I am having a question regarding a statistical analysis I am conducting. Let's say I have a continuous variable that I measure (Plant Weight) and I have 2 factors with 2 levels (sufficient watering/little watering and fertilizer/no fertilizer). One way to look at this would be a model like this: Plant Weight~watering*fertilizer
I could do a Two-Way Anova and depending on the outcome (e.g. significant interaction), I could do a post hoc test to compare all combinations.
Now I've repeatedly seen people who just combined two factors into one grouping variable with 4 levels like this: Treatment A (water/fertilizer),Treatment B (little water/fertilizer), Treatment C (water/no fertilizer).....
This would be a one-way Anova (Plant Weight~Treatment).
Now if I wanted to know something about the overall influence of the main effects of watering and fertilizer scheme on Plant Weight, I should probably go with the Two-Way Anova, but is there, from a statistical point of view, something wrong with the second way? Is it up to me to make that decision, depending on what I am interested in? In my case, I would like to do a post hoc test that allows for heteroscedasticity (for a data set were a weight function was not sufficient to correct it) but can only deal with 1 factor and not with interaction terms. Would it be correct to do a One-Way Anova and compare each Treatment Group to each other (which would give me exactly what I want to know)?