Thanks for the prompt responses @SteveDenham and @sld. Would it be incorrect to generalize the analysis to a one-factor rbd despite having an incomplete factorial with two factors, inoculum and fungicide? I did consider this prior to posting and ran the analysis as mentioned above but also ran it simply as treatment with 5 levels (one-factor). Results look largely the same but I do have some concerns about this. One noted difference is a results of my LSD, where the estimates are the same, but significance is slightly different when running the analysis as two factors versus one factor. Is one method more "correct" than the other? If I'm understanding this right, by turning this into a one-factor analysis, my significant indicator (p-value) is the interaction term or close to an interaction term. When running it as a two-factor analysis, I am provided with the main effects and there associated significance, but fail to receive an estimate and significance for the interaction term. Would it be improper to use the one-factor analysis for my interaction and the two-factor analysis for my main effects? All of these p-values are highly significant (p<0.0001) so there isn't much need to interpret the main effects due to the significance found within the interaction term. But in theory would this be incorrect under these circumstances? See the images below. To answer your other questions about the bonus question. I did read that paper which I found to be very insightful, but got the impression that pseudoreplication was always a bad or improper form of replication. In my case I don't find this to be true. I would suggest that pseudoreplication of a binary measurement provides greater precision of the treatment. I'm sure there is some reason I am unaware of for why this shouldn't be included in my analysis, which I would be OK with because there are work arounds. I could simply average the binary response variable of the pseudoreplicates and use this average as the response variable. For example 10 of my 18 seedlings emerged in one of the treatments so I'd use 0.55 and ditch the "rep" as one my variables and simplify the analysis whilst providing myself a precise treatment response. Sorry if that is not articulated clearly enough. In response to some of your other questions, my replication would be metareplication where I am simply showing repetition and repeatability. These are greenhouse trials, same location and same year, so more of an exercise of repeatability across time than space perhaps. I understand ideally this would be done in another growing season and another location but I have some limitation. Is the suggestion here that I consider this block 9, 10...to 18 and just add this into the analysis? I was under the impression I would need to include this as another variable to show the "contrast" for lack of better words between the experimental replicate 1 versus 2. Just adding blocks sure would make the analysis easier, just want to make sure I'm following modern/conventional statistical procedures the best I can. One other question I had was in regard to my error terms. Is there a helpful source on determining these error terms dependent on my design and which factors I choose to run. I know if I do a one-factor rbd or a two factor rbd its just block. But for the binary study as a two-factor with replicates and the binary study if I just do one-factor or average the replicates is where I have some confusion.
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