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States Ranked by Religiousness


02012010, 07:10 PM  #2 
Banned

That people who are impoverished, targets of crime (including murder), and are unhappy with their personal life and marriages often turn to religion for solace in their times of need?
And that religion provides for the emotional, moral and personal support they need when they are down and out? That people with lower IQ more often get worse jobs that pay less, live in communities targeted more for crime, and have the hardest time making marriages work due to the adversities of all of the above? Not sure where you are going here... 
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02012010, 08:53 PM  #4 
Captain

I think he's just trying to show the correlation between religion and different aspects (IQ, crime, etc).
I agree with all of your points. Actually I may go ahead and run up SAS and see the correlation between all of these. I'm interested in the r value myself. Last edited by Zell; 02012010 at 10:07 PM. 
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02072010, 12:09 AM  #6 
Captain

My analysis:
So, out of my curiosity, I wanted to find out if being religious has a correlation with IQ. I say that it does not. Time and time again people view data, look at the possible trend, and then assume that it's completely true. Some parts of this data are stupidly subjective; for example, one person's "contentment" ranking is not the same as what someone else would rate it as. It's a stupid measure, but I digress. I did not check any of the data to see if it were accurate or how it was gathered, as it takes too much time and I don't feel like spending that much time trying to figure out how it was collected (even though I really should). Therefore, for lack of better data at hand, let us make a very, very loose assumption that all of the data are correct. Let us start off with the big one: IQ vs. religiousness. Here is the oneway ANOVA of the data: Notice that the SSE (Sum of Squares error) takes up a HUGE majority of the total; it is over 3 times that of the SSM (Sum of Squares Model). We can calculate R^2 from this, but it is given to us anyway. Notice that R^2 = .2308. This says that only 23.08% of the data are described by a least squares regression line. That is very little data; it does not describe it very well in any way. We can safely say that IQ is not correlated with being religious. Notice that the pvalue is 0.0002; it is statistically significant from this data that religiousness affects IQ (H0: mean=0 vs. Ha: mean does not equal 0); we can easily reject the null at an alpha of both 0.01 and 0.05; however, due to the fact that only 23.08% of the data are described by a trend line, it is difficult to accept that answer and a such we cannot say that IQ is not very affected by being religious. Remember, R^2 doesn't care what is x or y; I can swap religiousness and IQ on the axes and get the same R^2 value. Let's look at this one in some more detail. Here is the residual plot of IQ vs. religiousness: Poor. Look at the obvious linear relationship on the residuals plot. It is not evenly distributed in any way about the residuals=0 line; as a result, we cannot use a linear line to measure this. Let's look at the plot to get some more info: Can you make a good approximation for any of that data with a trend line? Obviously not; the data are extremely random. There is virtually no relationship between IQ and being religious. What about political affiliation? Is that affected by being religious, according to the data? That F is huge. 62.38 is phenomenally large. We get a pvalue of way, way less than 0.001. Note that in these oneway ANOVAs with one degree of freedom due to the single independent variable, the p value from t is exactly equal to the t value from the ANOVA F test. F of 62.38 is hugely statistically significant at 0.05, 0.01, and even 0.001, and with that R^2 value describing 55.61% of the data, we can pretty safely reject H0 and say that being religious tends to correlate with your political affiliation. In this case, it is conservative. And what about theft? Only 16.96% of the data are described, but the pvalue is 0.0017. It's statistically significant at 0.05 and 0.01, but the data are practically randomly scattered and this isn't a good model. So no, your religiousness and amount of theft that you do is uncorrelated. I will not go into detail with the others, as it will take too much time to perform the contrast analyses. So, instead, let's consider what happens if we put all of these variables together such that, mathematically, have an 8th dimension linear equation where we measure how religious you are vs. all those other factors. Note that R^2 is 0.8099, and the Ftest produces a value less than 0.0001. Let's look at the partial linear equations: IQ is 0.5730, divorce is 0.5649, and the rest are all statistically significant at at least 0.05. The partials of IQ and divorce are incredibly poor indicators; so, they do not have much to do with being religious at all; this definitely follows with what we have seen thus far with IQ, and the divorce rate can be explained through its own analysis that I will not get into for reasons I have stated above. This states only if those factors influence your religiousness. Now let's take a major factor, say, theft, and see if all of the factors affect it: Here's a very interesting case of Simpson's Paradox! All of the variables themselves alone do not influence it very much, but the factors combined do! The R^2 is .4451, which is decent for describing it but not excellent. Now, let's see how much theft is affected if we remove religiousness, thus creating a 7thdimensional linear equation (y=x1 + bx2 + bx3 + ... + bx6 + e, e > N(0, sigma)). R^2 = 0.4553, and the rest of the values are hardly affected. It, in fact, made it more accurate without religiousness being there. What does this say? Relgiousness has little to do with theft rates. Note how R^2 went up! Let's check out IQ. A very good R^2 of 0.7913, and good pvalues for the most part. That is, except religion and a few others. Let's take religion away: Well now, the R^2 value is now 0.7952. A very slight increase, and a very slight change in the other pvalues, too. That's hardly a difference at all. Interesting, is it not? So, in conclusion, don't look at graphs that show pretty colors and assume there is correlation. People skew data all the time; you should ask yourself how biased the data are each time you see something. This entire graph proves itself wrong. It just puts on a pretty face to make it seem like there is a correlation when there really is not. Good game. Statistics 1, biased morons 0. Last edited by Zell; 02072010 at 03:35 PM. 
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02072010, 08:54 AM  #7 
Colonel

You certainly have some time on your hands. It appears the author may have used Excel to build the table and applied some simple conditional formatting to colorize the cells.
Based on your analysis does it not appear the those with higher IQ are more likely not to be religious? Even with the small data set the graph you put together does display that those in the upper IQ trend center left (less religious), those with lower IQ trend center/right (more religious). 

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02072010, 03:38 PM  #9  
Captain

Quote:


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02082010, 04:16 AM  #12 
there's something different about him



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02082010, 08:54 AM  #13 
Colonel

Based on your plot, if we only include only those with highest IQ and those with lowest IQ it definitely does show that those states with higher IQ tend to be center/left (less religious) while those with lowest IQ tend to be center/right (more religious)


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02082010, 09:02 PM  #14  
Captain

Quote:
Let's call the highest IQ 104 and lowest 9497 (there is only one data point for 94, and 7 for the rest). I don't know what states those are from just the plot you produced alone, so I'll just choose what is the highest and lowest. Well...I guess I could figure them out by matching the numbers with the data set, but that'd be incredibly tedious Looks pretty similar with the trend line; there is a huge gap of data. As one who does statistics, I'd look at that and say, "Well, obviously data are missing here and we aren't getting the full picture. Either they didn't take enough samples, or someone is leaving out data on purpose." Then I'd have to figure out if any of those are outliers and stuff and try to explain them and stuff; it'd be a big ol' mess. Let's check the ANOVA (Analysis of Variance): 24.17% of the data are described by that trend line, and the data are now no longer statistically significant. It fails at the generally accepted pvalue of 0.05. So no, even if one were to bias the data and pick and choose what to show, it isn't statistically significant nor is it described by a trend line very well. Picking a choosing data to show is a high form of bias; in order to get the full picture, all data must be shown and no data in the middle should be lost. That is why I said above that I was going to choose what is the highest and lowest IQ. What is the highest and lowest? Are we going off of subjective intuition as to what we consider high, or are we going off of what is statistically significant as considered high or low based upon the mean IQ of all states? As you can see, it can become very fuzzy and really changes how data are produced big time. Sometimes data are lost and can be interpolated through the trend line; a good example would be all the divorce stuff. I can tell SAS to go ahead and fill in the missing data from divorce rates through interpolation if I wanted to, but I'd have to record that that's how I got it. If a few data points are lost, then it's not too big of a deal. But if entire sections are lost, then it's a very big deal and introduces a tremendous amount of bias. This is really good SAS programming practice It's always good to review statistical concepts and such using realworld examples. Last edited by Zell; 02082010 at 09:09 PM. 

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02202010, 05:17 PM  #16 
I like cars

Someone failed to read the thread.
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05152010, 10:42 PM  #20 
¡Barça!
Drives: Rainbow Sandals Join Date: May 2008
Location: Ohio

hmmm interesting... I will be moving to a more religious, smarter, less murderous, more theft, less generous, more conservative and healthier and happier state This was a good read, thanks.
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05182010, 02:19 PM  #21 
Major

My conclusion: The people who say religion is necessary for people to be good, to help families stick together, to help form a strong, healthy, peaceful society etc. are not only wrong, but might even have it backwards.
Biggest surprise: That Utah wasn't higher on the religiousness list. Mormons, for all their ridiculous beliefs, seem to disproportionaltely practice the values they preach, and are the only major religion disproportionately underrepresented in the prison population (with the nonreligion of atheism being way, WAY underrepresented) 
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05182010, 02:48 PM  #22  
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Quote:
(That's a joke, before anyone gets offended) I'm actually a little bit surprised IN isn't higher on the list. I think with some of these places with larger urban populations the numbers are probably very different depending on the area you're looking at. I would expect that rural IN is at the extreme end of the scale, and the numbers are moderated to a degree by the cities, with reasonably large higher learning institutions. It's also interesting to note that the crime numbers are very inverse to IQ. It's not a surprise, but the numbers confirm it very well. 


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