I am doing a mixed ANOVA in SPSS where I am currently comparing the duration of certain script handwriting in 2 conditions (1=eyes open and 2=eyes closed) for the same 40 participants in both conditions and I want to use handedness as my Independent Variable. So I have 2 groups (1=right-handed and 2=left-handed) by 2 conditions.
The right-handed subjects are 37 and the left-handed are 3. That to me would seem like a major problem theoretically.
I have ran a simple paired t-tests comparing just the two conditions mentioned above and have found significant differences between means. When I ran the ANOVA with the between subjects factor however, the within-subjects effects came out not significant and so did the interaction between duration and handedness.
On the other hand, group variances appear equal according to Levene's test.
My question is this: Is there a cut-off point where group sizes are so unequal that there is no validity (or point) in doing statistical comparisons (ANOVA in particular) or is there a way to analyse this 2x2 design despite the large group sample differences ?