Best statistical test for a particular biological experiment I have run an experiment in which I measure the expression of a particular gene under three different medium conditions (neutral,ATPlo,ATPhi). We took samples who have two different genotypes for a particular SNP (AA,AG).
What I would like to show is that for samples with the AA genotypes the medium has an effect on the expression of the gene while for samples with the AG genotype there is no effect.
Which is the best test to prove this?
If I do an Anova for samples with genotype AA considering the medium as a factor I get a significant pvalue. If I do Anova for samples with genotype AG the pvalue is not significant. If I do a two-way Anova(medium/genotype) with interaction effects the genotype is the only variable that comes up significant.
What can I conclude about my hypothesis? Are there other tests which are more appropriate?
 A: Assuming you have sufficient biological and technical replicates that you have not mentioned, a regression analysis should be sufficient. If you have a one-off experiment you are unlikely to get any robust results due to the natural variance associated with this type of experiment.
There are 2 ways I would go about this, given enough statistical power. The second option will require a larger sample size, but will give 'better' results (the exact size will be specific to your experiment and methods).
Option 1: Stratified Linear Regression
Perform a stratified analysis - first analyze the cells with genotype AA, then with genotype AG, with expression of your gene as the outcome and the type of media as a factor variable. In this way you can see the effect of the 2 ATP media compared to the 'neutral' media, assuming that the neutral media is coded as the bottom, or lowest, category.
By then comparing the associations between the expression and media in the separate genotypes you could determine if the expression was more associated with the media type in the AA or AG cells.
Option 2: Instrumental Variable Analysis
Again using a linear regression, you can determine the variance in the gene expression data that is determined by the genotype. To do this simply use a linear regression with the expression as the outcome, and the genotype as the only independent variable. Extracting the 'fitted values' from the model gives the predicted expression using only the genotype.
This variable you have now extracted can be used as the new outcome in a linear model, again with the media-type as an explanatory factor variable. This model shows you the association between each ATP media-type (compared to the neutral media) and the expression variance caused by the genotype. If this association is significant, there is a causal association between the genotype and the expression, in the context of the different media.
