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I have a question about a data analysis that I am running. I am analyzing the results of a survey in which (expectedly) there exists far fewer people in one group than in another. This survey is an Honours project about enhancement drug use, and I have ~40 users and ~590 non-users. Obviously there is a huge difference between the sizes of these groups! I am interested in differences in means on a particular study processes scale. I have the following questions:
Is it a problem to use an ANOVA in this case (where the groups are so different in sample size)?
I know that the Levene's test is sensitive to differences in sample size (such that it is far more likely to be significant); and this is the case in my data, p < .05. Regardless, Welch and Brown-Forsythe tests still reveal a statistically significant differences in mean scores on this scale.
Given that the Welch and Brown-Forsythe tests still reveal significant differences between groups, would I be wrong in concluding that these do in fact exist (despite violating the initial Levene's assumption)?
Is there are more robust way to investigate this research question, taking into account the disparity in group sizes?