Gender gap = 2.5 points

GRE vs. brain size per Professor Rushton