A question about choosing one way ANOVA or two way ANOVA

[Dimothegreat]

Hi,

I have recently encountered a situation where I find choosing an appropriate statistical test quite difficult.

The scenario is: To test the effect of two mutations on a G-protein coupled receptor, the experimenter introduced these mutations in cells and examined the cAMP response after the ligand stimulation. Hence, in total there are four treatment groups:
Control, Mutation 1, mutation 2, and mutation 1 and 2 combined.

The question is, shall we consider these groups as four separate treatments and use one-way ANOVA, or shall I consider these as the combination of two treatments (the presence of mutation 1 and the presence of mutation 2), and use two way ANOVA?

Many thanks in advance.

[valegiunchiglia]

Hi! I am not 100% sure to be honest. Let's see if somebody else has a different opinion. I think I would do a two way ANOVA and consider "Mutation 1" and "Mutation 2" as the two independent variables, and cAMP response as the dependent one. In addition, I would add an interaction effect in the model, in this way you can see whether there is an interaction between the variable in Mutation 1 and 2. So for example if you use R, it would look like something like this:

test = aov(amp ~ mutation1 * mutation2, data = my_data)

Where mutation2 and mutation1 are two columns of the dataframe my_data. This would give you information both about mutation1 and 2 alone, and their interaction. Then I would plot an interaction plot to see how the interaction between the two mutations affect cAMP response.

Remember to check if your data satisfy the two assumptions of the ANOVA, which are that the residuals are normally distributed and that the variance across groups is homogeneous. To check the normality you can use a Q-Q plot and shapiro test, and to check the homogeneity you can use the Levene's test. If the assumptions are not satisfied then your results might not be reliable.

This is at least my thought, but let's see what other think!