Using GraphPad Prism, when I carry out a 2-way ANOVA with an interaction term, data between two groups is not significant. The post-hoc tests shows non significant interaction between my column and row data. So I did redid the analysis using a 2-way ANOVA without an interaction term, and now I get significance between two groups of data, which is more like what I think happens biologically speaking. But why does the p values change when I use an interaction term versus when I don't use an interaction term, given that the interaction term is not significant anyway? Which is the correct way to analyse the data?
- Probably the cause of the model terms being non-significant when the interaction is added is because the interaction terms takes degrees of freedom away from the residual degrees of freedom. This should all make sense if you look at the degrees of freedom in the output from each way you analyzed it, and the way that the F-test is calculated.
- As to what to do, you'll find different suggestions. There is a philosophy that says that it's fine to drop out non-significant terms from a model. There's another philosophy that says you should conduct the analysis you planned to conduct before you saw the data.
- You should also take a look at the residuals from the analysis and see if either of your models meets the assumptions of the analysis.
Thank you so much! If it is the first one, how do I know which way I should have analysed it - with or without the interaction factor? I have my caluculations of the degrees of freedom and the F-test, but how do I interpret these in the context of the interaction term?
As for the predicted versus the actual residuals - this should plot a straight line, but mine is more of a sigmoidal curve with and without the interaction factor, so neither seems to do a very good job of fitting the model!
- What I mean is, compare the residual degrees of freedom with and without the interaction term, and then look at how the F-test is calculated. Simply adding additional terms to the model might make the other terms in the model not significant.
- The only solution to this is to have more observations. Or, use a model with fewer terms.
- In all cases, examine the residuals. If the residuals suggest the model assumptions aren't met, then, well, the inference (p-values) in the model might not be correct.
- But if you say that the model without the interaction makes more sense biologically, that's probably the one you should have used.
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