A Z score is simply your score on a particular measure (i.e. height, weight, income, IQ) minus the average score on that measure (in a particular population), divided by the standard deviation in that population:
Z score = (score – average score)/standard deviation
So the average Z score by definition is 0.
On the IQ scale, where the average IQ (among white Americans or among all Americans) is often defined as 100 and the standard deviation is often defined as 15, someone with an IQ of 70 has a Z score of -2, someone with an IQ of 85 has a Z score of -1, someone with am IQ of 100 has a Z score of 0, someone with an IQ of 115 has a Z score of 1, someone with an IQ of 138 has a Z score of 2.5 etc.
Of course it depends who the reference group is. If you’re comparing your IQ not to the general white population, but to white PhDs where the average IQ is about 123 and the standard deviation is about 13, then an IQ of 70 has a Z score of -4.07 and an IQ of 138 has a Z score of 1.15.
Why is this useful?
A good analogy is if you had 50 British pounds, 50 South African rands, and 50 Euros, and you wanted to know which of these three monies was worth most, you would convert them all to U.S. dollars, which serves as a kind of universal financial yardstick.
Analagously, Z scores are like a universal yard stick. Let’s say a white man has a height of 200 cm, a weight of 200 lbs, and an IQ of 200. He wants to know whether he should be become a basketball player where he needs height, a football player where he needs weight, or a scientist where he needs IQ.
If he knows that white men have a mean height of 179 cm (SD = 6.52 cm), a mean weight of 185 lbs (SD = 35 lbs) and a mean IQ of maybe 101 (SD = 15.5), then using the formula:
Z score = (score – average score)/standard deviation
he could calculate that relative to white men, he has a Z score of 3.2 when it comes to height, 0.42 when it comes to weight, and 6.4 when it comes to IQ.
All three Z scores are positive, so he is above the average for white men in all three traits, but he is most impressive in IQ and least impressive in weight, so he might decide to become a scientist and not a football player. Further, if these three traits are normally distributed, he can apply this calculator. By clicking the “one sided” option and then entering his Z scores, he would learn that for height (Z = 3.2), he’s taller than 99.9313% of white men, for weight (Z = 0.42), he’s heavier than 66.2757% of white men, and for IQ (Z = 6.4), he’s smarter than roughly 100% of white men.
Normalized Z scores
Z scores are most meaningful when traits are normally distributed. When traits are not normally distributed they can often give silly results. For example, Bill Gates net worth, at his peak, was $100 billion dollars. According to one recent study, the average net worth of a sample of Americans was $145,837 with a standard deviation of $447,814.
So Bill Gates financial Z score = (100,000000000 – 145,837)/447,814 = 223,306.67
Given that Z scores of 6 or higher are only supposed to occur one in a billion times, a Z score of 2,23306.67 is kind of meaningless.
A brilliant Promethean told me that when calculating the financial Z scores of billionaires, I should instead use normalized Z scores. In other words, the financial Z score they would have if money were normally distributed.
So assuming there are 200 million American adults, the normal curve predicts the richest American adult (Bill Gates) should have a financial Z score of 5.73, so that would be his normalized Z score.
Z scores and correlations
If you know the correlation (r) of two variables, X and Y, then, assuming a bivariate normal distribution, you can estimate the average Z score on Y for people with a given Z score on X, by multiplying their Z score on X by r.
Conversely, you can estimate the average Z score on X for people with a given Z score on Y, by multiplying their Z score on Y by r.
So if the correlation between IQ and financial success is 0.4, people with a Z score of 2 on financial success should average a Z score of 2(0.4) = 0.8 on IQ, and people with a Z score of 2 on IQ, should also average a Z score of 0.8 on financial success.
The reason this happens is that a correlation can be thought of as a bunch of people plotted on a scatter plot, where each person’s IQ is the Y coordinate and each person’s income is the X coordinate (or vice versa as we see below):
As you can see, in a scatter plot, there is a line of best fit, which is just a line that comes closest to all the points on the scatter plot. This line allows you to predict the average level of Y for a given level of X.
Now if both variables in the above scatter plot were expressed as Z scores, and a bivariate normal distribution is assumed, then the correlation between both variables can be thought of as the slope of the line of best fit. Thus multiplying a given Z score on X by the correlation between X and Y allows you to deduce the average Z score on Y for said value of X (i.e. the Y coordinate for that value of X on the line of best fit).
Of course, traits like income are not normally distributed, particularly at the extremes, so trying to estimate the intelligence Z score of Bill Gates from his financial Z score of 223,306.67 by multiplying 223,306.67 by the IQ-income correlation of 0.4 would lead to an intelligence Z score of 89,322.67 and thus an IQ above one million!!!
Clearly that’s nonsense. As a brilliant Promethean once told me, the correct procedure would be to use the normalized financial Z score of Bill Gates (5.73), and multiply that by the IQ-income correlation to get his expected IQ.
Of course, given that the IQ-income correlation is only 0.45, there would be an enormous amount of scatter around the line of best fit, so it would not be very accurate for a specific individual.
I once used a similar approach to estimate the IQ of Jesus (not from wealth, but from influence). This was disputed by the highly respected commenter Misdreavous who wrote:
““Fame” (both academic and otherwise) is not normally distributed. Knowing that Jesus is the third most influential man alive (according to whom?) does not allow you to convert a rank order into a z-score. You would think this would be obvious to anyone who passed high school statistics.
However, if the approach was good enough for a brilliant Promethean, it is good enough for me. Though I should note that the conventional method for normalizing non-Gaussian data is not to convert the data into normalized Z scores as I do, but instead to take the natural logarithm which I have not tried doing yet.
and a mean IQ of maybe 101 (SD = 15.5), then using the formula
So it mean that white women have an average IQ of 99 (SD = 14.5) ?
So assuming there are 200 million American adults, the normal curve predicts the richest American adult (Bill Gates) should have a financial Z score of 5.73, so that would be his normalized Z score.
How do you obtain this normalized Z score ?
I’m going to do a post on sex differences soon
You can google for Z score percentile tables. I can’t find any good ones to link to
Women are incomplete men
Wat do you ****
If all the planet was composed of Ashkenazi Jews (IQ 110, SD = 17), what would be the IQ of the smartest man of the world ?
If entire world were Ashkenazi, that would be 7.3 billion Ashkenazi Jews.
In a normal curve, the highest Z score in 7.3 billion is 6.33.
So 6.33(17) + 110 = 218
But their SD is unlikely to be that big
I saw that on a site which was also saying that subsaharan Africans have a SD of 12. May be their SD is not so unlikely to be that big because of the genetic diseases causing their high IQ which would not be part of normal genetic variation of IQ.
In my opinion, Misdreavus has high verbal IQ and high social IQ (Theory of Mind), but lacks the self-awareness to stay in his lane when it comes to math.
Is he good at maths, yes or no ?
He says he is. He says he got a degree in a STEM field from a university that ranks in the top 15 worldwide without affirmative action & a GRE quant score is in the 98th percentile. Assuming only college grads write the GRE (mean IQ 110, SD = 14) a math score in the 98 percentile (Z = 2) implies a math IQ of 138.
What is a “math IQ” ?
I think it’s kinda something Pumpkin made up to represent overall math ability. Although SAT and GRE math, and WAIS Figure Weights (and maybe Arithmetic) are probably pretty good measures of this ability.
Does this have some real biological origin like spatial, social, verbal IQ and executive fonction ?
Are you Cale?
Probably. i’ve seen studies showing that even birds and young children have a “number sense”.
http://www.scientificamerican.com/article/how-animals-have-the-ability-to-count/
So pure “math IQ” = ability to count things ?
At its most basic, “math IQ” seems to be the ability to make rapid and accurate estimates of the size/quantity of things.
But the math IQ (being able to do more complex math) would be more like a mix between pure math IQ, verbal IQ (math use a language of numbers and sometimes letters) and spatial IQ (you often need to visualize things in math ) ?
It appear that some low IQ races have a pretty good ability to estimate the size/quantity of things but that doesnt make them good at math, probably because they lack the verbal IQ to translate it into numbers and to master complex arithmetic rules and even more the spatial IQ needed in more complex math.
Possibly.
Pumpkin, what do you think about that ? What were you thinking about when you were talking about math IQ ?
Pumpkin, what do you think about that ? What were you thinking about when you were talking about math IQ ?
Math IQ was just a term I used to describe one’s performance on a standardized test that emphasizes math abilities. Of course a lot of what we call math talent might just be a combination of spatial IQ, working memory IQ and verbal IQ.
Only a very thorough factor analysis could answer that question. I know Howard Gardner considered logic one of his seven types of intelligence, so maybe that’s what math IQ is at a fundamental level. Only factor analysis can tell the story.
Misdreavus is probably the smartest person without a blog.
I would like to meet h
Him*
Yep, it’s kinda silly to try to extrapolate IQ from traits that have power law distributions, although you show one can get sensible predictions with normalized z-scores.
Speaking of power laws, it’s probably the most exciting distribution after the normal/Gaussian distributions. If you’re near a university campus, you should try reading this article, which I got from Dr. Steve Shoe’s website:
http://www.annualreviews.org/doi/full/10.1146/annurev.economics.050708.142940
Or read anything by Nassim Nicholas Talbe.
Most things in economics and finance (including wealth, income) are best described by power laws.
Pumpkin do you know anything about factor analysis? I got an old book called Applied Factor Analysis by R.J. Rummel and it’s hard because my linear algebra skills suck 😦
I have a rough idea but I’ve never actually tried it. Emil would probably be a lot better at it than anyone else in the HBD-o-sphere.
Hey Pumpkin, I see you like to take the position of a teacher, then I have an interesting game for you.
Let’s pretend HBD is an accepted academic subject. First, I would like to have an idea of what category it belongs to: is it STEM, business/administration or social sciences/humanities ? Second, I would like you to tell us when it should start being taught: kindergarten ? primary school ? middle school ? high school or tertiary education ? Then, just for fun, you could tell us how you would organize your HBD lessons for each grade you chose to be appropriate to teach HBD, give us tests, assignments and grades. Lastly, you could tell us what kind of careers our college HBD major makes us ready for.
You could create a whole other blog: Pumpkin’s Academy, that would work for certain.
HBD is not really a field it would just be integrate to what we know in ethnology and anthropology.
Nope, those fields seldom make mention of IQ nor do they back their claims by Rushton & cie’s theories. Moreover, they use a different method of studying populations, they don’t rely on meaningless statistics and stereotypes but on long term direct observation and that’s why they always end up producing very different conclusions from HBD’s.
But you’re right, HBD is not a field, it’s an ideology. Anyway, I want to know how would Pumpkin transform HBD into a rigorous academic discipline, how would he make a 40 hours course per year of it.
Like I really would like to know how would Pumpkin teach an European class made of student from different backgrounds in a non-racialist society, how would he force his fantasies over their lived experience, how would he tell them that those who will succeed in his course are those who have the genes and IQ for it. You know like, what if HBD was a real world thing ?
Anthropology + human genetics + psychometrics + evolutionary biology/sociobiology + biosocial criminology + demography
Anthropology + human genetics + psychometrics + evolutionary biology/sociobiology + biosocial criminology + demography
Exactly. HBD is a multidisciplinary subject.
Yet HBD relies on the works of less than a dozen of scholars and bloggers who are not anthropologists, geneticists, biologists, criminologists or demographists. Most of them are psychologists, which is barely considered a science whereas psychometrics is mostly restricted to designing arbitrary tests of cognitive function. Moreover, most psychometricians are careful when evaluating the validity of their tests and very few of them would say IQ = your life in a number, much less your genes and brain in a number.
So no, HBD is not a multidisciplinary subject, it is something on its own, its scholars are amateurs in every discipline that is not related to psychology. I searched on google scholar to see what kind of academic papers cited Rushton’s most influential publication (Race, evolution, and behavior: A life history perspective, only 669 citations and here) and what I found is really bad news for HBD because:
1 – You guys are alone
2 – very few people care about you and what you say
By the way pumpkin, I think it would be great if you accept my challenge, show me how and why would you teach HBD.
Yet HBD relies on the works of less than a dozen of scholars and bloggers who are not anthropologists, geneticists, biologists, criminologists or demographists.
Not true, check out John Hawks (paleo-anthropologist), Steven Pinker (linguist, cognitive scientist, evolutionary psychologist), Gregory Cochran (physicist, geneticist), Henry Harpending (anthropologist), Ben Southwood (biosocial criminologist), Charles Murray (political scientist), James Flynn (political scientist) (not an HBDer himself, but he’s helped, not hurt, the HBD argument), Garrett Jones (economist), Robin Hanson (economist and futurist, doesn’t explicitly identify with HBD but supports some of its ideas). Should I go on?
Most people are too afraid to cite Rushton, even if they’ve read him.
Afrosapians u are too stupid to understand hbd
1 – You guys are alone
2 – very few people care about you and what you say
I feel very sorry for you because the same can be said for yourself. And to think you spend most of free time here, arguing with people who think you’re delusional.
I have zero math creativity but I have creativy artistic politics
Why my comments are awaiting moderation ?
Because you’ve said very vulgar disgusting obscene things and tried to give yourself a very vulgar disgusting obscene name.
Can you be more precise ? I dont see what you are talking about ?
No, gentlemen never talk precisely about such matters. Just not the way I was raised.
Gentlemen never precise they are gentlemen.
Hey Pumpkin,
Share your thoughts about behavioral genetics.
Do you really think the way you’re raised matters?
I think how you’re raised affects your absolute score on some measures, but not your Z score on said measures. That is, people with good genes tend to get raised in good homes and people with bad genes tend to get raised in bad home, so the absolute difference between people gets magnified by upbringing (depending on the trait), but the rank order (which is what psychologists study) stays the same. So both extreme HBDers and extreme HBD deniers might be correct.
the absolute difference between people gets magnified by upbringing (depending on the trait), but the rank order (which is what psychologists study) stays the same. So both extreme HBDers and extreme HBD deniers might be correct.
Ah yes, you’ve mentioned that before. But most behavioral genetics data show your childhood home environment has 0 impact on adult outcomes. Notwithstanding some exceptions you’ve brought up.
LOL! Don’t mess up this blog, Pumpkin’s got a good thing going here.
And what s the utility of z score in real life ?
Iqfetichists every where…n
Z score is not creativity
A Z score is a just a unit for measuring any variable. If you’re extremely creative, you have a huge creativity Z score.
Yes but z is nothing i prefer have a low z and a big creativity
If you have big creativity then you have a big Z in creativity. Z is just the unit of measurement.
No having a big creativity is not like hqving a big z, having a big creativity is to being able to create real thing that is what ypu little iqfetichist/iqtard pamp and judasphere (groupie of jayman) dont understand
LOL! Pumpkin, can you ban this guy?
buddy, you’re retarded.
Z score is for technic smart people nit for true creators
Pamp, ur big z score bring you nothing in life
wtf
“Wtf”
What**
Afrosapiens: Who built your Nairobi? It’s safe to assume Sub Saharan blacks didn’t lift a finger to make this happen.
And yet, you go on to make comments that Africa was too harsh for development. The same goes for a country like Ghana, but on a smaller scale.
Gorgeous!
Of course black couldnt have built this beautiful thing 100% agree with you JS
Accra, Ghana, is another one of those cosmopolitan countries in Sub-Sahara. It is smaller and not as modern as Naroibi.
A few Ghanians whom I’ve met in the states, tell me that Ghana is heavily invested by foreigners, especially from the Chinese, and to a lesser extent, East Indians.
The modernization of all these Sub-Saharan African “entrepreneurial” cities, are solely the work of non-blacks.
http://www.applauseafrica.com/innovation/394-africa-s-most-entrepreneurial-cities
Now look at Hong Kong, it was completely built by Chinese hands, and not by the British, after a certain time, especially when they left the colony in the 1990s.
Can one make a case that Sub-Saharan Africans will tell foreigners to stop what they are doing, because they will take over with their urbanization process?
Wow, that is beautiful
what is a high school drop out and Canadian trying to understand basic math?
oo! oo! mistah kottah!
the answer is…
peepee!
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