[ snip, previous problem] > > This is similar to a problem I have come across: the measurement of a > serum value against exposure. > My theory is that they are correlated. But the data says that they > have an R^2 of 0.02 even though the p-value for the beta is p=1E-40 > (ie. zero). > > As you explain this is possible. My reasoning is that the exposure is > happening many hours before the measurement of serum and so that is
You should take note that R^2 is *not* a very good measure of 'effect size.' It only works when you are repeating something familiar. You have seen so-much before, and you may be happy to see as much again; but it does not tell you as much as knowing that there is a 4-fold Odds Ratio for a factor -- which is the usual measure when you have a rare dichotomy, or something that can be conveniently described that way. [ snip ] > . R^2 is very useful though, for example if > you want to know in the american population what is the highest source > of fat, you would use R^2 on the food frequencies, not the beta > coefficient.. because the R^2 would tell you the food that most > predicts, rather than the "strength" of the effect of the food.. ie. > low fat foods may be main source of fat in diet.. > > -just thinking outloud hehe.. Well, maybe R^2 is useful. But you need to know how it is anchored. Do you have continuous variables? - I thought you had dichotomies, where the Odds Ratio is rule, when you have small rates. A 'coefficient of determination' or R-squared of 0.18 reflects *at least* a 4-fold increase in Odds Ratio when the 4 cells are all around 50% -- For that 0.18, the OR is higher, if the margins are less balanced. And also. The R-squared is going to describe the sample-on-hand: If you sample with too-narrow variation, you get R-squared that is too-small. Similarly, for large. The beta describes co-variation in another way; the raw beta (not the standardized) is usually what is more interesting, if you really have a large enough N that the actual coefficients are interesting (mine usually are not). -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =================================================================
