find out correct procedure if significant interaction in CRD and RCBD

[msimmond]

Currently, we are doing the following: if there is a significant interaction between 2 treatment factors (A and B) in a CRD or RCBD fixed effects model (e.g. y ~ A + B + A:B + Blk), we perform an LSD on the combination of all levels of both factors (e.g., in a 3 x 3 factorial, we would do an LSD on 9 treatments), as opposed to first subsetting the data for each level of A and re-running the ANOVA on B (y ~ B + Blk #for each level of A) and doing LSD test if significant effect of B, and vice versa for A. I am not sure if both approaches are valid (i.e. looking at all combinations versus subsetting). In the latter approach we'd have to retest all ANOVA assumptions for each individual ANOVA. YUCK

[msimmond]

Example where the first approach is used (looking at all combinations): https://cran.r-project.org/web/packages/agricolae/vignettes/tutorial.pdf (see p 36-37)

Example where the second approach is used (subsetting): http://www.unh.edu/halelab/BIOL933/lectures/lect_14_reading.pdf (see p 9)

[msimmond]

After consulting an expert, I think what we have is fine for CRD and RCBD.

This was their response:

"The first link you sent (unh.edu notes) does analyze subsets of data. Do not do this. You kill your power and prevent comparisons across levels of a factor. You may notice that the author does not dwell on the example.

The example in agricolae is fine. It does not look like they create a new variable. The code simply requests that all cell means be “separated.” There’s probably a default method being used implicitly to protect familywise alpha because all comparisons are made. Power is greater because the larger dfe than by subsetting. Everything you can do with subsetting, you can do better by using all data in a single analysis (with exception of specifically weird situations in specific datasets)."

However, we need to be sure for split-plot with signicant mainplot x subplot interaction. I emailed agricolae author to ask.