Low IQ and genetic disorders?

[James T]

Well, since James T and Alexander acknowledge that IQ has predictive power and is mostly genetic, I presume they also advocate using eugenics to better humanity by increasing intelligence (not IQ though unless intelligence was measured against today's norms).Similarly to youngalexander, I'll have to point out that you have misrepresented my position. I don't find this surprising, since most people who hold your view hold a number of contradictory beliefs to be true. This is normally an indication that you have a fucked up belief system, but I've rarely found people who will even allow this to be exposed. Cognitive dissonance is only useful, it seems, for people with sufficient intellectual honesty to allow the process to work.

[Jesse]

And you are right - the data would have been standardised on the whole sample, not separately for black and white participants. So while the histogram of normalized scores would have been, by definition, Gaussian, the histograms for black and white groups certainly wouldn't fall neatly on the normal curve, and may or may not have been normally distributed. I don't think it's even true that the histogram of all scores in the sample would automatically have been Gaussian--I think whatever institution is responsible for putting out IQ tests would periodically change the "official" scoring practices based on some large reference group, so that the scores of that reference group would be normalized and the average score would be 100, but if the test is subsequently administered to some other group they wouldn't re-normalize the scoring to make sure the test is normalized and centered on 100 for that particular group (for example, if you gave an IQ test to a group of Mensa members, their average would be higher than 100!) The wikipedia page on the Flynn effect (http://en.wikipedia.org/wiki/Flynn_effect) supports this: IQ scores are re-normalized periodically, such that the average score is reset to 100. The revised versions are standardized on new samples and scored with respect to those samples alone So, even if you plotted the scores of all participants in that study together, rather than plotting the "black" scores separately from the "white" ones, it would probably not look like a perfect normal distribution.

[James T]

For some reason, I have a feeling that the scores and score distributions were deliberately normalised, in average, SD and curve shape.

[JamesBannon]

Yeah. Where's the Glenlivet.... ;)
Can't drink the stuff as it makes me ill. I used to like whisky a long time ago but now just the smell makes me heave. Good spiced rum or nice plum brandy are different matters though.:)

Actually as soon as people start throwing stats around I get very "jumpy", especially when I think there is a subtext somewhere, and when it comes to stats about humans there usually is. A hundred-and-one questions start jumping into my head:

How was the sample determined?
What size is it?
How was the data analysed?
What are the underlying assumptions of the distribution used?
How were the parameters determined?
How were they measured?
Has everything else been excluded?
Have all possible models that fit the data been eliminated?

And so on.

And I'm no statistician, just a rank amateur (I've always meant to fix that but never found the time).

[barbos]

For some reason, I have a feeling that the scores and score distributions were deliberately normalised, in average, SD and curve shape.
It is not important. Plot is illustration, nothing more.

Well, if it is that important for you I can say how this picture was drawn.
They calculated average IQ score for blacks and whites and plotted two gaussian distribution with these averages and same SD.

It is fucking illustration, nothing more.

[Jesse]

What is the point of commenting on it ?
You are not going acknowledge you were wrong anyway Are you going to acknowledge your mistake about normalization in the "plots are not data" argument, or do you claim that it is standard practice to normalize the scores of each individual group of test-takers, so that it is impossible that any group could ever have a distribution other than a perfect Bell curve?

[Febble]

I don't think it's even true that the histogram of all scores in the sample would automatically have been Gaussian

Well this particular set was the actual WAIS 1981 US standardisation sample. So they would have derived their normed scores from the percentiles scoring each raw score in their sampled (stratified by age). Anyone using the 1981 WAIS would be using those norms, until the next edition.

--I think whatever institution is responsible for putting out IQ tests would periodically change the "official" scoring practices based on some large reference group,

Well, this was the 1981 reference group.

so that the scores of that reference group would be normalized and the average score would be 100, but if the test is subsequently administered to some other group they wouldn't re-normalize the scoring to make sure the test is normalized and centered on 100 for that particular group (for example, if you gave an IQ test to a group of Mensa members, their average would be higher than 100!) The wikipedia page on the Flynn effect (http://en.wikipedia.org/wiki/Flynn_effect) supports this:

Yes, absolutely. I use the WASI a lot, which is a four-item version, and use the US norms (even though I am in the UK). Depending on my sample I can get non-normal distributions and means that are a long way from 100.

The Flynn effect is fascinating though. It's still a bit mysterious. The slopes are quite uncannily linear.

[James T]

It is not important. Plot is illustration, nothing more.I think it is important. I don't think there is such a reference group as Jesse suggests. It seems more likely there was some thought over what form the distribution should take and some massaging to make it take that form. This is not surprising, but worth noting.

[Febble]

What is the point of commenting on it ?

Well, either you will find out that you don't understand IQ scores, or you will form the opinion that Flynn doesn't. It will be interesting to know which.

You are not going acknowledge you were wrong anyway

Wrong about what?

[Jesse]

For some reason, I have a feeling that the scores and score distributions were deliberately normalised, in average, SD and curve shape. I doubt it. To "normalize" the scores of an individual group in this way--and especially to normalize black scores and white scores separately--would not be an accepted practice, it would make it meaningless to compare their graph with a graph of IQ tests scored in the standard way, since the same number of right answers would yield a different score using their method than using the standard scoring method. More likely, someone just took the average black score and average white score in that study, scored in the standard official way, and then decided to draw two arbitrary bell curves around each score.

[Febble]

I think it is important. I don't think there is such a reference group as Jesse suggests. It seems more likely there was some thought over what form the distribution should take and some massaging to make it take that form. This is not surprising, but worth noting.

No, I checked it out. The actual data from which the plot was derived were from the 1981 WAIS standardisation sample, so the distribution of the scores from that entire sample would, by definition, have been normally distributed. However, the plot with the two curves is simply an "idealised" plot based on the means, and, one hopes, the SDs of the "black" and "white" groups of that sample. The sample size for the "black" group was something like 192, so it certainly wouldn't have been smooth, and we don't even know if it, or that of the "white" group, would have been symmetrically distributed. No operational definition of "black" or "white" was given in the paper that gave the aggregate data, which simply referenced the WAIS sample.

[barbos]

Are you going to acknowledge your mistake about normalization in the "plots are not data" argument, or do you claim that it is standard practice to normalize the scores of each individual group of test-takers, so that it is impossible that any group could ever have a distribution other than a perfect Bell curve?
What ?
Where did I say it is normilized individually ?

[barbos]

Well, either you will find out that you don't understand IQ scores, or you will form the opinion that Flynn doesn't. It will be interesting to know which.

You did not answer my question.



Wrong about what?

I told you about what few times already

[Jesse]

I think it is important. I don't think there is such a reference group as Jesse suggests. It seems more likely there was some thought over what form the distribution should take and some massaging to make it take that form. This is not surprising, but worth noting. If there's no reference group used to establish a "standard" scoring method for a given year, then what do you think the wikipedia page means when they say the IQ test is periodically rescored so that the average is always 100? Do you think "periodically" means "every time a new study is performed", and that therefore each individual IQ study would automatically have an average score of 100? If I did a study involving only Mensa members, or involving only people with severe mental retardation, do you think the average would still be 100 in these cases?

[Jesse]

They might "normalize" the standard scoring method so that the scores for some large reference group would be guaranteed to have a normal distribution, but I'm pretty sure they wouldn't change the scoring standard for each individual group of people who take the test in order to guarantee that that particular group's scores have a normal distribution, and I'm sure it wouldn't be standard practice to normalize "black" scores separately from "white" scores! I completely agree, that is exactly how it is done. So what was your initial point ? Sorry, I didn't see this post before. But does this mean you acknowledge that if they had graphed the complete set of scores in the study under discussion, they might not have looked like two neat Bell curves (or even if they did look close to Bell curves, the variance might be noticeably larger or smaller than the curves in the illustration). If you acknowledge this, then isn't it correct to say that the curves themselves do not represent actual "data", even if the position of the peaks does?

[Febble]

You did not answer my question.

Try reading the answer.

I told you about what few times already

You told me I was clueless. I've yet to figure out what I'm supposed to be clueless about.

[barbos]

I think it is important. I don't think there is such a reference group as Jesse suggests. It seems more likely there was some thought over what form the distribution should take and some massaging to make it take that form. This is not surprising, but worth noting.
IQ score has to be normalized on reference group.

[barbos]

Try reading the answer.


I did, no answer.


You told me I was clueless. I've yet to figure out what I'm supposed to be clueless about.
Try reading my posts.

[James T]

IQ score has to be normalized on reference group.Bullshit. Simply wrong. has to be my arse.

[barbos]

Sorry, I didn't see this post before. But does this mean you acknowledge that if they had graphed the complete set of scores in the study under discussion, they might not have looked like two neat Bell curves (or even if they did look close to Bell curves, the variance might be noticeably larger or smaller than the curves in the illustration). If you acknowledge this, then isn't it correct to say that the curves themselves do not represent actual "data", even if the position of the peaks does?
That is nice example of nitpicking.
By your logic no curve ever represented "actual" data, simply because histogram is not smooth curve. See,

Noticing that curves are not data was pretty well lame, anyone with IQ>80 would know it is not data, and anyone with IQ>90 would know that illustration and "actual" data can have a difference.
In this particular plot two averages is what is important.

[barbos]

Bullshit. Simply wrong. has to be my arse.
To get IQ score, raw IQ score has to be normalized on some ( usually large and representative) group.
otherwise it is meaningless number which can only be compared to the results from same test.

[Jesse]

That is nice example of nitpicking.
By your logic no curve ever represented "actual" data, simply because histogram is not smooth curve. A best-fit curve is still constructed mathematically using the complete data set. In contrast, in this case they just drew an arbitrary made-up bell curve and centered it on the average score. So again, if they had drawn some completely different curve like the one I posted earlier, as long as they centered this curve on the average score, it would have been "based on the data" to exactly the same degree as the curves they drew. Noticing that curves are not data was pretty well lame, because anyone with IQ>80 would know it not data, and anyone with IQ>90 would know that illustration and "actual" data can have a difference. It would be quite natural to assume that the curves were best-fit curves taken from actual data, rather than being based on absolutely nothing except the fact that IQ scores are "supposed" to have a Bell curve distribution.

[barbos]

A best-fit curve is still constructed mathematically using the complete data set.

It is my turn to nitpick:
Technically it is not fit, fit would involve fitting only two parameters - average and SD, and no raw score distribution would fit nicely because they are not normally distributed to begin with.

In contrast, in this case they just drew an arbitrary made-up bell curve and centered it on the average score.

And it is perfectly fine.

So again, if they had drawn some completely different curve like the one I posted earlier, as long as they centered this curve on the average score, it would have been "based on the data" to exactly the same degree as the curves they drew. It would be quite natural to assume that the curves were best-fit curves taken from actual data, rather than being based on absolutely nothing except the fact that IQ scores are "supposed" to have a Bell curve distribution.
May be it is natural, may be it is not. Either way you would not notice any difference.

As I said before two averages are important on that illustration.

[OripahsTrebor]

What, that I'm a she? Or that the plot isn't data?



Actually it's the one thing it references - it gives the instrument, the WAIS, so we can look that up.



So you've read the Flynn paper, have you? Any comments to make? And FWIW, I do have a bit of a clue. I've administered a great many Wechsler tests, and analysed a fair bit of IQ data. Have you?

So, in general, do those tests have predictive validity of educational achievement?

[barbos]

So, in general, do those tests have predictive validity of educational achievement?
Apparently not :D

[Febble]

So, in general, do those tests have predictive validity of educational achievement?

IQ scores tend to covary with achievement scores. What is much more interesting is what accounts for the unshared variance.

In a technical sense IQ scores "predict" achievement, but achievement also "predicts" IQ scores. Causality is almost certainly bi-directional - being smart helps you achieve, but achieving helps you be smart. And other latent variables almost certainly contribute to both. "Reading exposure" is one.

[Jesse]

It is my turn to nitpick:
Technically it is not fit, fit would involve fitting only two parameters - average and SD, and no raw score distribution would fit nicely because they are not normally distributed to begin with. Are you sure of that? With polynomial best-fit curves the least squares (http://en.wikipedia.org/wiki/Least_squares) method is usually used, I don't why you couldn't use that to find the best-fit gaussian curve too. Of course in this case the peak of the curve need not be exactly lined up with the average of all the data points, but it would be a better overall fit to the data. "Best fit gaussian" turns up a lot of hits on google, and section E of this page (http://www.physics.sfsu.edu/~bland/courses/490/labs/b2/b2.html) does seem to be talking about using the least squares method to find the best fit gaussian curve to some data set. As I said before two averages are important on that illustration. But it's misleading to include those curves if the averages are the only thing that has any basis in data. Among other things, the identical shape of the curves would suggest (if you are under the impression that the curves are based on actual data) a large sample size, which isn't true. Also, since the chart displays typical abilities for people with IQ ranges outside the averages, it's implied that the curves are supposed to be telling us something about the proportion of whites and blacks with IQs in these other ranges as well.

[barbos]

Are you sure of that? With polynomial best-fit curves the least squares (http://en.wikipedia.org/wiki/Least_squares) method is usually used, I don't why you couldn't use that to find the best-fit gaussian curve too.

I told you why, because raw score distribution is not gauss. Shape is usually close to gauss but it is not exactly gauss . Basically what you need to do is find monotonous function of raw score which distributed normally. To do that one need to sort results and then integrate them, no fitting is involved in that process.

You can make it harder than it actually is but, in reality there are no "fitting" of data


Of course in this case the peak of the curve need not be exactly lined up with the average of all the data points, but it would be a better overall fit to the data. "Best fit gaussian" turns up a lot of hits on google, and section E of this page (http://www.physics.sfsu.edu/~bland/courses/490/labs/b2/b2.html) does seem to be talking about using the least squares method to find the best fit gaussian curve to some data set. But it's misleading to include those curves if the averages are the only thing that has any basis in data. Among other things, the identical shape of the curves would suggest (if you are under the impression that the curves are based on actual data) a large sample size, which isn't true. Also, since the chart displays typical abilities for people with IQ ranges outside the averages, it's implied that the curves are supposed to be telling us something about the proportion of whites and blacks with IQs in these other ranges as well.
It is fucking illustration, and it illustrate very well.

[Febble]

Are you sure of that? With polynomial best-fit curves the least squares (http://en.wikipedia.org/wiki/Least_squares) method is usually used, I don't why you couldn't use that to find the best-fit gaussian curve too. Of course in this case the peak of the curve need not be exactly lined up with the average of all the data points, but it would be a better overall fit to the data. "Best fit gaussian" turns up a lot of hits on google, and section E of this page (http://www.physics.sfsu.edu/~bland/courses/490/labs/b2/b2.html) does seem to be talking about using the least squares method to find the best fit gaussian curve to some data set.

There are lots of tests of normality, and some use OLS.

But it's misleading to include those curves if the averages are the only thing that has any basis in data.

Exactly. Even if the SDs were used, it wouldn't tell us that the distributions were normal. We'd actually have to check the data. To which no reference was given.

Not that any of this is germane to anything except the principle that people shouldn't distribute plots that are divorced from their source data.

What is of a great deal more interest is the Flynn paper which barbos is continuing to ignore.

[JamesBannon]

IQ scores tend to covary with achievement scores. What is much more interesting is what accounts for the unshared variance.

In a technical sense IQ scores "predict" achievement, but achievement also "predicts" IQ scores. Causality is almost certainly bi-directional - being smart helps you achieve, but achieving helps you be smart. And other latent variables almost certainly contribute to both. "Reading exposure" is one.
Which is exactly what we would expect even if we assume, for the sake of argument, that there is a genetic complex we can point to which affects IQ.

[Febble]

It is fucking illustration.

And you haven't yet told us what it is a illustration of.

[OripahsTrebor]

Febble, have you done any work on the Progressive Matrices?

[Febble]

Febble, have you done any work on the Progressive Matrices?

I've analysed datasets with Ravens scores, but I've only administered Wechsler scales (which includes a Matrix Reasoning subtest).

[Febble]

Check out the dictionary.

How the hell will a dictionary tell me what you think that plot illustrates? Huh?

[barbos]

And you haven't yet told us what it is a illustration of.

It illustrate difference of IQ scores between blacks and whites, I believe it is quite clear.
Stop asking idiotic questions.

[Febble]

It illustrate difference of IQ between blacks and whites
Stop asking idiotic questions.

American black and white people? All black and white people? African black people and American white people? British black and white people? How black? How white?

Over what age range? At what date?

Are you aware that IQ differences of similar magnitude are found between groups of white people living in different decades? Does this fact cause you to question whether the blackness and whiteness of the groups has anything at all to do with the IQ difference you think is "illustrated" in this plot?

[barbos]

American black and white people? All black and white people? African black people and American white people? British black and white people? How black? How white?

Over what age range? At what date?

What time of day test were taken ?
What height ?
What mass ?
Height/mass ratio
Smoking ?
...
...
...
Food preferences.
Position of the moon.
Air Temperature
Air Pressure.
Speed of sound

You got the Idea.



Are you aware that IQ differences of similar magnitude are found between groups of white people living in different decades? Does this fact cause you to question whether the blackness and whiteness of the groups has anything at all to do with the IQ difference you think is "illustrated" in this plot?
Are you aware that blacks an whites in these tests are from different decades ? no ? then stop posting BS

[Jesse]

I told you why, because raw score distribution is not gauss. Shape is usually close to gauss but it is not exactly gauss . Yes, of course. Did something in my post suggest I thought otherwise? The point of the least-squares method is to find a curve of a certain specified type--whether straight line, 3rd-order polynomial, or gaussian curve--that is the closest possible fit for the data for a curve of that type, in terms of minimizing the sum of the squared difference between each data point and the curve at that point (if the data exactly fit a gaussian distribution, then the sum of the squares would be zero). Basically what you need to do is find monotonous function of raw score which distributed normally. To do that one need to sort results and then integrate them, no fitting is involved in that process. Your description of the process isn't clear to me, are you just talking about calculating the mean and standard deviation and basing the curve on that, as you seemed to say in an earlier post? I'm not doubting that this would be an acceptable method, but the page I linked to suggests it is also possible to find a gaussian distribution to fit the data using the least squares method, although this would presumably result in a different curve then the one generated by the method you're talking about.

In any case, you did previously said that the method you were discussing "would involve fitting only two parameters - average and SD", and I'm fairly certain they didn't actually calculate the standard deviation when drawing those two curves (it would be a pretty big coincidence if the standard deviation was precisely the same in both cases). It is fucking illustration, and it illustrate very well. Illustrates what very well? What exactly does it accurately "illustrate" aside from the position of the peaks? If someone constructed an "illustration" using gaussians with twenty times the standard deviation or one twentieth the standard deviation of the ones depicted there, or even non-gaussian curves like the one I provided before, would you have any good basis for saying these would be less valid as illustrations?

[barbos]

Yes, of course. Did something in my post suggest I thought otherwise?

Yes, word "fit" suggested it. Normalization is not fitting.

The point of the least-squares method is to find a curve of a certain specified type--whether straight line, 3rd-order polynomial, or gaussian curve--that is the closest possible fit for the data for a curve of that type, in terms of minimizing the sum of the squared difference between each data point and the curve at that point (if the data exactly fit a gaussian distribution, then the sum of the squares would be zero).

Nope, The point of least-squares method is to find parameters of the curve not the curve itself. The point of normalization is to find function which if applied to raw score distributed normally.

Your description of the process isn't clear to me, are you just talking about calculating the mean and standard deviation and basing the curve on that,

No, it is what you suggest. Normalization does not assume raw score distribution to be normal. Fitting does, And if raw distribution is not then fitting is not going to make it normal.

as you seemed to say in an earlier post? I'm not doubting that this would be an acceptable method, but the page I linked to suggests it is also possible to find a gaussian distribution to fit the data using the least squares method, although this would presumably result in a different curve then the one generated by the method you're talking about.



In any case, you did previously said that the method you were discussing "would involve fitting only two parameters - average and SD",

No, It is fitting what fit the two parameters only, what I suggested does not fit these two parameters. It is not even fitting.


and I'm fairly certain they didn't actually calculate the standard deviation when drawing those two curves (it would be a pretty big coincidence if the standard deviation was precisely the same in both cases). Illustrates what very well? What exactly does it accurately "illustrate" aside from the position of the peaks? If someone constructed an "illustration" using gaussians with twenty times the standard deviation or one twentieth the standard deviation of the ones depicted there, or even non-gaussian curves like the one I provided before, would you have any good basis for saying these would be less valid as illustrations?
I told you it illustrate difference of IQ scores between blacks and whites.

[David B]

Hey, run me past one thing again.

How many black people were in the study? How many white people?

How were they selected?

This thread has got very long, now, but I seem to remember figures like a couple of hundred white people, and a couple of tens of black people.

I don't remember (and at this time of night am not going back through the thread to see) how, if the topic has been addressed at all, how the people in the study were selected.

How they were selected could make a BIG difference. But might not, depending on the selection parameters.

David B (retains vague memories of his studies in econometrics a few decades ago, and is not happy about a sample of a couple of tens)

[barbos]

Hey, run me past one thing again.

How many black people were in the study? How many white people?

How were they selected?

This thread has got very long, now, but I seem to remember figures like a couple of hundred white people, and a couple of tens of black people.

I don't remember (and at this time of night am not going back through the thread to see) how, if the topic has been addressed at all, how the people in the study were selected.

How they were selected could make a BIG difference. But might not, depending on the selection parameters.

David B (retains vague memories of his studies in econometrics a few decades ago, and is not happy about a sample of a couple of tens)
What kind of questions is that ?
OK, I will answer :)
There were 5 white university professors
and 5 black high school dropouts :)


Yeah, and tests were administered to blacks by KKK members :)

[Well]

IQ is a only measure of how well a person solves intelligent tests and how quickly.

IQ-tests basically measure what you've learned already, and how fast you can regurgitate it.

IQ-tests are not intelligent, nor can they accurately determine a person's intellectual potential, and possibilities.

More intelligent people are thinking IQ-tests are obsolete.

[David B]

What kind of questions is that ?
OK, I will answer :)
There were 5 white university professors
and 5 black high school dropouts :)


Yeah, and tests were administered to blacks by KKK members :)

Ho fucking Ho.

Now - are you going to answer the question properly?

David B (is not impressed by smileys after untruths)

[barbos]

Now - are you going to answer the question properly?

Sorry, there are no proper answers to improper question.

[David B]

Sorry, there are no proper answers to improper question.

Please explain how it is improper to ask about sample size and selection procedure.

David B

[barbos]

Please explain how it is improper to ask about sample size and selection procedure.

David B
Well, Lets say your car is broken, you get it to the car mechanic, and then give him/her a 2 hours lecture/instructions on how to fix cars. Do you think it is proper way to talk to a mechanic ?

Of course fucking sample is large enough, of course there were no selection bias.
Why do you assume they are idiots ? They have done these studies thousands times.

[Jesse]

Hey, run me past one thing again.

How many black people were in the study? How many white people?

How were they selected?

This thread has got very long, now, but I seem to remember figures like a couple of hundred white people, and a couple of tens of black people.

I don't remember (and at this time of night am not going back through the thread to see) how, if the topic has been addressed at all, how the people in the study were selected.

How they were selected could make a BIG difference. But might not, depending on the selection parameters.

David B (retains vague memories of his studies in econometrics a few decades ago, and is not happy about a sample of a couple of tens) In post #193, Febble said (talking of the similar graphic on p. 541 of Implications of Cognitive Diversity (http://www.udel.edu/educ/gottfredson/reprints/2005cognitivediversity.pdf)): Well, at least this paper actually references the source of the data used to generate the plot (which the one referenced in Wiki did not), and which I have now managed to download. It turns out to be a study done on the data from the US standardisation sample of the 1981 WAIS, in which there were 1,664 "white" participants, 192 "black" participants and 24 "other non-white". So, not a particular large sample size for the "black" group, and not sure how representative they'd have been, although if it was "the US standardisation sample" they probably made an effort to have it be a good random sample.

[Jesse]

Yes, word "fit" suggested it. Normalization is not fitting. The phrase "best fit curve" has a standard meaning in statistics, it does not mean a curve that actually goes through all the data points. Try doing a google image search on "best fit curve", or read up on curve fitting (http://en.wikipedia.org/wiki/Curve_fitting), if you don't believe me. Nope, The point of least-squares method is to find parameters of the curve not the curve itself. This is a meaningless distinction, since the "parameters of the curve" uniquely specify "the curve itself". For example, if you want a second-degree polynomial of the form y = ax^2 + bx + c, the parameters would be a, b, and c, there's only one possible curve for each choice of the three parameters in this equation. The point of normalization is to find function which if applied to raw score distributed normally. Yes, but the normalization would have been done on some kind of "reference group" to calibrate the scores, I was going on the assumption that this graph was generated from some study where they used an established scoring method, and thus the data from the study itself would not be automatically normalized. However, looking back over Febble's comment which I quoted in my last post, it occurs to me that perhaps this data was taken from an analysis of the "reference group" itself--is that your understanding? Even so, it would be the total set of scores that would be normalized, they wouldn't normalize "black" scores and "white" scores separately, so even if the total data set was guaranteed to lie perfectly on a neat bell curve that wouldn't mean the set of scores for each group would lie on their own bell curves, you'd need to do some type of curve-fitting which would find a bell curve that most scores for that group were close to. I told you it illustrate difference of IQ scores between blacks and whites. The position of the peaks shows the average difference in IQ scores between a group of 1,664 self-identified white people and 192 self-identified black people. And I asked specifically what is illustrated by the curves aside from the position of the peaks. It would help if you would answer my question about whether the "illustration" would be any more or less valid if we kept the position of the peaks the same but changed other things: If someone constructed an "illustration" using gaussians with twenty times the standard deviation or one twentieth the standard deviation of the ones depicted there, or even non-gaussian curves like the one I provided before, would you have any good basis for saying these would be less valid as illustrations?

[barbos]

The phrase "best fit curve" has a standard meaning in statistics, it does not mean a curve that actually goes through all the data points. Try doing a google image search on "best fit curve", or read up on curve fitting (http://en.wikipedia.org/wiki/Curve_fitting), if you don't believe me.

I don't disbelieve you, I am saying that you are wrong.



This is a meaningless distinction, since the "parameters of the curve" uniquely specify "the curve itself".

Well, you are wrong It IS meaningful distinction.
Normalization is not fit.


For example, if you want a second-degree polynomial of the form y = ax^2 + bx + c, the parameters would be a, b, and c, there's only one possible curve for each choice of the three parameters in this equation.

Now, try to fit gauss by this y = ax^2 + bx + c function :)
or y = ax^2 + bx + c by gauss :)


Yes, but the normalization would have been done on some kind of "reference group" to calibrate the scores, I was going on the assumption that this graph was generated from some study where they used an established scoring method, and thus the data from the study itself would not be automatically normalized. However, looking back over Febble's comment which I quoted in my last post, it occurs to me that perhaps this data was taken from an analysis of the "reference group" itself--is that your understanding? Even, it would be the total set of scores that would be normalized, they wouldn't normalize "black" scores and "white" scores separately,

Who said they would ? me ? where ?
I would never say such stupid thing.




so even if the total data set was guaranteed to lie perfectly on a neat bell curve that wouldn't mean the set of scores for each group would lie on their own bell curves, you'd need to do some type of curve-fitting which would find a bell curve that most scores for that group were close to. The position of the peaks shows the average difference in IQ scores between a group of 1,664 self-identified white people and 192 self-identified black people. And I asked specifically what is illustrated by the curves aside from the position of the peaks. It would help if you would answer my question about whether the "illustration" would be any more or less valid if we kept the position of the peaks the same but changed other things:

[Jesse]

The phrase "best fit curve" has a standard meaning in statistics, it does not mean a curve that actually goes through all the data points. I don't disbelieve you, I am saying that you are wrong. Well, that shows you need to work on your statistics vocabulary, "best fit" has a standard meaning in the context of regression analysis (http://en.wikipedia.org/wiki/Regression_analysis), and it definitely doesn't mean a line or curve that always goes through every data point. Can you find a single reference that supports with your notion of "best fit"? I can show you as many as you want to support mine--as one example, my google image search turned up this page (http://www.sanger.ac.uk/Users/sgj/thesis/html/node103.html) with the following graph and explanation: http://www.sanger.ac.uk/Users/sgj/thesis/html/pngs/ubq_4gnhcl_ph4.png
Figure 7.5: Temperature dependent stability of native ubiquitin in 4.0 mol l -1 Gn.HCl at pH 4.0 determined from the relative populations of folded and unfolded states. The line of best fit from non-linear regression analysis is shown and leads to the thermodynamic parameters shown in table 7.1. Or look at the page on Sampling and Data Analysis (http://www-unix.oit.umass.edu/~mcclemen/581Sampling.html), which in section 2.4.6 discusses regression analysis and includes a diagram: 2.4.6. Standard Curves: Regression Analysis
When carrying out certain analytical procedures it is necessary to prepare standard curves that are used to determine some property of an unknown material. A series of calibration experiments is carried out using samples with known properties and a standard curve is plotted from this data. For example, a series of protein solutions with known concentration of protein could be prepared and their absorbance of electromagnetic radiation at 280 nm could be measured using a UV-visible spectrophotometer. For dilute protein solutions there is a linear relationship between absorbance and protein concentration:

http://www-unix.oit.umass.edu/~mcclemen/Sampling6.gif

A best-fit line is drawn through the date using regression analysis, which has a gradient of a and a y-intercept of b. The concentration of protein in an unknown sample can then be determined by measuring its absorbance: x = (y-b)/a, where in this example x is the protein concentration and y is the absorbance. How well the straight-line fits the experimental data is expressed by the correlation coefficient r^2, which has a value between 0 and 1. The closer the value is to 1 the better the fit between the straight line and the experimental values: r^2 = 1 is a perfect fit. Most modern calculators and spreadsheet programs have routines that can be used to automatically determine the regression coefficient, the slope and the intercept of a set of data. You can see that in both cases the "line of best fit" does not actually cross all the data points. More examples can be provided if needed, but again, if you think you are using the terminology correctly you should be able to find some references that support you. Well, you are wrong It IS meaningful distinction. OK, find a single example of a function for which you can specify all the "parameters" and yet still not have a unique curve. Normalization is not fit. I never said it was, and I wasn't talking about normalization at all in the section you're quoting! I was talking about finding a best-fit normal curve for some existing data, which is completely different (with normalization you're actually adjusting the scores to make them fit a normal curve, but I was just talking about finding a good curve to approximate some existing scores which you don't adjust, like the scores of the 'black group' or the 'white group' individually). Again, I was assuming that although the scoring method had been obtained by normalizing the number of questions answered correctly by some reference group, the scores used as a basis for the graph were not themselves normalized, they were just based on that preestablished scoring method; even if this assumption was wrong, normalization is still irrelevant if you agree that the scores of each group were not individually normalized. For example, if you want a second-degree polynomial of the form y = ax^2 + bx + c, the parameters would be a, b, and c, there's only one possible curve for each choice of the three parameters in this equation. Now, try to fit gauss by this y = ax^2 + bx + c function :) I have no idea what you're trying to say here, you can't fit one smooth curve to another, you only fit a curve to a discrete set of data points. And is this question supposed to somehow refute my claim that there's no difference between finding the parameters of a curve and finding the curve itself? Again, please give a single example of a curve which is not uniquely specified by knowing the parameters for that curve. Even so, it would be the total set of scores that would be normalized, they wouldn't normalize "black" scores and "white" scores separately, Who said they would ? me ? where ? I wasn't saying that anyone had argued that, just pointing out that even if the total data set the graphs were taken from was normalized, that wouldn't justify the assumption that the data set from each group would have a Bell curve distribution too. The reason I make this point is to show that your talk about normalization is a red herring, since they couldn't have gotten those two different bell curves through anything related to normalization, and the problem of finding a normal curve to match an existing data set (whose values you don't change, unlike with raw scores vs. adjusted scores in normalization) has nothing to do with normalization.

[barbos]

Jesse :)
There is no need to post lectures on fitting because it is not relevant to the IQ score normalization.

[barbos]

I have no idea what you're trying to say here.

That is exactly the problem here :)
Try to understand it

[Jesse]

Jesse :)
There is no need to post lectures on fitting because it is not relevant to the IQ score normalization. Um, I never said fitting was "relevant to the IQ score normalization". I brought up fitting because it was relevant to where they got those two normal curves for the "black" and "white" groups, which as I pointed out was obviously not through normalization. It's you who keeps bringing up the topic of normalization here.

Please try to remember where this whole tangent about fitting and normalization got started. I said: But does this mean you acknowledge that if they had graphed the complete set of scores in the study under discussion, they might not have looked like two neat Bell curves (or even if they did look close to Bell curves, the variance might be noticeably larger or smaller than the curves in the illustration). If you acknowledge this, then isn't it correct to say that the curves themselves do not represent actual "data", even if the position of the peaks does? To which you replied: That is nice example of nitpicking.
By your logic no curve ever represented "actual" data, simply because histogram is not smooth curve. To which I responded that smooth best-fit curves are at least based on the complete data set: A best-fit curve is still constructed mathematically using the complete data set. In contrast, in this case they just drew an arbitrary made-up bell curve and centered it on the average score. It was then that you brought up the stuff about IQ normalization (although I didn't immediately realize you were talking about normalization, which contributed to the confusion): Technically it is not fit, fit would involve fitting only two parameters - average and SD, and no raw score distribution would fit nicely because they are not normally distributed to begin with. But this was a non sequitur, because I hadn't been talking about "raw scores" in the first place, I was talking about the "black" scores vs. the "white" scores when their tests were scored in the standard manner (where the 'standard' scoring system was presumably originally created by taking some raw scores of a reference group normalizing them, but once you have the standard scoring system the details of how it was created aren't important), and finding best-fit curves for each group individually. No normalization involved at all! My point was to refute your argument, quoted above, that "by my logic" all smooth curves fail to represent the "actual" data--if they had actually generated the curves for the black group and the white group using a best-fit method, then I'd say this would have been a pretty decent way of representing the data. But they didn't, whoever drew the diagram just pulled the two curves out of their ass. That is exactly the problem here
Try to understand it Sorry, "Now, try to fit gauss by this y = ax^2 + bx + c function" doesn't make any more sense if I think about it some more. Perhaps you could clarify what you were getting at here, and explain how this is relevent to your claim about there being a meaningful distinction between finding the parameters of a curve and finding the curve itself?

[barbos]

Well, you used word "fit", where we all (i think) now know that there is no fitting during normalization of anything.

I can only reiterate my point again:
Plot is perfectly fine and no amount of quoting and discussing normalization will ever change that fact.

[Jesse]

Well, you used word "fit", where we all (i think) now know that there is no fitting during normalization of anything. I never brought up normalization, you brought it up. I wasn't talking about normalization in the first place, I was responding to your comment 'By your logic no curve ever represented "actual" data, simply because histogram is not smooth curve' by pointing out that best fit curves do represent actual data by my logic. See? Nothing to do with normalization. I can only reiterate my point again:
Plot is perfectly fine and no amount of quoting and discussing normalization will ever change that fact. You brought up normalization, not me. And it's not a plot, it's a fantasy curve that has no connection to data aside from its peak. Once again, a simple question: If someone constructed an "illustration" using gaussians with twenty times the standard deviation or one twentieth the standard deviation of the ones depicted there, or even non-gaussian curves like the one I provided before, would you have any good basis for saying these would be less valid as illustrations?

[barbos]

I never brought up normalization, you brought it up.

What is wrong with that ?
Yes I did, and you then insisted that normalization is done via fitting, which is not the case.

I wasn't talking about normalization in the first place, I was responding to your comment 'By your logic no curve ever represented "actual" data, simply because histogram is not smooth curve' by pointing out that best fit curves do represent actual data by my logic.
See? Nothing to do with normalization. You brought up normalization, not me. And it's not a plot, it's a fantasy curve that has no connection to data aside from its peak. Once again, a simple question:
As I said earlier, it is perfectly fine illustration. There is absolutely no way you can make it look "better" that is decrease visible difference between white and black.
What you are doing is nitpicking.

[Jesse]

What is wrong with that ?
Yes I did, and you then insisted that normalization is done via fitting, which is not the case. Nope, I never argued anything like that. I wasn't talking about normalization when I discussed fitting, if you thought I was connecting the two that was your own misunderstanding. If you disagree, look for a quote from any of my previous posts where I "insisted that normalization is done via fitting", you won't find one. As I said earlier, plot is is perfectly fine illustration. And you still haven't answered my questions about whether the alternative illustrations I suggested would be equally "fine". There is absolutely no way you can make it look "better" that is decrease difference between white and black. I didn't say you could "decrease difference between white and black" by basing the shape of the curves on actual data, although I did argue that the perfectly even curves mislead people into thinking they are graphing a large data set, when in fact it was actually pretty small in the case of the "black" group. Also, the probability that a randomly selected black participant will have a higher IQ than a randomly selected white participant depends not just on the average of each group but also on the standard deviation which determines how "fat" the curves are, and therefore how much they overlap, so this is another reason that using a totally made-up shape for both curves is misleading.

[barbos]

Nope, I never argued anything like that. I wasn't talking about normalization when I discussed fitting,

Then we return to the fact that YOU brought up fitting, why you did that, I have no Idea.



if you thought I was connecting the two that was your own misunderstanding. If you disagree, look for a quote from any of my previous posts where I "insisted that normalization is done via fitting", you won't find one. And you still haven't answered my questions about whether the alternative illustrations I suggested would be equally "fine". I didn't say you could "decrease difference between white and black" by basing the shape of the curves on actual data, although I did argue that the perfectly even curves mislead people into thinking they are graphing a large data set, when in fact it was actually pretty small in the case of the "black" group. Also, the probability that a randomly selected black participant will have a higher IQ than a randomly selected white participant depends not just on the average of each group but also on the standard deviation which determines how "fat" the curves are, and therefore how much they overlap, so this is another reason that using a totally made-up shape for both curves is misleading.
I am getting tired of "I didn't say that"
What did you say ?
I know what I said, I said - picture is perfectly fine illustration, it was never supposed to be a distribution of data.
And what you do is nitpicking

[barbos]

Nope, I never argued anything like that. I wasn't talking about normalization when I discussed fitting, if you thought I was connecting the two that was your own misunderstanding. If you disagree, look for a quote from any of my previous posts where I "insisted that normalization is done via fitting", you won't find one. And you still haven't answered my questions about whether the alternative illustrations I suggested would be equally "fine". I didn't say you could "decrease difference between white and black" by basing the shape of the curves on actual data, although I did argue that the perfectly even curves mislead people into thinking they are graphing a large data set, when in fact it was actually pretty small in the case of the "black" group. Also, the probability that a randomly selected black participant will have a higher IQ than a randomly selected white participant depends not just on the average of each group but also on the standard deviation which determines how "fat" the curves are, and therefore how much they overlap, so this is another reason that using a totally made-up shape for both curves is misleading.
Statistical error on average for the black group of 200 is 1.1 point, therefore group is large enough.

I was never misled into thinking that there were large statistics, because is clearly fucking illustration, and not fucking data.

[Jesse]

Then we return to the fact that YOU brought up fitting, why you did that, I have no Idea. Already explained this several times: I was responding to your comment 'By your logic no curve ever represented "actual" data, simply because histogram is not smooth curve' by pointing out that best fit curves do represent actual data by my logic. What part of this do you find difficult to understand? I am getting tired of "I didn't say that" And I am tired of you repeating the same misunderstandings over and over even when I have already explained why they are misunderstandings. What did you say ? See above. Once again, the context was:

barbos: That is nice example of nitpicking.
By your logic no curve ever represented "actual" data, simply because histogram is not smooth curve.

Jesse: A best-fit curve is still constructed mathematically using the complete data set.

See, I was just talking in the abstract about how best-fit curves do represent "actual" data, and elsewhere I also said that if they had generated the curves for the white and black groups using best fit methods, then I wouldn't have the same problem with the curves being "made up". Nowhere in that post did I bring up normalization. I know what I said, I said - picture is perfectly fine illustration. Yes, and yet you have refused to address any of my questions about your standards for "perfectly fine" or my arguments about why I think it is misleading.

[barbos]

Yes, and yet you have refused to address any of my questions about your standards for "perfectly fine" or my arguments about why I think it is misleading.
Give me standards for for "addressing" then I will address,
You seems to have a lot questions and absolutely no positive statements :)

[Jesse]

Statistical error on average for the black group of 200 is 1.1 point, therefore group is large enough. Statistical error "on average" would be smaller than, say, the statistical error in the worst 25% or worst 10% or worst 5% of cases. And of course, there's a 25%/10%/5% chance that this particular group would happen to be in the worst 25%/10%/5% of cases if you picked a large number of groups of 198 self-identified black people and gave them IQ tests. I was never misled into thinking that there were large statistics, because is clearly fucking illustration, and not fucking data. Good for you, but it's misleading as long as other reasonably intelligent people might have thought the curves were based on data (James T seems to have thought that, for example).

[Jesse]

Give me standards for for "addressing" then I will address,
You seems to have a lot questions and absolutely no positive statements :) I'm not "giving you standards" (what does that even mean?), I'm asking questions about your standards for what does or does not constitute a "fine illustration." If you had any clear standards, then you would have no trouble judging specific cases.

[barbos]

Statistical error "on average" would be smaller than, say, the statistical error in the worst 25% or worst 10% or worst 5% of cases. And of course, there's a 25%/10%/5% chance that this particular group would happen to be in the worst 25%/10%/5% of cases if you picked a large number of groups of 198 self-identified black people and gave them IQ tests. Good for you, but it's misleading as long as other reasonably intelligent people might have thought the curves were based on data (James T seems to have thought that, for example).
I don't understand a single word of it.

[barbos]

I'm not "giving you standards" (what does that even mean?), I'm asking questions about your standards for what does or does not constitute a "fine illustration." If you had any clear standards, then you would have no trouble judging specific cases.
I told you my standard - "Go and try to make it better"

[Jesse]

I don't understand a single word of it. Well, what did you mean by "statistical error on average"? I would interpret that to mean if you randomly selected a large number of groups of 198 self-identified "black" people, found the average IQ of each group, and compared the average of each group to the national average, then the average 198-person group would deviate from from the national average by 1.1 points. Likewise, if you took a large number of random groups and found the average IQ for each group, then threw away the bottom 75% of groups whose average was closest to the national average, you'd be left with the 25% of groups whose average was furthest from the national average, or what I called the "worst 25% of cases". The average deviation among just these cases might be significantly more than 1.1 points.

[barbos]

Well, what did you mean by "statistical error on average"?

I meant statistical error on average, which is error due to the sample being random set of only 198 scores, I assumed usual 15-16 point SD for distribution.


I would interpret that to mean if you randomly selected a large number of groups of 198 self-identified "black" people, found the average IQ of each group, and compared the average of each group to the national average, then the average 198-person group would deviate from from the national average by 1.1 points. Likewise, if you took a large number of random groups and found the average IQ for each group, then threw away the bottom 75% of groups whose average was closest to the national average, you'd be left with the 25% of groups whose average was furthest from the national average, or what I called the "worst 25% of cases". The average deviation among just these cases might be significantly more than 1.1 points.
It is 1.1 points

[Jesse]

I told you my standard - "Go and try to make it better" That isn't a "standard" for judging whether a given illustration is "fine" or not. A "standard" would be a set of criteria which you use to make such a judgment about any possible case you're presented with.

[barbos]

That isn't a "standard" for judging whether a given illustration is "fine" or not. A "standard" would be a set of criteria which you use to make such a judgment about any possible case you're presented with.
It is my standard, deal with it.
Otherwise provide yours.

[Jesse]

I meant statistical error on average, which is error due to the sample being random set of 198 scores. Yes, that's pretty much what I said, if you pick a large number of random sets of 198 scores, and compare the difference between each set's average IQ and the national average for IQ, the average difference will be 1.1 points (assuming your number is correct, I'd have to review some statistics to check). It is 1.1 points That's the average. But if you take a large number of random sets of 198 scores, then look only at the 25% of these sets whose deviation from the national average is greatest, the average deviation in this group will be higher than 1.1 points. And there's a 25% chance that the group of 198 people whose data was used to make the graph fell into this group.

[barbos]

That's the average. But if you take a large number of random sets of 198 scores, then look only at the 25% of these sets whose deviation from the national average is greatest, the average deviation in this group will be higher than 1.1 points. And there's a 25% chance that the group of 198 people whose data was used to make the graph fell into this group.
OK, Yes that is average, and your point what exactly ?
Why do you repeat obvious facts ?

[Jesse]

It is my standard, deal with it. You're not using the word "standard" correctly, a "standard" for making a judgment is a set of criteria used to make that judgment. That's just what the word means. Otherwise provide yours. My standard is that when presenting statistical data on a graph, you should either actually include all the data points, or if you want to show a smooth curve it should be some sort of best-fit curve.

[barbos]

You're not using the word "standard" correctly, a "standard" for making a judgment is a set of criteria used to make that judgment.

I use it correctly, you just don't like my standard because it is too hard for you.


That's just what the word means. My standard is that when presenting statistical data on a graph, you should either actually include all the data points, or if you want to show a smooth curve it should be some sort of best-fit curve.

Well, then it wouldn't be illustration, so your standard is no good.

You can try your standard anyway, it is not going to help you :)

[Jesse]

OK, Yes that is average, and your point what exactly ?
Why do you repeat obvious facts ? Because you say things which seem to dispute my claims, like "it is 1.1 points". Yes, the average deviation may be 1.1 points (if your calculations are right--but wouldn't you have to make some assumption about the standard deviation of the national IQ curve to calculate this? If so, what assumption did you make?), but the average deviation for the 25% of cases which are furthest from the national average may be significantly larger. If it was, say, 10 points for this subgroup, then that would mean there'd be a 25% chance the actual national average is 10 points off from the average shown on the graph. If they had used a sample with a lot more than 198 people, then because of the law of large numbers there'd be much less difference between the average deviation for all groups of that size and the average deviation for the worst 25% of groups of that size, so we could be more confident that it was a representative sample. That's my point, I'm just disputing your claim that if the average deviation is 1.1 points, then that alone is enough to show that "therefore the group is large enough".

[barbos]

Because you say things which seem to dispute my claims, like "it is 1.1 points". Yes, the average deviation may be 1.1 points (if your calculations are right--but wouldn't you have to make some assumption about the standard deviation of the national IQ curve to calculate this? If so, what assumption did you make?), but the average deviation for the 25% of cases which are furthest from the national average may be significantly larger. If it was, say, 10 points for this subgroup, then that would mean there'd be a 25% chance the actual national average is 10 points off from the average shown on the graph. If they had used a sample with a lot more than 198 people, then because of the law of large numbers there'd be much less difference between the average deviation for all groups of that size and the average deviation for the worst 25% of groups of that size, so we could be more confident that it was a representative sample. That's my point, I'm just disputing your claim that if the average deviation is 1.1 points, then that alone is enough to show that "therefore the group is large enough".
Me ? I said 1.1 first, you replied to it saying it is not good enough.

What the hell was that ?
I know, i know you are going to say "I didn't say that"

[Jesse]

I use it correctly No, you did not--a command is not a standard. Out of curiosity, is English your first language?

[barbos]

No, you did not--a command is not a standard. Out of curiosity, is English your first language?

Yes I did,

[Jesse]

Me ? I said 1.1 first, you replied to it saying it is not good enough. Well, if the average deviation was 1.1 points, but there was a 25% chance or 10% chance or 5% chance the sample actually deviated from the national average by something significantly larger like 10 points, then no, I don't think that would be good enough. Instead of presenting the average deviation, it would be more helpful to follow the more common practice in statistics and give a 95% confidence interval.

[barbos]

Well, if the average deviation was 1.1 points, but there was a 25% chance or 10% chance or 5% chance the sample actually deviated from the national average by something significantly larger like 10 points, then no, I don't think that would be good enough. Instead of presenting the average deviation, it would be more helpful to follow the more common practice in statistics and give a 95% confidence interval.
95% is 2 SD , there is no chance of 10 point deviation, I repeat no chance.

[barbos]

here:

σ 68.26894921371%
2σ 95.44997361036%
3σ 99.73002039367%
4σ 99.99366575163%
5σ 99.99994266969%
6σ 99.99999980268%
7σ 99.99999999974%

[Jesse]

95% is 2 SD , there is no chance of 10 point deviation, I repeat no chance. I was just pulling a number out of a hat there. Checking my statistics textbook, I see that 95% confidence means a z-value of 1.96, where the difference from the mean is equal to z times the variance \sigma of the normal curve. So what is the variance \sigma for a normal curve representing the average IQs of randomly selected groups of 198 people?

edit: Ah, I'd forgotten that the variance of the probability distribution function is just the average deviation from the mean, so if you're correct that the average deviation is 1.1, that would also be the variance. So yes, now I agree that 198 people gives a good 95% confidence interval, again assuming your 1.1 figure is right, and assuming the people really were selected in something close to a random manner.

edit 2: Well, variance squared = \sigma actually, but either way \sigma is the average deviation.

[barbos]

I was just pulling a number out of a hat there. Checking my statistics textbook, I see that 95% confidence means a z-value of 1.96,

As I said 95% is 2 SD.

\sigma of the normal curve. So what is the variance \sigma for a normal curve representing the average IQs of randomly selected groups of 198 people?
For the tenth time it is 1.1 points !

[Jesse]

For the tenth time it is 1.1 points ! Yes, if you look at the edit to my last post, it took me a little while to realize that the symbol \sigma used in my textbook chart and appearing in the equation for the normal distribution is just equal to the average deviation from the mean.

edit: OK, I also just checked your 1.1 figure and I agree with that as well--if anyone else is curious about the calculation, in my textbook's section on "sampling distributions related to the normal distribution", it says that if you take a random sample of size n from a normal distribution with mean \mu and variance \sigma^2, and the average value of your random sample is Y, then Y will have a normal distribution with \mu_Y = \mu and \sigma_Y^2 = \sigma^2 / n. So, for a sample of 198, if the average deviation for individual IQs is designed to be 15 as stated here (http://iq-test.learninginfo.org/iq04.htm), then \sigma_Y = \sqrt{ 15^2 / 198} = 1.1

[barbos]

Yes, if you look at the edit to my last post, it took me a little while to realize that the symbol \sigma used in my textbook chart and appearing in the equation for the normal distribution is just equal to the average deviation from the mean.
You see, there is nothing wrong with illustration :) it is perfectly fine, and people who made it are not idiots.

BTW for someone who look into textbook to get number of sigmas for 95% CL you argue too much about statistics.

[Jesse]

You see, there is nothing wrong with illustration :) it is perfectly fine, and people who did it are not idiots. Well, my main argument was about the curves not being based on data, not about the sample size being too small, which is what this discussion of sigmas and confidence intervals was about. I agree now the sample size is OK, but that doesn't change my other argument. BTW for someone who look into textbook to get number of sigmas for 95% CL you argue too much about statistics. I don't make any claims about knowing stuff off the top of my head, and I made it clear that I hadn't actually calculated the deviation of the worst 25% of cases and so forth, it was just my reason for saying the 1.1 average deviation figure alone was not enough to convince me that a random sample of 198 could give us high confidence that the sample average was close to the national average, but now that I have figured out the 95% confidence interval I agree 198 is a good number (assuming the sample was really random, which I can't be sure of).

[barbos]

Well, my main argument was about the curves not being based on data, not about the sample size being too small, which is what this discussion of sigmas and confidence intervals was about. I agree now the sample size is OK, but that doesn't change my other argument.

Well I say you are wrong in your "main" argument as well. You can play with the shapes as long as you want but you are not going to make that picture look any better (or worse). In reality of course both shapes are close to gauss distributions with sigma around usual 15-16 points.




I don't make any claims about knowing stuff off the top of my head, and I made it clear that I hadn't actually calculated the deviation of the worst 25% of cases and so forth, it was just my reason for saying the 1.1 average deviation figure alone was not enough to convince me that a random sample of 198 could give us high confidence that the sample average was close to the national average, but now that I have figured out the 95% confidence interval I agree 198 is a good number (assuming the sample was really random, which I can't be sure of).
I am sorry but you have to know 95% CL as well as sigma of average.

[Febble]

That plot:

The problem, guys, is that IT WAS NOT REFERENCED. It appeared to come from Wiki, where there was a reference given, but the reference given did not itself reference the data, so I hit a dead end. Youngalexander then found a source that DID have a reference, and it led to a perfectly decent study of data that in turn was referenced to the 1981 US WAIS normalisation sample.

So we now KNOW the source of the data that generated the plot. HOWEVER, the plot itself is not OF the data - it is an idealized plot, showing the INFERENCE made from the data, given the means and SDs (probably, I haven't peered at the plot long enough to check the SDs of the gaussians) from the study. The study did NOT report whether the two distributes were gaussian, and there is NO reason to suppose they would be, although no reason to suppose they wouldn't be. In other words, the correct way to report the information in the plot would be to say:

In the 1981 WAIS normalisation study, "black" participants scored a mean of - with an SD of - and "white" participants scored a mean of - with an SD of -.

No plot is necessary, and is misleading because the plotted distributions are an INFERENCE from that study, and you can't make a comprehensible inferential statement about a population without giving the population from which the sample was drawn.

OK, but now we KNOW what the sample was, and we can, if people want to, talk about WHY it gave the results it did, for which purpose people should READ the Flynn paper.

And the point of the "Flynn effect", which is an astounding effect, is that it implies that there is a very large NON-genetic factor that drives IQ scores up over over time. And when we know that there is a very large NON-genetic factor that drives IQ scores up over time the FIRST question that should strike anyone looking at differences in IQ scores between two populations, one of which is considerably less advantaged than the other, is that the SAME non-genetic factor that drives up IQ scores LONGITUDINALLY (with increased advantage) may also drive them up LATERALLY (with increased advantage).

So READ the FLYNN paper, guys (barbos, I'm looking at you) if you want to talk about the phenomenon that the unreferenced plot was supposed to be "illustrating", namely mean IQ differences in the black and white samples for the WAIS normalisation in the US in 1981.

[Jesse]

Well I say you are wrong in your "main" argument as well. You can play with the shapes as long as you want but you are not going to make that picture look any better. In reality of course both shapes are close to gauss distributions with sigma around usual 15-16 points. That's likely to be true, but it's still just a speculation, not based on the data. After all, just because sigma is designed to be 15 for the set of all people's IQ scores, it could be different for some specific subset of people whose mean IQ is different than the national mean (say, Mensa members). I am sorry but you have to know 95% CL as well as sigma of average. Why do I "have" to? I took statistics about 8 years ago and I never had much need for anything beyond basic probability theory since then, not even in any of my subsequent physics classes (but I was concentrating on theory rather than analyzing experimental data, obviously there'd be more use for statistics there). If I've made any definite claims about statistics on this thread, it's only about stuff that I've actually looked up to make sure I'm right about.

[barbos]

That's likely to be true, but it's still just a speculation, not based on the data. After all, just because sigma is designed to be 15 for the set of all people's IQ scores, it could be different for some specific subset of people whose mean IQ is different than the national mean (say, Mensa members).

If blacks had sigma=30 that would be noticed by now.
significant deviation from the gauss shape would be "Huston, we have a problem"

BTW About Mensa, You can not select group of people based on their IQ and then look at their IQ, it is 100% biased and really pointless.



Why do I "have" to?

Because you argue about statistics and sigma of average is the first thing one has to know about it.

[Febble]

If blacks had sigma=30 that would be noticed by now.
significant deviation from the gauss shape would be "Huston, we have a problem"

If you want to know the sigma for black participants in the 1981 WAIS standardisation sample, check the study.

But for Chrissakes stop making generalised statements like "if blacks had sigma = 30". "Blacks" don't "have" a sigma. A population has a sigma, and "blacks" does not describe the population from which the sigma for black participants in the 1981 WAIS study was derived.

"Blacks" is a meaningless term unless you say what population they were drawn from and who they were being compared to.

And if you want to discuss the data from the 1981 US WAIS normalisation sample READ THE FLYNN PAPER FIRST.

[youngalexander]

Never seen such blather over an illustrative plot. Since you are so keen, you might check out the data in Levin's Why Race Matters pg 34-37 Race Differences in Intelligence

Just hit this (http://www.amazon.com/gp/reader/0965638359/ref=sib_dp_pt/002-4213104-0777635#reader-link) and search for Table 3
then choose pg 35 or 36.

You can dig the references out for yourself.

[Febble]

Never seen such blather over an illustrative plot. Since you are so keen, you might check out the data in Levin's Why Race Matters pg 34-37 Race Differences in Intelligence

Just hit this (http://www.amazon.com/gp/reader/0965638359/ref=sib_dp_pt/002-4213104-0777635#reader-link) and search for Table 3
then choose pg 35 or 36.

You can dig the references out for yourself.

Which again references a US population, which the plot there was a "blather" over DIDN'T.

Thanks for providing the references BTW. It was the LACK of those that made the plot misleading. An "illustrative plot" is fine as long as it is clear what it is illustrating. Perhaps you'd like to edit the Wiki entry.

[Febble]

And perhaps it is time to point out, given the title of the OP, that the reason I have been at such pains to identify what those plots were supposed to "illustrate" is that low IQ has been equated with a "genetic disorder", and skin colour is genetic.

So it is of vital importance to know why, when considering the correlation of IQ with genetic factors, whether any observed correlation between IQ and a particular genetic marker (skin colour) has anything to do with the genetic component of IQ scores. We can't do that by comparing IQ score between radically different countries (because IQ scores are normed for a specific population) we can only do it within a country, and the US is a country with a sizeable black population. BUT it is also a country in which skin colour correlates with factors KNOWN to correlate with IQ. Moreover, IQ raw scores are KNOWN to rise steadily and rapidly over time, suggesting a strong environmental factor associated with increasing standard of living. The mean IQ raw scores of black participants in the 1981 WAIS sample would have been equivalent to the mean raw scores of a WHITE sample a generation or so earlier.

So to equate "low IQ" with a genetic disorder is tantamount to alleging that our immediate forbears were genetically disordered. Yet it is their genes that we carrry.

In other words "low IQ" is NOT a genetic disorder, heritable though it may be. If we want to know why some substantial groups of people have "low IQ", genetics is unlikely to be the place to look. A divided society might be a more fruitful avenue to explore.

Which is not to say there are not preventable genetic/chromosomal conditions that cause mental retardation. There are. But dealing with those is called medical research, not eugenics.

[youngalexander]

Perhaps you'd like to edit the Wiki entry.
Touche!:)

[OripahsTrebor]

Febble, what do you think of Richard Lynn? I think his scholarship is irrefragable.

[JamesBannon]

Anyone who writes stuff like this:

"What is called for here is not genocide, the killing off of the populations of incompetent cultures.[15] (http://www.splcenter.org/intel/intelreport/article.jsp?aid=361) But we do need to think realistically in terms of "phasing out" of such peoples. If the world is to evolve more better humans, then obviously someone has to make way for them. ... To think otherwise is mere sentimentality. Elsewhere Lynn makes clear which "incompetent cultures" need "phasing out": "Who can doubt that the Caucasoids and the Mongoloids are the only two races that have made any significant contributions to civilization?" (cited in New Republic, 10/31/94)"

is immediately suspect. Just another racist irrespective of his credentials.

[James T]

Attacking Lynn (an easy target) is not the same as attacking the facts, which tend to remain despite which way the wind of political correctness happens to be blowing today.

[premjan]

"What is called for here is not genocide, the killing off of the populations of incompetent cultures.[15] But we do need to think realistically in terms of "phasing out" of such peoples. If the world is to evolve more better humans, then obviously someone has to make way for them. ... To think otherwise is mere sentimentality. Elsewhere Lynn makes clear which "incompetent cultures" need "phasing out": "Who can doubt that the Caucasoids and the Mongoloids are the only two races that have made any significant contributions to civilization?" (cited in New Republic, 10/31/94)"
Well, most of the damage to the world has also been caused by caucasian and mongolian people - from Genghis Khan to global warming. I think a suitable terror campaign could be reasonably launched against any attempt to phase out certain groups of people. In fact it would be poetic justice as terror and domination has been a principal tool of caucasians in the last few centuries.

[Febble]

Attacking Lynn (an easy target) is not the same as attacking the facts, which tend to remain despite which way the wind of political correctness happens to be blowing today.

Of the problems facing humankind, people who score low on IQ tests scarcely register on my radar as a problem. Greed strikes me the biggest threat to our species, and bigotry as one of the biggest threat to our welfare. I know of no association between IQ scores and either greed or bigotry.

And in my experience people who talk about "the facts" rarely know what a "fact" is. It is not a fact that black people are less intelligent than white people. It is not a fact that IQ scores measure current intelligence. It is not a fact that IQ scores measure potential intelligence. It is a fact that mean IQ raw scores rise over time within the same genetic gene pool. This last observation calls into question ANY inference made from differing mean IQ scores of subgroups within the same generation of a population, especially when those subgroups differ from each other on the same indices that differ between generations of the same group.

[JamesBannon]

Attacking Lynn (an easy target) is not the same as attacking the facts, which tend to remain despite which way the wind of political correctness happens to be blowing today.
That I could care less about genetic differences in IQ! So what if there are. So what if my white skin makes me better at intellectual pursuits on average that those with black skin. Am I a "better" human for that reason? Bah, don't get me started! Those who wish to perpetuate and emphasise the differences are not part of the solution, they're part of the problem!

[OripahsTrebor]

Of the problems facing humankind, people who score low on IQ tests scarcely register on my radar as a problem. Greed strikes me the biggest threat to our species, and bigotry as one of the biggest threat to our welfare. I know of no association between IQ scores and either greed or bigotry.

And in my experience people who talk about "the facts" rarely know what a "fact" is. It is not a fact that black people are less intelligent than white people. It is not a fact that IQ scores measure current intelligence. It is not a fact that IQ scores measure potential intelligence. It is a fact that mean IQ raw scores rise over time within the same genetic gene pool. This last observation calls into question ANY inference made from differing mean IQ scores of subgroups within the same generation of a population, especially when those subgroups differ from each other on the same indices that differ between generations of the same group.

Richard Lynn sez the rising IQ scores are due to improved nutrition.

Am I a "better" human for that reason? Bah, don't get me started! Those who wish to perpetuate and emphasise the differences are not part of the solution, they're part of the problem!

No, you're a better human not due to skin color, but due to your intelligence.