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Regression towards the mean, Regression towards mediocrity

Regression towards mediocrity is a statistical mathematical law that

a) explains why children of bright Blacks tend to be much less bright than their parents. and tend to drift back into lower social classes
b) is another incontrovertible mathematical proof for heredity of IQ and heredity of the black white IQ gap [See below]
when black families attain middle-class status, the likelihood that their children will remain there, or do better, isn’t high. [How Black Middle-Class Kids Become Poor Adults [Amren]


End of summary

Supporting texts and links follow below


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In his book, The g Factor, [Page 471] Arthur Jensen gives a striking example of regression to the mean. He collected the IQ scores of all the elementary school students in one California school district. He then picked out all the students—both black and white—with IQs of 120, a score well above the white mean but even further above the black mean. He found that the average IQ scores for the brothers and sisters of these children was 113 for the white children and 99 for the blacks. [1, 2]

 


 

Slides above are from

Pitfalls in Statistical Analysis - Regression to the Mean | Slideshow

An excellent explanation of mistakes and pitfalls and artifacts due to regression towards the mean. Must watch.


Historically, what is now called regression toward the mean has also been called reversion to the mean and reversion to mediocrity. [Wikipedia]
[...] The effect can also be exploited for general inference and estimation. The hottest place in the country today is more likely to be cooler tomorrow than hotter, as compared to today. The best performing mutual fund over the last three years is more likely to see relative performance decline than improve over the next three years. The most successful Hollywood actor of this year is likely to have less gross than more gross for his or her next movie. The baseball player with the greatest batting average by the All-Star break is more likely to have a lower average than a higher average over the second half of the season.  [Wikipedia]

 

 Regression towards the mean, or regression towards mediocrity, is a concept of mathematical statistics. If both you and your wife won the genetic lottery and thousands of your genes gave you an IQ of 120, your children will, on average, have less luck and have a lower then 120 IQ.

Rather, your children's IQ will be closer to the mean of your genetic group. Fatally, the IQ drop will be higher for Black children than for white children. The Black children drop in direction of the Black mean (IQ 85 for in the US, IQ 70 in large parts of Africa), and Whites to the 100 mean IQ.

 


Regression towards the mean, a ruthless law of statistics, explains the sad fact that the children of bright Blacks are much less bright than their parents. and tend to drift back into lower social Classes

 

 

In Jewish families, almost no drop from parental IQ 120 would happen, as the Ashkenazi Jew's average IQ is around 115.

The exact effect size is a complex statistical issue. The strength of the regression towards the mean depends on many assumptions, and changes when high IQ ran in the family for many generations. (Bayesian statistics)

 

For below average parents, regression towards the mean is positive, their children have higher IQ.


[7]


How Black Middle-Class Kids Become Poor Adults [Amren]

But perhaps what’s most unsettling about the current economic climate in black America is that when black families attain middle-class status, the likelihood that their children will remain there, or do better, isn’t high.

Because of regression towards the Black mean of 85

“Even black Americans who make it to the middle class are likely to see their kids fall down the ladder,” writes Richard Reeves, a senior fellow at the Brookings Institution. In a recent blog post Reeves says that seven of 10 black children who are born to families with income that falls in the middle quintile of the spectrum will find themselves with income that’s one to two quintiles below their parents’ during their own adulthood.
A 2014 study from the Federal Reserve Bank of Chicago, which looked at factors such as parental income, education, and family structure, shows a similar pattern: Many black Americans not only fail to move up, but also show an increased likelihood of backsliding. According to the study, “In recent decades, blacks have experienced substantially less upward intergenerational mobility and substantially more downward intergenerational mobility than whites.”
The greater probability of slipping back applies to blacks across income groups. According to the Fed study, about 60 percent of black children whose parents had income that fell into the top 50 percent of the distribution saw their own income fall into the bottom half during adulthood. This type of downward slide was common for only 36 percent of white children.

Because of regression towards the Black mean of 85 vs. regression towards the White mean of 100.

 But the gap in mobility was significant for lower-class families as well. “For most of the bottom half of the income distribution, the racial differences in upward mobility are consistently between 20 and 30 percent,” writes senior economist Bhashkar Mazumder, the study’s author. “If future generations of white and black Americans experience the same rates of intergenerational mobility as these cohorts, we should expect to see that blacks on average would not make any relative progress.”

Well, Whites with an IQ of 85 have regression upwards towards the mean of 100, while Blacks would stay put.

 

See also Anti-Racism is Anti-Science

 


 

IQ Regression to the Mean : the Genetic Prediction Vindicated ...

But that’s not clear at all. What kind of luck explains the fact that the children of high-IQ parents have lower IQs while they are reared in cognitive stimulating environments, when the children of low-IQ parents who were raised in chaotic environments still have higher IQs than their parents ? The IQs regress halfway (50%) to the population mean at both sides of the IQ distribution. If we stick to the Dickens-Flynn model (2001) of feedback loops, one would expect that children of high-IQ parents have higher IQ and children of low-IQ parents an IQ even lower. But the opposite happens. This criticism, in the end, does not provide any explanation for the fact that the regression is homogeneous across the different levels of IQ. As Jensen made it clear, the IQ subgroups do not depart from linearity for an IQ range going from 50 to 150.

 

Why middle class blacks do as badly in school as poor blacks www.amnation.com/vfr/archives/009231.html Nov 15, 2007 ... Jared Taylor writing at Vdare summarizes the downward mobility as ... may be witnessing here is the last gasp of the Sixties egalitarian fantasy, ...

 

Steve Sailer: iSteve: Regression toward the mean and Francis Galton Jan 28, 2013 ... The concept of regression toward the mean is one of the more paradoxical notions ever discovered. Although it's a fundamental aspect of ...

A mediocre man's great son, a great man's mediocre son

Dec 24, 2011 ... What is more curious is how this related to the reality ofregression toward the mean. This is a very general statistical concept, but for our ...

Regression toward the mean and IQ - The Unz Review

Regression toward the mean is the curse of smart parents' lives. ... Libertarian economists have never heard of regression toward the mean, or perhaps are so ...

Steve Sailer: iSteve: Regression toward the mean and IQ

 A reader sends me an Excel file for calculating expected IQs of children based on their parents' IQs.

Regression Toward The Mean And IQ | VDARE - premier news ...

Jan 28, 2013 ... If one starts with two parents whose IQs are 160 and looks at the averageIQs across generations the speed of the regression to the mean is ...

Regression to the Mean - The Unz Review

Oct 21, 2015 ... The sum of all these individual regressions is going to be add up to regression towards the mean of the source population. (But as mentioned ...

Gene Expression: Regression to the Mean and Galton's Fallacy (not!)

Aug 17, 2004 ... Since Francis Galton was the first to identify, name, and explain the phenomenon of regression towards the mean, it would be reasonable to ...

David Brooks Tries His Hand At Explaining Regression Toward The ...

Feb 9, 2013 ... dismay of the more scientific-minded Tim Roth. Recently, we were kicking around Galton`s paradoxical concept of regression toward mean.

Information Processing: Assortative mating, regression and all that ..

Jul 22, 2010 ... Assortative mating, regression and all that: offspring IQ vs parental ... +.4n for regression toward the mean calculations, so this is a little higher.


			

Race/ IQ Explanation Gap at “Achievement Gap Summit” [Amren]

One thing he’s sure about: The problem is "absolutely, positively not genetic." [Email Jack O’Connell]
Likewise this week, newspapers reported on a Pew Charitable Trust study [Economic Mobility of Black and White Families] that found blacks are three times more likely than whites to drop out of the middle class into the lowest fifth of income earners. [Middle-Class Dream Eludes African American Families, by Michael A. Fletcher, Washington Post, November 13, 2007]
More specifically, 45 percent of black children whose parents were earning the 1968 median income grew up to be poor. Only 16 percent of white children from similar families hit the skids.
Columbia sociologist Ronald B. Mincy, [send him mail] who was an advisor to the Pew study, says they went over the results again and again to make sure they were right. "There is a lot of downward mobility among African Americans," he told the Washington Post. “We don’t have an explanation."
Well, I am not handicapped by a professorship at Columbia. So I do have an explanation—and Jack O’Connell and the Achievement Gap crowd ought to listen up, too.
Ever since IQ tests have been given in the US, the black average has been 85—a full 15 points below the white average.
There is a lot of overlap, of course, and some blacks are smarter than most whites. But while 50 percent of whites have IQs over 100, only 16 percent of blacks do. Likewise, whites are 20 times more likely than blacks to have IQs of 130 or higher.
One of the best-established facts in the social sciences—and something that is obvious to everyone—is that people with high IQs tend to do better in school and better in life than people with low IQs.
Clapping and chanting in church has nothing to do with it.
The evidence that racial differences in IQ are at least partly genetic is overwhelming, despite the outraged shrieks that greet anyone who points this out. (As the James Watson affair shows, the shrieks have become so hysterical we can be sure the guardians of orthodoxy are less sure of their position than ever.)
There is something else the hand-wringers should think about: regression to the mean, or the tendency for natural phenomena to draw back from extremes towards the average.
When very tall people have children, for example, they don’t keep getting taller and taller, generation after generation. The children are likely to be taller than average—but not as tall as their parents.
The process works in the other direction, too: Very short people don’t keep having even shorter children; the generations drift up towards the average.
The same goes for intelligence. Francis Galton noted in the 1860s that geniuses’ children are smart, but they usually aren’t geniuses. Likewise, dummies tend to have children smarter than themselves.
Regression is only a tendency, however. Occasionally parents at the extremes produce children who are even more extreme. But that is rare. The more extreme the parents are, the stronger the pullback towards the mean.
The people who agonize over the achievement gap would rather cover their ears than hear this—but regression explains what baffles both Mr. O’Connell in California and Prof. Mincy of Columbia. It explains both why the black-white (and Hispanic-Asian) achievement gap is greater at higher income levels, and why blacks are more likely to fall out of the middle class than whites.
Among blacks, IQ regresses to a mean of 85 rather than 100. So a black who has a high enough IQ to be comfortably middle class—say 120—is much further out toward the IQ extreme for his group than a white with an IQ of 120. Which means the pull towards the mean is much more powerful for the children of smart blacks than it is for the children of equally smart whites.  
Put differently, if you match black parents and white parents for IQ, the black-white IQ gap for the children increases sharply as the parents’ IQs go up.
And that, Mr. O’Connor, is why the black-white test score gap is greater for the children of rich parents than it is for poor parents. It may be a rotten shame, but it is just plain harder for middle-class blacks than for whites to pass on their intelligence—and therefore their social status—to their children. 
In his book, The g Factor, [Page 471] Arthur Jensen gives a striking example of regression to the mean. He collected the IQ scores of all the elementary school students in one California school district. He then picked out all the students—both black and white—with IQs of 120, a score well above the white mean but even further above the black mean. He found that the average IQ scores for the brothers and sisters of these children was 113 for the white children and 99 for the blacks.
It was to be expected that siblings have lower IQs than the hotshots. But these figures show just how much more freakish it is for black than white children to have IQs of 120. These very smart blacks were, on average, 21 points ahead of their brothers and sisters; the whites were only seven points ahead.
To repeat: Very smart whites have somewhat less smart children, but very smart blacks are likely to have markedly less smart children.
And there is something else going on that the uplift crowd refuses to hear: Blacks have disadvantages entirely apart from IQ. As Charles Murray and Richard Herrnstein note in the their book The Bell Curve even when they are matched for IQ, black women are still five times more likely than white women to have illegitimate children, and two and a half times more likely to go on welfare. And even with matched IQs, blacks are two and a half times more likely to have gone to jail.
This probably has to do with greater impulsiveness, or a lower willingness to sacrifice in the present for gains in the future. A classic 1961 study found that black children are much more likely than white children to ask for a small candy bar today than wait a week for a bigger one. (W. Mischel, "Preference for Delayed Reinforcement and Social Responsibility," Journal of Abnormal and Social Psychology 62, 1: 1-7.)
Richard Lynn has written that blacks consistently score higher than whites on tests of psychopathic personality, again, even when they are matched for the same IQ. (See Racial and ethnic differences in psychopathic personality, Personality and Individual Differences, 2002, Vol. 32, pp.273-316. Or his American Renaissance article on the same subjects: Race and Psychopathic Personality, July 2002  )  Psychopathic personality—and the misbehavior that goes with it—is just the kind of thing that contributes to bad grades, and drags middle-class black children into the underclass.
And I can promise you that not one of the 125 panels at the Achievement Gap Summit will talk about it.
Adlai Stevenson once said that given a choice between agreeable fantasy and disagreeable fact, Americans will go for the fantasy every time. The fantasy these days is that racial differences are (in California educrat O’Connell’s words) "absolutely, positively not genetic."
Until people such as Arthur Jensen and Richard Lynn and Charles Murray are on the achievement gap panels and are advising the Pew Charitable Trust, people who ought to know better will keep on finding they “don’t have an explanation” for simple problems.  [Source: Race/ IQ Explanation Gap at “Achievement Gap Summit” [Amren] ]


The Likelihood of Genetic Group Differences in IQ: The Black White Gap in IQ

Posted on October 7, 2009 | 33 Comments

I apologize in advance for the daunting length of this post. My sole excuse is that I should have made it still longer to cover the topic.

In dealing with any controversy, it’s usually healthiest to begin at the sticking point. On the question of the impact of biology on political ideology, it’s plain enough what that is: group differences in IQ in general, and the black-white gap in IQ in particular.

I believe the best evidence is that the black-white IQ gap is real, that IQ measures something basic about intelligence, and that the difference between the average IQ of blacks and the average IQ of whites is based in substantial part on genetic differences between the two groups.

I’ll focus on the claim regarding the substantial genetic basis for the IQ gap. The evidence is perhaps best summarized in the following sequence of papers. The series commences with an initial paper by Arthur Jensen and Phillipe Rushton, is followed by criticisms from some of the most prominent anti-heriditarians, and ends with a final response to their critics from Jensen and Rushton:

    1. Rushton, J. P., & Jensen, A. R. (2005). Thirty years of research on race differences in cognitive ability. Psychology, Public Policy, and Law, 11, 235-294.
    2. Sternberg, R. J. (2005). There are no public-policy implications: A reply to Rushton and Jensen (2005). Psychology, Public Policy, and Law, 11, 295-301.
    3. Nisbett, R. E. (2005). Heredity, environment, and race differences in IQ: A commentary on Rushton and Jensen (2005). Psychology, Public Policy, and Law, 11, 302-310.
    4. Gottfredson, L. S. (2005). What if the hereditarian hypothesis is true?Psychology, Public Policy, and Law, 11, 311-319.
    5. Suzuki, L., & Aronson, J. (2005). The cultural malleability of intelligence and its impact on the racial/ethnic hierarchy. Psychology, Public Policy, and Law, 11, 320-327.
    6. Rushton, J. P., & Jensen, A. R (2005). Wanted: More race realism, less moralistic fallacy. Psychology, Public Policy, and Law, 11, 328-336.
    7. Another paper that responds to the most recent criticism of the hereditarian hypothesis, in the book “Intelligence and How to Get It: Why Schools and Cultures Count” by Richard Nisbett, is this paper, again by Jensen and Rushton.
    8. Also a very good summary of the latest data regarding the black-white IQ gap can be found in Charles Murray’s article The Inequality Taboo, from 2005.

As these papers make clear, there exist any number of items of evidence that point to the conclusion that the black-white IQ gap is quite considerable, and its genetic basis substantial. It is of course that evidence considered in aggregate that most inescapably nails down those conclusions. Yet some items seem even standing by themselves quite powerful.

I would subsume that evidence under the rubric of “regression to the mean” effects. Jensen and Rushton in “Thirty years of research on race differences in cognitive ability”, linked to above, describe the phenomenon and some of the evidence:

Regression toward the mean provides still another method of testing if the group differences are genetic. Regression toward the mean is seen, on average, when individuals with high IQ scores mate and their children show lower scores than their parents. This is because the parents pass on some, but not all, of their genes to their offspring. The converse happens for low IQ parents; they have children with somewhat higher IQs. Although parents pass on a random half of their genes to their offspring, they cannot pass on the particular combinations of genes that cause their own exceptionality. This is analogous to rolling a pair of dice and having them come up two 6's or two 1's. The odds are that on the next roll, you will get some value that is not quite as high (or as low). Physical and psychological traits involving dominant and recessive genes show some regression effect. Genetic theory predicts the magnitude of the regression effect to be smaller the closer the degree of kinship between the individuals being compared (e.g., identical twin  full-sibling or parent– child  half-sibling). Culture-only theory makes no systematic or quantitative predictions.

 

For any trait, scores should move toward the average for that population. So in the United States, genetic theory predicts that the children of Black parents of IQ 115 will regress toward the Black IQ average of 85, whereas children of White parents of IQ 115 will regress toward the White IQ average of 100. Similarly, children of Black parents of IQ 70 should move up toward the Black IQ average of 85, whereas children of White parents of IQ 70 should move up toward the White IQ average of 100. This hypothesis has been tested and the predictions confirmed. Regression would explain why Black children born to high IQ, wealthy Black parents have test scores 2 to 4 points lower than do White children born to low IQ, poor White parents (Jensen, 1998b, p. 358). High IQ Black parents do not pass on the full measure of their genetic advantage to their children, even though they gave them a good upbringing and good schools, often better than their own. (The same, of course, applies to high IQ White parents.) Culture-only theory cannot predict these results but must argue that cultural factors somehow imitate the effect theoretically predicted by genetic theory, which have also been demonstrated in studies of physical traits and in animals.

 

Jensen (1973, pp. 107–119) tested the regression predictions with data from siblings (900 White sibling pairs and 500 Black sibling pairs). These provide an even better test than parent– offspring comparisons because siblings share very similar environments. Black and White children matched for IQ had siblings who had regressed approximately halfway to their respective population means rather than to the mean of the combined population. For example, when Black children and White children were matched with IQs of 120, the siblings of Black children averaged close to 100, whereas the siblings of White children averaged close to 110. A reverse effect was found with children matched at the lower end of the IQ scale. When Black children and White children are matched for IQs of 70, the siblings of the Black children averaged about 78, whereas the siblings of the White children averaged about 85. The regression line showed no significant departure from linearity throughout the range of IQ from 50 to 150, as predicted by genetic theory but not by culture-only theory.

 

What is peculiarly compelling about this evidence? The simplicity and directness with which the genetic hypothesis accounts for the data, the accuracy of that prediction across the range of IQs, and the sheer implausibility of any primarily environmental account of that data.

Of course, those promoting the primarily environmental hypothesis can put together a response that formally meets the objection: some unknown factor X that depresses the IQ of all blacks effectively uniformly across the range, imposing a nearly exactly one standard deviation hit on each black subject measured. Now, I must say this purported effect impresses me as quite magical and unprecedented. What other socioeconomic or cultural environmental factor can one think of that induces such a uniform effect across such a range on a group of human beings?

Given what the factor X is supposed to effect in particular, how plausible is its existence? Wouldn’t one expect that some black families in some more environmentally propitious situations would enable their children to escape, or at least significantly to avoid, any factor X that might depress IQ scores? How is it, then, that even for black children with relatively high IQs of 120, their siblings should average only 100, rather than 110, as with the siblings of white children with IQs of 120? Consider the parents of a black child with the relatively high IQ of 120. Wouldn’t one expect that that family, which had managed to find and develop an environment congenial enough to the intellectual development of one of their children that he or she achieved an IQ of 120, might likewise have secured an environment as well suited for the intellectual development of their other children? Here we have the same parents, the same socioeconomic status, the same childrearing practices, as well as the same schools and neighborhoods. If environment means anything to IQ — which of course is the claim — shouldn’t such similarities be exactly what one would expect to engender the same kinds of outcomes in IQ? How explain then the great and otherwise unexpected disparity?

I find it very hard to ponder facts like these without inferring that genes dominate the explanation for the black-white IQ gap.

Another set of facts that I would categorize as “regression to the mean” effects is the disparity between black and white performance on the SAT even when controlling for economic status and level of education of parents. This is well captured in two graphs. (I take as a reasonable assumption that the SAT, which correlates as well with IQ tests as they correlate with each other, can here work as a good measure of IQ).
Average 1995 SAT scores vs income by ethnicity
Average 1995 SAT scores vs parental educational level by ethnicity

Both of these graphs run very hard against the hypothesis of purely, or dominantly, environmental basis of the black-white IQ gap. Yes, as parental education and income increase, SAT scores rise: that much an environmental explanation might predict. But, remarkably, the children of blacks whose income is over $70K attain an average SAT score lower than that of the children of whites whose income is well into the poverty level of $0K to $10K. Likewise, the children of blacks who had achieved a graduate level degree score lower on average on the SAT than do the children of whites who only finished HS.

How might one contemplate these items of data without feeling that they are exactly what one would not expect to see if environment played the major role in determining IQ differences between these groups? The advantages that come with a high income and with a graduate level education confer the very sort of benefits that are routinely said to explain why the average black student can’t do as well as the average white student on an IQ test or the SAT. How is it then that the effects of this relative privilege in black children cannot overwhelm, and easily, those of the clear deficts in the backgrounds of white students against whom the black childen are being compared? If income and educational level of parents entail so little, what can the environment plausibly be said to ground here?

Of course, this regression to the mean is, on the other hand, exactly what one would expect to see if the genetic basis were dominant in determining IQ or SAT scores. The hereditarian hypothesis predicts this and the earlier IQ data neat as a pin.

Now, again, one can contrive an explanation that lets the primarily environmental explanation off the hook. One can say that blacks at any income level and at any level of education suffer from a “caste mentality” or from “stereotype threat” which systematically undermines their performance. I plan to address those issues in more detail in a later post. For now, suffice it to say that the only likely motivation I can see to adopt such a view is to save the primarily environmental thesis from otherwise incompatible data. It appears to me to be a posit born of desperation: a scientific Hail Mary thrown up when the game is otherwise lost. In practice, it appears to operate as little more than a fudge factor X whose impact and exact size is determined only by what otherwise can’t be explained under a given hypothesis.

I think, though, that if one doesn’t divert one’s attention from the basic facts being communicated by these graphs and the earlier example described by Jensen and Rushton, and allows oneself to stare into this sun long enough to take its reckoning, then the natural conclusion is that it is genetic, rather than environmental, differences that are more basic to the black-white IQ gap.