Comparing numbers of p-values from many linear models

Question

My current dataset has three conditions, and we've measured the activity levels of 10,000 genes in each condition. Replicated 8 times.

Using 10,000 linear models, we determine for each pair of conditions (ie for each of three contrasts) the number of genes with significantly different activity levels. This is standard procedure for this kind of microarray data.

We find:

• 2000 genes have significantly different activity levels between A and B
• 1500 genes have significantly different activity levels between A and C
• 100 genes have significantly different activity levels between B and C

This suggests that conditions B and C are more similar to each other than to C. PCA suggests the same result. Is there any way for us to quantify the extent to which "conditions B and C are more similar to each other than to C (ie to put a p-value on it?)

Thanks for your help, and apologies if this question is trivial.

Kind regards,

Answer 1

Prior to answering your question - is the distribution of effect of the genes justify using a linear model (e.g: are they distributed more or less normally?)

Now to your question - I might offer to go a different way about it. It sounds like what you are asking for is to measure the correlation (e.g similarity of behavior) between the different conditions. A simple way to do that is to take the mean (or maybe the trimmed mean or median) of the 8 replications and then you'd have 10K triplets you can use for creating a correlation matrix (between the 3 conditions).

The second step would then be to answer the question if one correlation (say between A and B) is significantly higher then the other two correlations (say, between --A and C-- and --B and C--). Here you can use the following nice online tool or you can code it yourself in R using the information given here.

Cheers, Tal