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I was trying to analyze a data with negative values. Is it possible to use ANOVA in this case?

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Certainly. Why not? The most usual ANOVA models assume normally distributed errors, and that introduces the possibility of negative values. The assumptions of the Gauss-Markov theorem are that errors have expectation $0$, all have the same variance, and are uncorrelated, and that doesn't rule out negative values and in some cases may necessitate them. I don't know of any ANOVA models that would assume all values are nonnegative. Sometimes one might have only positive values of a response variable and then do ANOVA with their logarithms as the response variable, but that response variable to which one applies ANOVA is not constrained to be nonnegative.

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