# Understanding, reporting and post hoc testing a 2x2 Mixed ANOVA

I one dependent variable, one between groups independent variable (intervention vs. control) and one within groups independent variable (time1 vs time2) so I am using a 2x2 mixed ANOVA.

These are my resulting tables:

I know I have a significant interaction effect, but I don't know what that means in basic non-stats language and I would really like to know!

I can also see that 'time' is producing a sig result, but 'group' is not, but I don't know if either of these things mean anything. (Please explain in the simplest of language possible if you can.)

I also get this error when I tried to run post hoc tests:

Post hoc tests are not performed for group because there are fewer than three groups.

Research I have done (e.g. Post-hoc for 2x2 mixed design ANOVA using SPSS) explains this, but I have also seen examples of a 2x2 mixed ANOVA where LSD post hoc tests were carried out (e.g. https://psych.unl.edu/psycrs/statpage/2x2mg.pdf). Despite trying to research I still don't really understand what post hoc tests mean, so I am not clear if I need to do them (or do t-tests?) or not, and what I'd learn by doing them!

Given all the above, I'm not too sure what I'd report from the above either. I'm sure I can put it together in terms of writing something down, but I don't know if I understand what it means yet - and I find that very frustrating.

I'm sorry that I'm so confused, if you can help with any of this I'd really appreciate it.

Thank you for any help!

Extra information...

It might be worth seeing the Estimated Marginal Means (from what I've read). They are displayed here (and so is a plot):

For me, this is saying that - the biggest effect is found from a combination of being in the intervention group and time passing. This makes sense to me... and I don't understand what information is even important/relevant from the estimates of group or time in isolation (I don't understand how that information is important/ if I should report it).

• stats.stackexchange.com/questions/380222/… Basically the third paragraph of my answer applies in your case. You have a group*time effect. So the effect of group DEPENDS on what time point you look at (and vice versa), so there's no single, unified effect of group anymore.Your intervention got worse over time while your control group didn't. Or another way to say it, your groups started not significantly different from each other at time 1, but got significantly different from each other at time 2. – Huy Pham Apr 7 at 21:01