How do I report this 4×4 interaction (this is part of a 4x4x2 ANOVA)? This is an interaction between the factors grouping (Gestalt heuristics for visual grouping of compound figures) and set size (number of images presented) in a visual search task. One of the hypotheses is "There is an interaction between grouping condition and set size." Do I report SD or SE?

Should it be something like this: There was a significant interaction effect between Grouping and Set Size, F(3.23, 42.04) = 3.107, p = .033, ηp2 = .193. Post-hoc comparison revealed that reaction times increased significantly as the set size increased in each of the grouping conditions, as can be seen in Figure 1.

It feels a little redundant to make a table of the 4×4 means as well, since I already have one for the descriptives of the 4x4x2. It would also take up a lot of my word count to put it in as text, not to mention how horrible it would be to read. I also have other main effects and interactions to report, so making a Resulsts section full of tables and graphs sounds like a bad idea to me.

Where do I mention the means and SDs? Should I report SD or SE? Can I just put in (see Appendix A for more information)?

Figure 1.

This is for a report I am writing, as a student, and I don't feel comfortable sending a bunch of e-mails asking my professor about every single thing. Any help would be greatly appreciated.

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#### Best Answer

What you presented here already looks very good to me. Using an appendix/supplementary material to provide more details is also generally a good way to proceed. It's a good idea to show the means and some index of variability but it seems you have that covered with the graph. One important thing missing is an explanation of what the error bars represent (SE, SD or CI). There is really no general standard in this area.

Beyond that, reporting standards are typically discipline-specific and your professor might have some very specific expectations that we cannot guess. The best approach would be to refer to the course material or perhaps a well-know guide in your discipline (in psychology that would be the APA publication manual).

Regarding SD and SE, for a given sample size, one can be deduced from the other so it's not necessarily a big deal but conceptually they are two very different things. Informally, the standard error of the mean gives you an idea of the variability of your estimate of the *mean*. If you have a bigger sample size, the precision of the estimate improves and its standard error becomes smaller. Intuitively, the more data data you have, the more confident you are that you are close to the “true” value of the mean.

The standard deviation on the other hand reflects the variability of *individual observations*. There is no reason why it should become smaller with bigger sample sizes (it's not because you observe more people that any two of them are less different from each other or from the “average” person).

Which one you should look at depends on the question you are trying to address. If the mere existence of a difference is the only thing of interest then using SE or confidence intervals make sense. But the practical impact of a difference will often depend on the effect size/overlap between both groups. Here, error bars based on the standard deviation might be more relevant. The important thing to understand is that with the proper sample size, it's possible to have tiny SE and error bars, a significant difference, and yet a huge overlap between two sets of observations.

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