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?
Thank you for your reply.
The way I understand what you write is that the assumptions of the ”pure” overall standard deviation and the total standard deviation from the random effects ANOVA are different. However, I still don’t quite understand why they yield different results.
I get that the ANOVA takes into account the fact that certain groups of data may come from different populations. But my understanding is that the ANOVA tries to decompose the total variation into components coming from e.g. within-run and between-run. If those are the only factors in you ANOVA (as in my example) why does the within- and between-run variances not sum up to the total variance?
I understand the math behind both types of total variance. What I am trying to understand is the real world meanings of those - or the difference in meaning explaining the different values.
I have searched quite bit for the answer, but all can find is how to calculate and interpret the different variance components – not the total variance.
It seems to me that if you break the total variance on two and put the pieces back together, you end up with a total variance larger than what you started with. Why?