# Within-subject and between subject-variability

#### wnjiang

##### New Member
Dear experts and users:

I was instructed to calculate the within-subject and between subject variability of a data set from one of my PIs. I would love any guidance on how to report them!

I have scoured Google and textbooks, but unfortunately there is a scarcity of guidance. Would a repeated-measures within subject and between subject analysis be a measure of variability? Or would I need to use a correlation?

Thank you!

#### oparairoegbu

##### New Member
In an ANOVA (ie analysis of variance) computation, Treatmet mean square is between-subject variability.That is; variability of the treatment means. On the other hand, residual (error) mean square is within-subject variability. That is; variability within the treatments. Does this help?
oparairoegbu

#### wnjiang

##### New Member
That gives me a great direction to explore! Thank you!

I assume the sum of squares for treatment mean would be the Type III sum of squares reported by SPSS in the "test of between subject effects"?

As for the residual error's sum of square, should I use the one for time effect (as all the within subject measurements were made at different time points)? Or the one for time (within subject) contrast (linear)? Or the error sum of square reported in the table of "test of between subject effects"?

Thank you very much!

#### oparairoegbu

##### New Member
I assumed a one-way ANOVA in my reply. It appears your ANOVA is a more complex one. Whether time was used as a blocking device or whether it was another variable is what I cant tell. All the same, variation due to time is another between-variation. Multiple factors create different between-variations. The within- variation I suggest is your "error sum of square reported in the table of 'test of between subject effects'"
oparairoegbu

#### wnjiang

##### New Member
Thank you! I am using a 2 way, 1 within (time) 1 between (treatment group) repeated measures ANOVA. However, the error of between group sounds right!