# Comparison of treatment differences in fully factorial design

I have a dataset from a fully factorial experiment aimed at looking at mortality rates in fish depending on chemical additions.

There are manipulations of Buffers (2 types), Nutrients (Ca and Mg) and pH. I am comparing to see if mortality rates differ accross treatments so my fist stab at it was to use aov ANOVA in r followed by a TukeyHSD. This revealed some differences relative to the control. I am wondering if this could be visualized a different way. Perhaps as an ordination or a GLM . Here is an example of what I have run so far: Any additional inputs on analyses would be appreciated. I bet I am just overthinking it here. My full RMarkdown Document is here:

The right-hand side of your glm formula needs some attention. If you have 3 factors which can potentially affect your outcome, you should define each of them separately in your data and then include them in your model. Something like this:

glm(Outcome ~ Buffers*Nutrients*pH, ..., data = Data)


where your Data would look like this:

Outcome  Buffers  Nutrients    pH
?      Type1      Ca        6.5
?      Type1      Mg        6.5
?      Type2      Ca        6.5
?      Type2      Mg        6.5
Etc.


It's not clear from your figure whether you have two levels for pH as well?

The formula

Outcome ~ Buffers*Nutrients*pH


implies that the effect of Buffers on the Outcome may be different for different combinations of levels of Nutrients and pH. Similarly, the effect of Nutrients on the Outcome may be different for different combinations of levels of Buffers and pH, etc. In other words, you have a 3-way interaction between the three factors.

You didn't provide enough information about your survival rate outcome to warrant more specific comments on the rest of your glm formula implementation. Do you run several trials for each combination of levels of your 3 factors? What do you measure in each of those trials? How do you use that information to determine the value of your outcome variable?