I have a dataset with the following properties:
- k > 2 groups
- normally distributed
- differing variance and sample size between groups
- non-independent samples within each group
- continuous variable
If the samples were independent, my understanding is that Welch's ANOVA could tell me whether the means of the groups were significantly different. However, in this case we know that the samples are not independent. Thankfully, in this case we know the conditional dependence structure of the variables.
This conditional dependence structure can be completely arbitrary - our data does not represent repeated measures, for example. However, it is known.
Is there a standard statistical test that can be used in this case to tell if the means of the groups are significantly different? If not, how would we go about this problem?
Thanks for your help!
