Though most statistical software packages will estimate both fixed and random models, it still is a good skill to be able to extract information about a random-effects model from a fixed-effects ANOVA summary table.  This is even more important when one considers the fact that SPSS does not generate a correct mixed-effects ANOVA summary table in its output.

Here is the ANOVA summary table for a two-factor fixed-effects ANOVA where there are two levels of factor A (curriculum intervention) and three levels of factor B (teacher).  Each cell includes 8 students.

Source	$\displaystyle {S}{S}$	$\displaystyle {d}{f}$	$\displaystyle {M}{S}$	$\displaystyle {F}$	$\displaystyle {p}$
$\displaystyle {A}$	311.3	1	311.3	3.834	0.0569
$\displaystyle {B}$	947.8	2	473.9	5.836	0.0058
$\displaystyle {A}\times{B}$	648.8	2	324.4	3.995	0.0258
Error	3410.4	42	81.2
TOTAL	5318.3	47

For the random-effects model, the F-ratios for the main effects change because the estimates for the error due to random (sampling) variability are different.  (Note, the estimates and resulting F-ratio for the interaction effect is unchanged.)  Along with the random variability estimate changing, the degrees of freedom for the denominator consequently changes.  For these problems, you are encouraged to use Excel's =FDIST() function to calculate significance values.

Calculate the random-effects test statistic and significance for the first main effect:
$\displaystyle {d}{f}_{{\text{denom}}}=$
$\displaystyle {F}_{{A}}=$
$\displaystyle {p}=$
(Please report the F-ratio accurate to 3 decimal places and the P-value accurate to 4 decimal places.)

Calculate the random-effects test statistic and significance for the second main effect:
$\displaystyle {d}{f}_{{\text{denom}}}=$
$\displaystyle {F}_{{B}}=$
$\displaystyle {p}=$
(Please report the F-ratio accurate to 3 decimal places and the P-value accurate to 4 decimal places.)

Final conclusions for the random-effects model (use $\displaystyle \alpha={0.05}$):
For the first main effect... For the second main effect...