Two-way ANOVA with interaction – what to do?

[mstaehr]

I have a set-up with 4 groups of mice; Genotype (+/+ and -/-) and diet (high salt and low salt), and am using Graph Pad Prism to analyze my data. Since I have to factors I use two-way ANOVA with a post-hoc Bonferroni multiple comparison test to compare all groups. In some of my analyzes there is a positive interaction between genotype and diet, and this leads to my question:
When I have positive interaction do I need to analyze my groups separately? Do I need to run an unpaired student t-test or one-way ANOVA? Or isn´t that what the post-hoc Bonferroni multiple comparison test from the two-way ANOVA already did?
I would appreciate your help.

[victorxstc]

Not at all. The significant interaction means that the effect of one variable is significantly different for each levels of the other variable. It has nothing to do with separate analyses. You should not do any other tests, and all your two-way ANOVA and Bonferronis are completely correct.

[Eugenie]

If you have interaction, it means you CAN'T simply do two one-way ANOVAS. The whole point of
doing a factorial experiment and 2 way ANOVA is to account for interactions. The 2-way anova will
give p-values associated to each main effect and to the interaction.

It sounds like you maybe need help interpreting the results of your analysis. What research
questions were you trying to answer, and what particular contrasts did you study with the post-hoc
Bonferroni procedure? It says above you compared all groups--do you mean you obtained confidence
intervals around the difference in group means for each pair (which is the same as tukey kramer)?

I am uncertain what you mean when you say "some of your analyses". If you just had one experiment,
you should just have one 2-way ANOVA to run. Did you have several experiments
of this sort with the same groups? What was the difference among these? perhaps you really need a
three-way ANOVA?

[mstaehr]

Thanks for your answers.
I have several experiments of this sort. By the end of the experiment I harvest tissue and plasma and analyze them for different factors such as expression of certain genes (mRNA and protein level), receptors and so on. I want to see if the high salt diet affects these molecules and if the genotype has anything to say.
When I do the two-way ANOVA I get p-values for genotype and diet. So lets say diet comes out significant, what I don’t get information about is whether it is significant for both genotypes. But when I do the Bonferroni multiple comparisons it tells me that this particular molecule is regulated by high salt diet in the +/+ mice but not in the -/- mice. So if I only do the two-way ANOVA, without the post-hoc Bonferroni I miss that information. Or have I misunderstood something?

[Eugenie]

The two-way ANOVA will give three p-values: one each for genotype and diet and one for interaction.
You are correct that the ones for the genotype and diet combine the groups for the other two factors, so
it is possible to miss that it may only effect one level of the other factor. That is why you don't just want to
do separate 1-way ANOVAs.

But, as you note, the Bonferroni shows what is going on (but you can only do this post-hoc test if the 2-way ANOVA
gives significant results). The correct interpretation is exactly what you have said: In +/+ mice, diet has a significant
effect, but not in -/- mice. When you report your findings, you should give all three p-values, as well
as any confidence intervals you have calculated to estimate the size of effects.

[noetsi]

I suggest running simple effects. The impact of one of your IV at levels of the other. Which you may have already done, I was not clear on this point.

[mstaehr]

So if the three p-values are significant I can do the post-hoc test, and if they are not (no interaction) should I then do two separate one way ANOVAs instead?

[victorxstc]

The results won't differ in that case, and even if you give a significant result, it is likely a "false" positive error. But I've seen some studies in which thy have incorrectly done two one-way ANOVAs.

[mstaehr]

So the correct way is to do one-way ANOVAs (when there is no interaction) - even though the result would be the same?

[victorxstc]

No, the correct way is to do a 'two-way ANOVA' (regardless of existing an interaction or not), even when the results would be the same with running two One-way ANOVAs.

[mstaehr]

Sorry about al the stupid questions, I hope this will be the last one :-)
So I should analyze all of my data with two-way ANOVA and if the three p-values are significant I can do the post-hoc Bonferroni test. But what if the three p-values are not significant, should I just report them then and do no further or can I use another post-hoc test? Or can I do the post-hoc Bonferroni test no matter what, and just report whether there was interaction or not?

[victorxstc]

Even if one of the three P values is significant, you can run a Bonferroni.
You "can" also run a Bonferroni, when there is "no" significant ANOVA P value. It is recommended not to do so, because usually the Bonferroni will also give you nonsignificant results. But you "can" do it.