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I am wondering whether there are acceptable ways to illustrate the presence of an interaction besides using an ANOVA. I can't use an ANOVA because I have unequal sample sizes, and due to the nature of the topic being investigated, there was no experimental design we could have used to avoid this.
Is using a scatterplot and adding R2 lines for both subgroups an acceptable method for demonstrating an interaction? If not, what are other methods? We replicated the effect twice (unequal sample sizes in both experiments) so we are confident the interaction exists. The only problem is demonstrating this in an acceptable-for-publication manner.

Thank you in advance, all help is tremendously appreciated.

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    $\begingroup$ What are your n's? Have you checked the ANOVA assumptions? Unequal n's by itself is not sufficient to completely invalidate an ANOVA. $\endgroup$
    – John
    Commented Nov 6, 2012 at 18:46

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Maybe a non-parametric permutation test for the interaction? See

Anderson, Marti, and Cajo Ter Braak. "Permutation tests for multi-factorial analysis of variance." Journal of statistical computation and simulation 73.2 (2003): 85-113.

A PDF is available at http://avesbiodiv.mncn.csic.es/estadistica/permut1.pdf. Section 5.1 recommends permuting residuals for testing the interaction hypothesis.

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  • $\begingroup$ I like permutation tests, so +1. Nevertheless, as @John remarks above, ANOVA may be fine even with unequal n, in which case a permutation test may have less power. (And it may be harder to implement and/or communicate.) $\endgroup$
    – Stephan Kolassa
    Commented Nov 6, 2012 at 20:08

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