So I am running MANY two-way ANOVAs in my current project (about 40 of them). My two independent variables are dose (2 mg, 10 mg, 20 mg) and vitamin form (A or B). My many dependent variables are either blood levels of this vitamin (ng/mL, continuous variables) or gene expression levels (dCt, continuous) - associated with this vitamin metabolic pathway / not important.
My question lies in how I should be writing these results in my thesis in an effective, yet concise manner. I can effectively write results if the interaction effect is insignificant. However, in the case where my interaction effect is significant, my simple main effects are so long to write out.
e.g. There was a significant interaction between the effects of dose and form on (DV), F(x, y) = X, p = Y. Simple main effect analysis showed that 10 mg supplementation showed significantly greater (DV) than 2 mg supplementation in the A vitamin, but not the B vitamin (p = X, p = Y, respectively). 20 mg supplementation showed significantly greater (DV) than 2 mg supplementation in both vitamin forms (p = X, p = Y). 20 mg supplementation showed significantly greater (DV) than 10 mg supplementation in B, but not A (p = Y, p = X, respectively). Additionally, A vitamin resulted in significantly greater (DV) than B during 2 mg supplementation (p = X), but not in 10 mg (p = Y) or 20 mg (p = Z) supplementation.
That is just a "shortened" example of how one of my results would look like. So considering I have almost 40 analyses, this would take forever to write. Does anybody have suggestions on how I could write this? ANY suggestions and advice would be greatly appreciated. If you need more information, I will happily provide for your help.
One way to deal with this is to show the results of each mean (with the standard error or standard deviation) in a table (or multipanel figure), with superscripted letters to show which means differ significantly. Typically, means with the same superscript do not differ significantly. Your table would be quite large, with columns for each of the condition means, and each of the main effect means. You will probably need a second table showing the results of each ANOVA. In the text, you can highlight the most important results--those you want to discuss--and refer the reader to the table(s) for the detailed analysis .
I would simply state that all three results were significant at the p < .xxx level and then proceed to a detailed analysis of the interaction. A main effect often doesn't make sense after an interaction has been analyzed. Why report that factor A > B and then turn around and say that A1 > B1, A2 > B2, but B3 > A3. A complete interaction analysis typically tells you everything you need to know about the interesting effects. Michael's comments are a good way to display the interaction effects.
Firstly, I would like to thank you both for your kind response and detailed advice.
I was told that if an interaction effect was significant, significant main effects of my two independent variables should be proceeded with caution. I was also under the impression that if interaction effect is significant, an analysis without the interaction is appropriate looking at simple main effects (SME); looking at the effects of one variable while the other stays constant (SME) and vice versa.
Michael, I do like and your advice in highlighting the most important results in my 2-way ANOVA table, however in the case where I would need to do a simple effect analysis (looking at comparable variables - i.e. A1 vs A2 vs A3 OR A1 vs B1... etc), my table would be gigantic.
I do not completely understand the first table you outlined. I have 6 different conditioned categorized into 2 independent variables (A1, A2, A3, B1, B2, B3) and therefore, I cannot make all comparisons (A1 vs B2 - doesn't make sense).
Douglas, do you think I should still report main effects (significant or not), even if the interaction effect is significant?
If you don't like using a big table, an alternative is to include 40 tables--one for each dependent variable. Each table would be 3 x 4, including cell means and main effect means, and each would use letter superscripts to denote significant differences. You could also include the the three results of each ANOVA as an additional row in each table. There is no need to include all 40 tables in the paper. A few of the most important of the tables could be in the main paper and the unimportant ones included as on-line supplementary material.
Here's an example of how I handled this in a recent paper.
Version 2. F1000Res. 2016 Oct 13 [revised 2017 May 4];5:2516. doi: 10.12688/f1000research.9544.2. eCollection 2016.
The refined biomimetic NeuroDigm GEL™ model of neuropathic pain in a mature rat.
Hannaman MR1,2, Fitts DA3, Doss RM4, Weinstein DE5, Bryant JL6.
How did you eventually write it out?. Am having the same problem and it's becoming a really steep learning curve.
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