On 16 Nov 2001 09:34:52 -0800, [EMAIL PROTECTED] (S.) wrote: > I performed the following experiment: > > Each user (U) used several interfaces (I). Both U and I are to be > treated as random factors. For each U and I combination, time (T), > errors (E) and satisfaction (S) were measured. The data looks > something like: > > U I T E S > --- --- --- --- --- > U1 I1 100 10 90 > U1 I2 200 20 80 > U1 I3 300 30 70 > U1 I4 400 40 60 > U2 I1 102 11 91 > U2 I2 198 18 81 > U2 I5 500 50 50 > U2 I6 600 60 40 > . > . > . > etc. > > Please note that NOT all the users used all the interfaces. > > The question is: I wish to find the correlations between T, E and S > (viz., nullify the effects of U and I). What is the best statistical > method of doing this? I think something along the lines of Anova or
For the little bit of data shown, the variable *I* has a huge effect, with R-squared of maybe 0.99 with each of the three variables, T, E and S, and that happens while I call it a continuous variable. So it would be just as important, with a waste of degrees of freedom, if it is used as categories; the table shows it coded as categories, I-1 to I-6. High R-squared puts you into the situation where subtle choices of model can make a difference. Is it appropriate to remove the effect of *I* by subtraction, or by division? - by category, or by treating it as continuous? > Variance Components should do that trick... I have SPSS, so any advice > on how to interpret the output will be most appreciated (please bear > in mind that I do not have a degree in statistics). If it is strictly correlation that you want, you can ask for the intercorrelations, while partial ling out the U and I variables. If *I* and U are to be partialled-out as categories, you can create a set of dummy variables, and partial-out those. The result that you get will *not* be robust against scaling variations (linear versus multiplicative, for instance). That is a consequence of the high R-squared and the range of numbers that you have. I suspect that the observed R-squared values might vary in a major way if you just change the raw data by a few points, too -- Note that prediction with an R-squared of 0.99 has *twice* the error of an R-squared of 0.995, and so on; that is approximately the same as the difference between 0.1 and 0.2, in certain, practical consequences. If it will please you to reduce the eventual intercorrelations to zero, a proper strategy *might* be to try alternative models to see if you can produce that result. Of course, in practice, it should be a great deal of help to know what the variables actually, are, and how they are scored, etc., to know what transformations are logical and appropriate. I suspect that data, as stated, leave out some conventional standardization, and so the observed correlations are mainly artifacts. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
