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I have LFS spanning 24 quarters, and I want to look at the effect of a policy on the sickness absence of a particular occupation. I want to use ANOVA to see if there is a statistically significant difference pre and post policy. However with LFS data, participants are in the survey for 5 waves (quarters) and so I am not sure if the pre policy and post policy groups can be said to be independent.

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Yes, if subjects participate in the survey multiple times, then their responses are correlated, and you would need to employ RMANOVA.

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