Can you please explain me what is the consequences of violation of independence assumption in ANOVA test?
I couldn't visualize it.
Does Cochran Theorem relates to independence assumption ?
2026-03-27 05:59:44.1774591184
Consequences of violation of independence assumption in ANOVA test
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The independence assumption allows us to use simple statistical concepts to quantify the evidence for/against the null hypothesis. That is, independence (among the other assumptions) allows us to say that the errors from the mean are normally distributed. Then we can use the Cochran Theorem to quantify the p-value (how extreme the actual data is given the null hypothesis), which we then use to make a decision.
The Cochran Theorem is the workhorse theorem for ANOVA and requires independence, so yes there is a very strong relation.