2. Ecological correlation
I.e., averaging subsets of data and then correlating the averages (such as comparing population traits after averaging by nation). This can overstate correlation because outliers have been averaged away before the correlation happens.

3. Regression fallacy
If you take data on a population twice and the correlation between the two data points is not 1, individuals with exceptionally high measurements in round 1 will tend to decrease in round 2 and those with exceptionally low measurements in round 1 will tend to increase (“regression toward the mean”). The fallacy is in attributing this to anything other than plain mathematics. One way to think about it is that if you are in the top ranks in the first measurement and you don’t have the same result on the second, there’s a lot more room to move down than up.

4. Application problems
Applying a technique to a data set that doesn’t meet the criteria for that technique to be applicable will at worst completely lie to you about the data. Choosing the wrong variables to compare might not give you any mathematical errors, but it could mask what’s “really going on.” For example, perimeter and area of rectangles are strongly correlated, but the real story is about each of those relating to length and width.

The post Hazards of correlation and regression appeared first on rweber.net.

Q. A lab assistant in charge of measuring how long it takes for rats to run a maze predicts that usually a rat will take less time on its second time through. A colleague of his, however, notes that the rats ought to regress to the mean maze running time, on average. Are these predictions compatible? Why or why not?

A. They are compatible. The lab assistant is predicting overall improvement, and his colleague is predicting the regression effect (if somewhat loosely stated). The key to their agreement is that we would expect the rats to (on average) have less extreme second maze running times relative to the second run’s mean and standard deviation than their first run time was, relative to the first run’s mean and standard deviation. If the second maze run has a lower mean time we could see general improvement of times without losing the regression effect (which of course is a statistical fact unless |r|=1, which seems unlikely). If the first run is assigned to the x-axis and the second run to the y-axis, visualize the graph of individual rat runtimes lying completely below the line x=y.

Note there is no regression fallacy here. Neither person is proposing an explanation for anything, just a guess at what the numbers will look like.

The post Regression Question appeared first on rweber.net.