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Wednesday, January 22, 2014

Mailvox: on the distribution of atheist intelligence

Kaneadvice fails to recognize how sampling bias will tend to skew the statistical results:
Every commenter who knows how to use the GSS has been able to disprove the claim of atheist over-representation among the low-IQ population.... Why did Vox fail to conduct an accurate analysis? Was it primarily a cognitive or emotional failing?

Either way, I suspect Vox is smart enough to know he is wrong. Even if his emotions are driving him to go through rationalization gymnastics to justify his faith in theist superiority, the part of his brain that is still thinking logically knows that he has been proven wrong.
I am not wrong. The claim of atheist over-representation among the low-IQ population has not been disproved at all. As it happens, there is absolutely no contradiction between the chart I posted and the charts posted by those who have failed to understand it or recreate it. I charted apples, they charted oranges. It's actually rather funny that they have had such a difficult time recreating my charts, considering that not only the data, but the second chart I posted, was literally right in front of their eyes. But let's see if any of you can spot the obvious source of the problem with their critique of my intelligence distribution charts.

What we have here on the left is a normal intelligence distribution chart. I didn't create it, I didn't cherry-pick it, and it is literally the first chart to appear when searching "intelligence distribution chart on Google. It's a standard bell curve.

Now let's look at the chart on the right, which was produced by indpndnt, who couldn't recreate the results of my charts despite putting considerable effort into it. What is the obvious difference between these two charts? They both peak at 100, but both lines on indpndnt's chart clearly overweight the right side at the expense of the left side, especially in the case of the blue God=1 line, which represents the "I don't believe God exists" answer. Why does it do so? The answer is very simple. I'll give you one guess.

Can't figure it out? The answer is that the GSS results are heavily biased towards high intelligence responders. Of the 9,920.5 responses tabulated with the default weighting, 420.8 were in the highest category and only 169.3 were in the lowest. This is not consistent with what we know of intelligence distribution in the general populace. Neither indpndnt nor Daniel Haas noticed this high-IQ bias nor took it into account, and so their results are naturally skewed by it. The consequence is that the legitimately higher percentage of atheists in the highest-IQ category creates an exaggerated effect when the comparison is made to the total number of respondents rather than as a percentage of distinct IQ categories. This is not to charge them with being intellectually dishonest, however, as it is apparent that they simply failed to observe a problem with the dataset. They are not superintelligences, after all.

Even if we simply chart all 9,920.5 responses without regard for religious belief and we exclude the 65- category because there is no corresponding 135+ category, the high IQ bias of the GSS bell curve is apparent. At (114-86) it is +12 percent, at (121-79) it is +40 percent, and at (128-72) it is +28 percent. There are 300 excess 121+ respondents, 13 more than there are total atheist respondents.

Given this statistically significant sampling bias towards respondents of higher intelligence, it should be obvious that the only legitimate way to calculate the intelligent distributions is to utilize the percentage of respondents within each separate category. That is exactly what I did: 8.5 percent of 169 respondents is manifestly a higher percentage than 6.4 percent of 420.8 respondents. All the critics have managed to show here is that 27 is more than 14.4, which is true, but also happens to be irrelevant. The claim stands.

As for the difficulty they had recreating my charts, I will simply show a screen capture of the chart produced by the very GSS site at Berkeley from which I took the data. This is the original chart with the zero column removed for the sake of clarity.


And below is the exact same chart with the non-atheist categories grayed-out and my Calc chart superimposed on top of it. Look familiar? The only difference is one of scale; my X-axis maximum was 7 percent compared to 100 percent for the GSS chart. Given the observed nature of the GSS bias towards higher IQ respondents, the use of percentages rather than numerical totals is more likely to be a statistically credible method than the one utilized by the critics.

Labels: ,

30 Comments:

Anonymous Anonymous January 22, 2014 9:23 AM  

"the part of his brain that is still thinking logically knows that he has been proven wrong..."
And that came with data, "work", citations, etc. supporting the point right, RIGHT?

Doesn't matter, the "demands" for "proof", when clearly met, are simply discounted. The
disproven antithesis will merely be installed elsewhere, only in ALL CAPS.
The science is settled. (fill in the blank) is a big poopy pants!

Anonymous Aeoli Pera January 22, 2014 9:24 AM  

This is beginning to be silly. Maybe you should introduce a rule requiring basic knowledge of statistics in order to debate IQ statistics. Something like "Calculate the standard deviation of these three numbers: 3, 5, 8. Show your work."

Anonymous Anonymous January 22, 2014 9:24 AM  

Crap, above CaptDMO

Anonymous Rantor January 22, 2014 9:24 AM  

I love a good beatdown in the morning...

Anonymous Peter Garstig January 22, 2014 9:37 AM  

I believe that statistics (together with probability) is harder to fully grasp than calculus and other more complicating areas in mathematics. It's very deceiving as it appears easy. That's why it's mostly used by charlatans.

Anonymous Aeoli Pera January 22, 2014 9:47 AM  

Ya know, scratch that. "Define atheism, possibly with the help of a dictionary" might be a more...illustrative test.

Anonymous Stilicho January 22, 2014 9:50 AM  

OT, but of interest to many of the Ilk is this excellent essay on Jefferson.

Blogger swiftfoxmark2 January 22, 2014 9:57 AM  

Statistics are the easiest way to deceive the public, especially polling data. Most of the time, the sample size is too small and not random enough to properly represent the general population.

So whether it is IQ distribution or media polling, understand that they did not do a good job collecting data.

Anonymous Rantor January 22, 2014 10:02 AM  

@PG, as Barbie said, "math is hard." While my senior level statistics class was three decades ago, I can still apply knowledge and facts to reading a lot of the crap thrown out there. While people use all kinds fo tricks to make data say what they want, there are many that do their best to make data reflect reality. Vox, Steve Sailer, and John Williams are among those trying to pry a little more truth out of the numbers. For that, I congratulate them.

Anonymous The other skeptic January 22, 2014 10:37 AM  

Obamacare is like the Soviet Union

Anonymous Max January 22, 2014 11:30 AM  

Agnostics rule, atheists drool.

Blogger wrf3 January 22, 2014 11:37 AM  

Aeoli Pera wrote: "Define atheism, possibly with the help of a dictionary" might be a more...illustrative test.

Rantor, quoting Barbie, wrote: "math is hard."

Another interesting thing to try is to guage people's reaction to the statement that the sum of the infinite series 1+2+3+4+5+... is -(1/12). That's been causing a bit of buzz on the internets this week. Lubos Motls, a conservative atheist physicist had some choice words to say about P. Z. Myers and Phryngula over this, including "P.Z. "Pharyngula" Myers, a self-described randomly ejaculating biological godless liberal (can't this disorder be cured?)..."

Vox might like this too, since the result that 1+2+3+... = -(1/12) is used by String Theory; something he views with skepticism, but Lubos is a big fan of.

Blogger Richard Sharpe January 22, 2014 11:39 AM  

Hollywood awards Woody Allen their Rape a Child award.

Roman Polanski got a Rape a Teenager award.

Anonymous JI January 22, 2014 11:48 AM  

The question Kaneadvice seeks to answer is, given that one is intelligent, what is the likelihood that one chooses to be an atheist? Well, the data say this likelihood is less than the likelihood that, given one is intelligent, one chooses to be a theist.

Kaneadvice is answering a different question. That is, given that one is an atheist, what is the likelihood that one is also intelligent? Now, in that case, the data show that this is larger than the likelihood that, given one is a theist, one is also intelligent. But it's not really an interesting question. An example shows why.

An interesting question is, given that one is fat, what is the likelihood that one gets Type II diabetes? An uninteresting question is, given that one has Type II diabetes, what is the likelihood that one is fat? The implied direction of causality is backwards in the latter question, suggesting that one becomes fat because one has Type II diabetes.

Anonymous lozozlo January 22, 2014 12:04 PM  

Related but OT

A common atheist myth is how horrible the Christianity-dominated "dark ages" were, filled with 'dumb superstitious Christians" but of course the truth is, as usual, *way* different than the indoctrination from modern atheist schooling.

Even if atheists were smarter, their education system is filled with lies.

Anonymous Anonymous January 22, 2014 12:57 PM  

I believe it was Mark Twain who said something like "There are lies, damn lies and statistics."

Blogger James Dixon January 22, 2014 1:41 PM  

> Maybe you should introduce a rule requiring basic knowledge of statistics in order to debate IQ statistics.

That would leave a very small pool of debaters. Very few people actually understand statistics. And even with a college level course on the matter, I'm not really one of them.

Anonymous Indpndnt January 22, 2014 2:05 PM  

Thanks for the update. It was bugging the crap out of me why I wasn't getting the same answers.

This is not to charge them with being intellectually dishonest, however, as it is apparent that they simply failed to observe a problem with the dataset. They are not superintelligences, after all

I will be the first to admit this! My question wasn't posted in the vein of "zomg VD is teh liar", but rather looking for this answer that I missed. My bad if I gave the impression that I was trying to knock anything down, I just wanted to bring myself up.

Anyway, thanks for the clarification.

Anonymous WaterBoy January 22, 2014 2:28 PM  

Is this becoming the new West Coast Invasion horse?

Anonymous Josh January 22, 2014 2:36 PM  

No, we'd need roughly a hundred more posts

Anonymous VD January 22, 2014 2:39 PM  

Thanks for the update. It was bugging the crap out of me why I wasn't getting the same answers.

NP. I was impressed with your detailed approach. I didn't get a negative impression from you at all, but there were one or two others who apparently didn't like the implications, which is silly. The thing is, if the distribution had been unbiased, your approach would have been more direct, but then we would have ended up with much more similar results.

One thing that might be worth keeping in mind when you're looking at statistical analysis is to look at the data set from a general perspective before getting into the number-crunching. I've seen no shortage of econometric models that are mathematically beyond me, but are based on obvious absurdities. It's usually worth taking a quick look at the forest before you get caught up in the trees.

Anonymous indpndnt January 22, 2014 3:05 PM  

I was impressed with your detailed approach.

Thanks. You give me too much credit with "detailed", though. It's about 15 minutes in Python with Pandas and a CSV file to do what I did.

The thing is, if the distribution had been unbiased, your approach would have been more direct, but then we would have ended up with much more similar results.

Yeah. What sent me down the path I took was your first plot on that post, which looked to me like you were approximating/smoothing a PDF of IQ (P(IQ | GOD = 1), etc.) from the PMF of WORDSUM. I went after those distributions, instead of the reverse that you looked at.

One thing that might be worth keeping in mind when you're looking at statistical analysis is to look at the data set from a general perspective before getting into the number-crunching.

My stats work has always been more focused on analyzing well-designed computer experiments, which eliminates the kind of bias that needs those steps back. Old habits/etc.

Anonymous Aeoli January 22, 2014 4:29 PM  

I blame the computers.

Anonymous zen0 January 22, 2014 7:43 PM  

I blame the computers.

A poor workman blames his tools.
Conversly, a poor tool blames his workman.

There is enough blame to go around for everyone.

Blogger tz January 22, 2014 9:10 PM  

As we find in grocery checkouts, don't look to wait in line for your eye-queue to improve.

A large HQ (hubris quotient) will override an even higher IQ.

"I just know I'm right" tends to prevent even retarded reason from kicking in.

Blogger Daniel Haas January 22, 2014 10:23 PM  

"They are not superintelligences, after all."

Dude, I'm hurt. I can assure you I am well off the right side of your inaccurate chart, posted in your original article. In fact, I'm off the right hand edge of the entire jpg that your chart is sitting in.

Not that it matters, I don't care if I'm 'right', I care if I'm correct. And so should you.

Why you think that the raw WORDSUM data should form a perfect Gaussian distribution is beyond me. It doesn't. No one has ever claimed that it does. The fact that it doesn't is not any indication of a biased sample set. But feel free to clear this up with the GSS team.

I'll copy/paste form the other thread as is appears to be more relevant here now:

There are two questions we can answer from the GOD/WORDSUM table:

1) Given a particular wordsum score, what is the probability that a respondent with that score is theist / atheist (column-wise percentage)

OR

2) Given a group of atheists (or theists), what is the likelihood that a respondent in that group is above or below average intelligence (or more completely, what is the probability distribution for all levels of intelligence) (row-wise N)

In your original post, you make the statements that “… the Low Church atheists actually outnumber the High Church atheists” And “most atheists have sub-100 IQs”. These are questions of the probability distributions of (2) above.

You then justify these claims with your chart, which is the answer to question (1) above. You cannot use one to justify the other. They are completely different metrics.

I suggest that you realised this and changed the proposition in your follow-up post to “atheist *over-representation* among the low-IQ population has not been disproved”. This was not your original proposition, as it has nothing to do with the absolute number of high IQ atheists.

So to be clear, do you still believe that “most atheists have sub-100 IQs”?

The problem with the charts has nothing to do with skew – just a misunderstanding of what the data represents.

Daniel.

Anonymous VD January 23, 2014 3:07 AM  

Why you think that the raw WORDSUM data should form a perfect Gaussian distribution is beyond me. It doesn't. No one has ever claimed that it does. The fact that it doesn't is not any indication of a biased sample set. But feel free to clear this up with the GSS team.

I don't think it should. But you can't seem to get your head around the fact that because it doesn't, your method won't work. Indpndnt understands this. Why don't you?

I suggest that you realised this and changed the proposition in your follow-up post to “atheist *over-representation* among the low-IQ population has not been disproved”.

I didn't change the proposition. You clearly didn't understand that it was an answer to the challenge posed.

So to be clear, do you still believe that “most atheists have sub-100 IQs”?

Of course. The math indicates they have to, in order for atheists to have the 105 IQ average that has been reported. If you are as smart as you claim to be, this should be entirely obvious. For every 135 IQ atheist, there must be either one 70 IQ atheist or two 90 IQ atheists to compensate for him.

Anonymous 204 January 23, 2014 4:25 AM  

Fascinating stuff!

But shouldn't that be 'either one 75 IQ atheist'?

Anonymous VD January 23, 2014 6:32 AM  

But shouldn't that be 'either one 75 IQ atheist'?

Ah, yes. Yes, it should.

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