Calculating $ MSE$ given $ F$, $ df_{\text{group}}$, and $ SS$

Given:

$\displaystyle F = MS_g/MS_e$ (1)

Where $ g$ indicates the group, or treatment. Rearranging this equation gives:

$\displaystyle MS_e=MS_g/F$

Given

$\displaystyle MS_x = SS_x/df_x$

Substitute $ MS_e/df_e$ for $ SS_e$ in the first equation

$\displaystyle F=\frac{SS_g/df_g}{MS_e}$

Then solve for $ MS_e$

$\displaystyle MS_e = \frac{SS_g}{df_g\times F}$ (2)

$\displaystyle df_{\text{total}}=(df_a+1)\times(df_b+1)...\times(n)-1$ (3)

which depends on the experimental design:

for factors a, b... (usually 1 or 2, sometimes 3) where $ n$ is the number of replicates within each treatment combination.



Subsections
David 2011-10-07