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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 ?

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    $\begingroup$ Is there any reason why you don't just use a mixed effects model, which can handle unbalanced designs ? $\endgroup$ – Robert Long Aug 9 '16 at 18:38
  • $\begingroup$ Well lack of experience mainly... I was not aware of that model and how to run and interpret it using SPSS $\endgroup$ – John St Aug 14 '16 at 23:15
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    $\begingroup$ But you used the "mixed model" tag ! $\endgroup$ – Robert Long Aug 15 '16 at 0:38
  • $\begingroup$ Thank you for mentoning it. I have now removed this tag. It verifies my lack of experience because I thought it refered to mixed ANOVA! I have been looking into the mixed linear model for the last couple of days and I cannot seem to understand how to include factors such as gender or (as mentioned above) handedness apart from my DV and my Condition variable in the long format dataset. $\endgroup$ – John St Aug 17 '16 at 15:56
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If you can perform a bootstrapped analysis, I would. I wouldn't know how to do this in SPSS though. Sorry.

Basically,

  1. Resample n observations for each group.
  2. Caluculate the t-statistic (or ANOVA parameter estimate)
  3. Repeat these steps about 1000+ times
  4. Plot the histogram of your statistics
  5. If 95% of your simulated statistics are above a meaningful cut off, then you're overall results are meaningful.

However, say only 80% of your generated statistics are above a meaningful cut-off, then your results may not be valid. From here, your options are to either bootstrap more or conclude that there is no significant difference between group 1 and group 2.

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