[EMAIL PROTECTED] writes:
> I have run a Univariate ANOVA in SPSS but have included a
> random factor. The inclusion of a random factor, rather than fixed
> factors, seems to remove the r squared from the output. Can anyone
> tell me how I can calculate the r squared from the following three
> output tables?
With a random factor, you have two sources of variation, within subjects and between subjects. You can adapt r squared to two sources of variation, but it is tricky. Fit a null model (one with no fixed factors, but it should still include random factors). Estimate between and within variation. Add the two together to get total variation. Then fit your full model. Re-estimate between and within variation and total variation. You can then extend the definition of r squared in an obvious way to estimate the proportion of total variation and within variation explained by your model.
The R squared for within variation is a measure of how much the model helps when trying to predict a new observation on one of the subjects already in your study. The R squared for total variation is a measure of how much the model helps when trying to predict a new observation on a new subject.
In theory, you could also do this for between variation, but the interpretation is tricky, and it is quite easy to get a negative percentage.
I have a paper somewhere in my bibliography that talks about this, but it would take me a while to track it down.
Steve Simon, [EMAIL PROTECTED], Standard Disclaimer.
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