I will be performing my analysis in R but any general mathematical-based answers will be appreciated.
I realize similar questions have been asked before but I am new to statistics so please excuse my ignorance. I do not know enough to be sure that approaches used in other threads I viewed are valid for my case so I would like to be sure.
Here is the context, simplified for those unfamiliar with this kind of data: I am looking at gene expression data. Essentially, I have a number of categories that each have a set of genes in them. Each gene has an associated expression value (amount present in my sample, log2 transformed). I also have three different test conditions (these conditions are completely independent of one another!). What this amounts to is a distribution. As an example:
Biological Process A:
- Contains X genes and their expression levels for Condition 1
- Contains Y genes and their expression levels for Condition 2
- Contains Z genes and their expression levels for Condition 3
I would like to compare these three distributions. By compare I mean that I want to see if there are any large shifts in either the shape or spread of the distribution. EDIT: as Peter has pointed out, what I am really interested in is 1. Location, 2) Spread and 3) Shape with regards to the three distributions under comparison. For example, if Condition 1 moved such that it was almost entirely below the x-axis and Condition 2 was entirely above it, that would be a very interesting shift. Additionally, if two Conditions went above the axis and one went down, this would also be an interesting shift. Essentially, I need a way to compare the distributions for the biggest changes in mean density above or below the x-axis.
I have about 400+ "Biological Processes". The problem is that for some of them, the sample sizes may vary considerably (genes (n) = 3, 25, 10 for the three conditions respectively would be an extreme example in my case) so I do not think simply comparing the means is a fair approach. Visual comparison will take a very long time with 400 beanplots to look at and I would also like some statistics to back up the conclusions I may be making. I want to essentially say something like "Treating tissue with Condition 1 had the effect of increasing expression for most genes known to be involved in Biological Process A".
Additionally, if this approach is invalid or there is a better way to look at this data I would be open to suggestions. Thank you.