On Correlations

there's a great post on the basics of correlations (including a couple amusing examples) from good math, bad math today.  an excerpt:

So when someone shows you a correlation, what you should do is look for a plausible causal mechanism, and see if there's any experimental data to support it. Without a demonstrable causal mechanism, you can't be sure that there's a causal relationship - it's just a correlation.

here's a fun example from swivel.

Comments

[Chris Keane]

This consideration (correlation vs. causality) make the "How related are these items to one another?" section on the Swivel pages seem a little misleading. What is that section calculating?

[Mono]

Ah, I love Good Math, Bad Math.

[John]

I think it would be wildly helpful if on the "how related are these items to one another" you included a link to an explanation about how you're calculating this--what assumptions are being made about the variables (ordinal vs. continuous, frequency distribution assumptions, etc.) and the statistical test being used.

[huned]

chris, john,

thanks for asking! swivel calculates a linear correlation coefficient, which is what you see as the percent related. the "b" value that appears near the relatedness meters is the slope of the (linear) regression line.

so, concretely, take a quick look at this graph, which compares the price of oil and president bush's approval rating (http://swivel.com/graphs/show/1000837). it has a b value that is very close to -1, which roughly means that every dollar increase in the price of oil causes a one point decrease in bush's approval rating. (or maybe it's the other way around? :)

wikipedia is a great starting point for learning more about linear correlations. http://en.wikipedia.org/wiki/Linear_correlation

mono,

it's a great blog, no?