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I am analysing some data using a two-way ANOVA followed by Sidak's multiple comparisons post hoc tests. I am looking at the effect of age and genotype (the independent variables) on the levels of a certain protein (the dependent variable) expressed in the brain of mice.

After performing the two-way ANOVA, the interaction effect is statistically significant (p-value = 0.0254), but neither of the main effects are statistically significant (p-value > 0.05).

I am new to two-way ANOVA analysis and I have learnt about it from online tutorials. In the examples on the tutorials, I have seen cases where the interaction effect is statistically significant, along with one main effect.

I am wondering if it is common for result of two-way ANOVA to have only the interaction effect be statistically significant? Further, would the correct interpretation of my results be that neither age or genotype alone has a significant impact on the levels of the protein; however the age and genotype in combination does have a significant impact on the levels of the protein?

Any insights are appreciated.

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Yes it is very common. A significant interaction term indicates that protein levels do not differ consistently according to either age or genotype but that differences are dependent on what age group and genotype you look at. So for example, protein differs significantly for juveniles of genotype A, but does not differ for juveniles of genotype B..or protein content may differ for adults of genotype A but not for juveniles of genotype A. So in the case of a significant interaction term you would not do post hoc tests on the single upper level factors regardless of whether they are significant or not, but only do post how tests on the interactions term investigating in which levels of the interaction term there are differences.

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  • $\begingroup$ Thank you for you reply. I performed two Sidak's multiple comparisons tests after doing two-way ANOVA. For each factor I had two levels. In the first family of comparisons, I compared means between different age groups (where the genotype was constant). In the second family of comparisons, I compared means within the genotype groups (where the age was constant). I think Sidak's multiple comparisons test only looks at a single independent variable (age or genotype). Do you know what post hoc tests can be used for investigating the interaction term? $\endgroup$
    – ceno980
    Jul 27, 2021 at 9:57
  • $\begingroup$ You could probably just do a Tukey's post hoc test, no real need to correct for multiple comparisons considering you have relatively few pairwise test comparisons. Also not sure why you would want to use mean data and not the raw values unless i have misunderstood you. It sounds like you are generally not very familiar with two-way ANOVA so i would read up a bit more on it and perhaps look over a few online tutorial video's.. $\endgroup$
    – Sean
    Jul 27, 2021 at 12:13

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