I am comparing glutamate concentrations across groups (2 groups). I planned on controlling for age and IQ, simply because this is what is always done in cognitive neuroscience. When doing this, age was a very useful co-variate but IQ makes the model very very messy.
I am thinking of excluding it for the following reasons...
Reason 1: When IQ is added as a co-variate, it makes the variance in the sample unequal (Levene's test). When it is out, Levene's test is less significant (although still significant). I have tried to transform the data and this makes no difference.
Reason 2: Both groups are well matched on age and IQ. There are no significant differences. However, even though they are well matched - age is a significant co-variate to glutamate. This association is not significant for IQ and glutamate.
Reason 3: There is an extremely week linear relationship between IQ and glutamate concentrations (see below). I have only included the output for the control group, but it is similar for the other group. It is also not correlated with glutamate (Pearson Correlation = .203, sig=.213, N=33).
My main problem is that I get different results depending on what I do. With IQ in the model, there are no significant differences between groups. With IQ out, there are significant differences. For greater simplicity, I am thinking of excluding IQ as a co-variate. I don't have a very large sample size (N=33). How justified am I in doing this? Will I be eaten alive by reviewers even if I have a justified reason for excluding it from the model?
Question 2: If there is a significant difference in variance between groups. Is this meaningful and what can I conclude from this? Most of the information about unequal variance reports that it needs to be cleaned up. However, can I make any useful inferences about the fact that my groups have different variances of glutamate?
Question 3: Does it make any difference statistically if you use a Type II or Type III sum of squares. From reading it looks like a Type II is preferred if you don't have any significant interactions and Type III if you do. What if you have some significant interactions for other metabolites and no significant interactions for my main metabolite of glutamate(I am looking at other things besides glutamate). I assume it must be standardized and you should go with either or for the entire analysis. What's the best way forward in this regard?
Thank you for any help you can provide. I have been agonizing about these problems and just want to represent the data in the most appropriate way.