Why is the total variance fron a random effects ANOVA not equal to the total variance of the data?

JesperJohansen

Hi

I am hoping someone can explain this to me in an intuitive way.

Why is the total variance of all data (last column in attached table) not equal to the total variance from the random effects ANOVA (script in the attached table)?

What does this difference mean?

Jesper

data.jmp

Paul_J

Variance (and standard deviation) of all data assume all results are independent, random results from one population. If you have a random effects model, results in the same SIRINDEX group may be more alike than results in another group. Or, to put it another way, each SIRINDEX group may be a different population with a different mean. The total variance in the random effects ANOVA takes into account group mean differences and effectively "adjusts" the variance. In particular, the random effects ANOVA calculates separate within group and between group variances, then adds those up. (The random effects ANOVA does assume each group has the same / similar within population variances.)

l Don't have a good reference off-hand, but something on ANOVA will be where you can learn more about this.