Making box plots when analyzing a case with 3 predictor variables? When there are 3 predictor variables to consider, what is the correct procedure?
Do we make box plots for all the possible 2 combinations or is there a way to compare 3 variables?
Sorry if this is a basic question.
The response is uranium response and there are 3 predictor variables: time, temp, and acid strength. All 3 predictor variables have 3 levels, low, medium, high. I would like to try to run a 3-way ANOVA analysis on the data set, it's an exercise question for a class, but not too sure how to start, so I'm using box plots to see how the data looks like first.
 A: So I understand that your DV is numerical and your 3 IVs are categorical (3 levels). Boxplots is a good choice. You will have 9 boxplots, 3 for each IV.
Plot each IV separately. On the y axis will always be the DV (uranium). On the x-axis will the the IVs. For example, temp low, temp med, temp high. Do this for all 3 IVs. 
If you want to look at the interaction between the IVs, plots will be more complicating (as will be your analysis). There's no easy way. You're just going to have to divide up the data into 6 when looking at 2 IVs, and 9 when looking at all 3 at once, and make boxplots for each. I don't suggest you do this. Given your skill level and because it is for a class, looking at one IV at a time is probably good enough.
A: Thanks for the clarification. You can capitalize on the paneling and clustering designs and put together a compact boxplot like this:

The boxplot will be useful for assessing group-wise distribution and outliers. However, since it's an ANOVA, I'd also recommend visualize the mean and 95% CI as well using error plot:

By comparing and contrasting the positions of each mean and CI across panels and across clusters, one may gain a bit more insight on what the interactions between the group means will be like.
Start from just two variables (uranium vs. temperature, uranium vs. time, etc.) and the build up from there. If your class has not covered interaction yet, then I'd suggest asking the instructor if he/she will allow you to experiment.
A: Here's the '9x boxplot' approach in R:
### make reproducible
set.seed(1)
pred1 <- factor(c("low", "med", "high"), levels=c("low", "med", "high"))
df1 <- data.frame(ur=10*abs(runif(100)),
                  time=sample(pred1, 100, replace=TRUE),
                  temp=sample(pred1, 100, replace=TRUE),
                  str=sample(pred1, 100, replace=TRUE)
                  )
library(ggplot2)
g1 <- ggplot(data=df1, aes(y=ur, x=time, fill=time))
g1 + geom_boxplot() +
 facet_grid(facets = str ~ temp, scale="free_y", labeller=label_both)

giving:

(Note y-axis scales vary per row).
