Which test should I use?


I made repeat measurements of depth and velocity at ~700 locations in a river at three different flow rates. The data was clustered at each flow, resulting in 7 hydraulic habitats at each flow. I would like to compare each habitat across all 3 flow rates to see if there are any significant changes in depth and/or velocity. I have looked into MANOVA and MANCOVA but the data are not random (due to prior clustering) or normally distributed and do not have equal variances. Does the fact that data was collected at the same place at three different flows invalidate the indepedence assumption too?

Could anyone advice me of a suitable non-parametric test to compare the means of 3 (non-independent) samples, each with two (covariant?) variables please?

Its hard to tell what your data problem is since I am not familiar with the kind of research that you are doing but it sounds like you have a situation where you have nested data, eg. your observations violate the assumption of independence typical of most statistical techniques including ANOVA.

You might want to look into multilevel modeling techniques (also known as hierarchical linear modeling). David Kenny has a book devoted entirely to the issue of non-independence called "Dyadic Data Analysis" and there is a book by Judith Singer and John Willett that deals with an multilevel approach to longitudinal data, which also deals with non-independence. These techniques are presented from a social science perspective but it might give you a place to start looking.