# ANOVA - independence assumption

I have conducted a study in which I have gathered 3 sentences per participant. These sentences were then classified and the words per sentence were counted. I want to test if there are significant differences in the word count means for the different categories of the classification.

However, because the sentences are not fully independent (each participant has entered 3 sentences), I am worried that ANOVA would not be the right analysis, since it assumes the independence of the cases.

Would it be better to carry out non-parametric statistics on transformed word counts, or is it okay to do an ANOVA?

PS I have asked a related question about using the $\chi^2$ test in a similar situation to identify interactions between factors.

• Could you elaborate a little bit more on the "different categories of the classification"? I'm thinking a multi-level model might be useful here... – Dominic Comtois Apr 14 '12 at 23:18
• Each sentence was classified using 3 classifications: type of sentence (nominal: {phrase, question, keywords}), data set (nominal, 3 choices, selected by participant), and distance to data set (6 levels, ordinal). – Lars Grammel Apr 15 '12 at 0:20

In this case, unlike your $\chi^2$ question, the unit of analysis is a sentence and the randomness is very much associated with the sentence level, and hence you do need to worry about their independence. As @dominic999 suggests, a multi-level model (also known as a mixed effects model) will probably be appropriate, with participant as a grouping level and number of words as the response. Because the response is a count, you will probably find a mixed effects generalized linear model with a Poisson distribution is what you want.