Justification for t-tests instead of 2-way ANOVA (no interaction)

HI there,

I need help with justification for why I should use a t-test instead of a two-way ANOVA. My two-way ANOVA gave me a main effect of Diet (ethanol and control) and a main effect of Drug (drug and no drug), but no Diet x Drug interaction. Since there is no interaction, I don't feel justified doing post-hoc Tukeys multiple comparisons tests. However, an interaction was not expected and it makes sense that there was not one (the drug decreases my dependent variable whether or not the animal gets ethanol). I would like to do some test (planned t-test or planned Tukey's comparisons) to look specifically at the comparisons i need to make to answer my question - but I need justification and I'm worried I can't just say, "well I didn't expect an interaction so I ignored the fact that it was required for me to do Tukeys". Statistics is not my strong suit and I really could use any help that anyone is willing to provide. Please ask me for more clarification if you need it and thank you in advance for your help with this issue. You have no idea how much it is appreciated!!


Fortran must die
I would normally suggest doing planned contrasts, although you are supposed to plan these before you see the results. If you have seen the results and base the contrast on this, your power will be too high. I am not sure why interaction or the lack of it means you should not use Tukey or any post hoc test. If you don't like Tukey and can't do a planned contrast, why not pick one of the many other ad hoc tests?

I don't think you are really asking whether you should use Anova or multiple t-test. Regardless when you have two or more variables it is going to be hard to justify running a series of separate t test regardless of whether you have interaction or not.
Thank you so much for your response. You are right, I guess I am asking if it is OK to do Tukeys even when my interaction is not significant. Or will someone say, "well you didn't have an interaction so you can't run any post-hoc tests like Tukey's". What is a planned contrast? Is that Tukey's or Bonferroni? Thank you so much for your help explaining this, I truly appreciate it!!


Fortran must die
I must be missing something. Not having interaction makes using any post hoc test easier to defend not harder. A post hoc test tells you if some level of an IV impacts the DV differently than another level. When you have no interaction this makes perfect sense to do. If you did have interaction, I have not seen this addressed so I am guessing, then using a post hoc test would be more problematic because the impact of a specific level of the IV on the DV will vary at specific levels of another IV. I don't know if post hoc tests deal with that, or how they do. But in any case this does not apply to you.

All a post hoc test does is tell you if some level of an IV differs than some other level on the DV. It is what you typically look at after a significant model F test. Its better to do planned contrast simply because they have more power - but formally planned contrasts assume you are not comparing all possible levels of the IV at all possible levels of the IV, you have some theory behind what you are doing. So its really not valid to do planned contrast after you run the results, you should use a post hoc test which adjusts for this issue [it really is adjusting for familywise error inherent in this].

A planned contrast says something like I expect that this level of the IV will have this impact on the DV relative to this level or levels of the IV. Typically they are coded to sum to 0 and take many forms depending on your theory and the number of levels. They tests what impact your variable is having. All commercial software generates them, any decent book on ANOVA covers them.