## Oops! df! [Study As­sess­ment]

Dear Helmut,

❝ ❝ ❝ Degrees of freedom?

❝ ❝

❝ ❝ Presumable YES. ... Maybe they are or can be different, IIRC. Why ever.

❝ ANOVA: 30 (well…)

❝ TaaTP:

❝   B/A 8

❝   C/A 8

❝   D/A 9

❝ 8? 9?? What the heck? ... I don’t get it.

Ok, something like that I have expected.
Let's try a 'theoretical' approach. Since we do not recode the periods and / or sequences the df can be obtained via (model without decomposition of the subjects effect into sequence and subject within sequence, design 4x4)

source    df ------------------------------- Total    2*n-1 = 23 treat    t-1   =  1 period   p-1   =  3 subject  n-1   = 11 ------------------------------- error    n-4   = 23-1-3-11 = 8 -------------------------------

So far so good. Two numbers of three 'explained'. Why the heck the comparison D/A has one degree of freedom more: Duno .
We have already noticed a similar effect for the EMA 'crippled' model for replicate designs. See this post.

Nevertheless: The degrees of freedom are different for the 2x2 design and the design of the TaaTP. We can mimic the df's, at least approximately, if we use the robust df's.

Regards,

Detlew