I'm trying to run a two-way ANOVA on a 375-sized dataset. I'm trying to navigate my way through the assumptions but need some assistance. Specifically, I have two groups as the IVs (1: Boys and Girls; 2: Yes and No), and a real number between 0 and 1 as the DV.
Firstly, I know there is no assumption related to equal sample sizes, but mine are really quite different:
Yes = 190.
No = 58
Yes = 102.
No = 25
Assuming the fact that one group has 190 and another only has 25 is OK (it may not be?), I am having some difficulty with the normality assumption. Both 'boys' subgroups have a low skewness (less than double the std. error) and a non-sig Shapiro-Wilk stat. However, the two 'girls' groups have a negative skewness of 0.8 and 0.3 respectively, and a sig SW.
I have tried a log-transform, however this does not resolve the issue. Is there anything else anyone can think of? With the info provided, should I abandon parametric tests here in favour of non-para, or is OK to continue with these (hopefully) minor shortcomings?
Edit: To provide some more clarity around the problem itself, the DV is a rating score regarding how similar the speech of the person (in this case girl or boy) is to another girl or boy (where theoretically 1 is the absolute repetition of speech, and 0 is the absolute divergence) - all DV values are between 0.75 and 0.95. The 'yes', 'no' IV is merely how they answered a particular question in a previous data collection exercise.
I have initially run a t-test looking at the differences between the mean of girls and the mean of boys, and wanted to further break it down using this additional question variable