When conducting research we are restricted in the number of variables that can be examined at one time. For any particular sample, it may be that two variables are very highly correlated and can not be distinguised from one another numerically in a particular sample. Such data is said to be confounded. There are only so many patterns to go around so some confounding is bound to happen, especially when the variables have few levels and small sample sizes. That is, when we do not look very deeply into things. The issue of confounding has come up in discussions of corresponding regressions lately and I thought I would throw out a method I use when interpreting factor analyses and correlations.
Lets say we have two variables x1 and x2 that are highly correlated. I try to imagine all of the possible combinations of these two variables, whether theyexist or not. The frequency of their occurance beyond even one possibility does not much concern me. Let's say x1 is honesty and x2 is professional status and that these two variables are highly correlated. If I can think of any examples where dishonest people have high professional status, then I realize the independence of these constructs. This would be a test that all scientists should ask themselves when confronting the complexity of phenomena. If you can imagine exceptions to the correlation, then you should acknowledge that the constructs could be sampled in such a way that the high correlation is replaced by a zero correlation. Let's take the example of mileage and engineering design in automobiles. If the engineers know what they are doing and have the power to implement their designs, then it is highly unlikely that they will build a model that does not obtain the mileage standards desired. In this case, it is very difficult to imagine a model of car that is manufactured to conserve x amount of gasoline but that in fact does not so conserve. For this reason, design or intention is confounded with mileage. Can you think of variables that could be confounded by this logical orthogonalization method? Do "professional" statisticians all do this anyway? Would such a method point the way to intentional sampling rather than reliance on convenience samples? Bill Chambers . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
