How useful is a statistical correlation?

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AlanM
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How useful is a statistical correlation?

Post by AlanM »

I just ran across this image and just HAD to share it.

Back in pre-history, when I was in high school, I read that someone had found a very high positive correlation between ice cream sales by street vendors in New York City and the daily death rate in Calcutta, India.
Obviously that meant that every time a New Yorker had a treat they killed someone on the other side of the world.
(What it actually meant was that it was summer in both locations.)

For your consideration and amusement:
Image
AlanM
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dorminWS
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Re: How useful is a statistical correlation?

Post by dorminWS »

Correlation does not prove causation. Anybody who ever stayed awake through a basic statistics course will (or ought to be able to) tell you that. I remember the example of that in my own basic statistics book. It was a .9999 coefficient of correlation between the Dow Industrials and the team batting average of the old Washington Senators. (Or something very close to that - - it’s been a looooong time.)

If you stayed awake for the second week (or maybe month) of that basic stats course, you learned about something call the coefficient of determination. For those of you who don’t know, have forgotten, or just don’t care, the coefficient of determination is held to be a measurement of the extent to which movement in the independent variable(s) in a regression model determines the movement in the dependent variable, while the coefficient of correlation is merely a measure of the extent to which they move together. That coefficient of determination is computed by taking the coefficient of correlation (designated “R”) and SQUARING it. Since “R” can never be any bigger than 1 and is as a practical matter always less than 1, it reflects that unless the coefficient of correlation is 1 (which is meaningless because that means the two series you are regressing against each other are identical), the coefficient of determination will ALWAYS be less than the coefficient of correlation. Hence, it will already have become apparent to them as can count any a-tall that the coefficient of determination declines much faster as the coefficient of correlation declines.
R R-SQUARED
.999 .998
.95 .9025
.90 .81
.8 .64
.7 .49
.6 .36
.5 .25

So it is apparent from the table above that by the time R gets down to .7, R-SQUARED is less reliable than flipping a coin because it drop below 50% (an exaggeration, because I reckon with a regression model you would presumably at least capture a trend that flipping a coin lacks) . And, by that way, all of the above assumes the model passed the tests of parameter significance for the model and each independent variable (designated T-tests and F-tests if memory serves – like I said, it’s been more than 40 years). If those tests aren’t passed, none of those numbers mean anything because the coefficients derived are not statistically different from zero.

Some of you younger heads with better math skill can probably catch me out in mistakes and make fun of me, but I am confident I’m basically right on this.

And it occurs to me that I’ve got damn little to do today and may be getting soft in the head for going down this road to begin with. Oh well, at least I’m not one of those dirty old men who is addicted to porn.
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Re: How useful is a statistical correlation?

Post by SHMIV »

What I want to know, is just who the hell has the time to find a correlation between random events, then record them?

That is amusing, though. It would certainly be fun to show that chart to my old stoner buddies from back in the day, and explain that, the more margarine they consume, the more failed marriages in Maine. Then listen to them explain to me why that makes sense. Maybe I can get one of these hippie hitchhikers that I always see to fall for such a conspiracy theory, lol.

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Re: How useful is a statistical correlation?

Post by MarcSpaz »

Reminded me of this...

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kelu
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Re: How useful is a statistical correlation?

Post by kelu »

If you torture numbers long enough, they will tell what you want.
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Re: How useful is a statistical correlation?

Post by WRW »

kelu wrote:If you torture numbers long enough, they will tell what you want.
"Figures lie, and liars figure" was the way I always heard that sentiment.

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Re: How useful is a statistical correlation?

Post by MarcSpaz »

Just remember, there are three types of lies. Lies, Damn Lies, and Statistics.
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