# Comparing two groups by the counts of their features

Imagine there are two different groups of individual samples. I know they are different but I don't know why. For example in biology a group of sick individuals and a group of healthy ones.

Now for each individual in the group there is a set of features, let's imagine there are 100 features where each is independent and represents a count of something. So there are features F_0 to F_n.

Each individual in each group has it's 100D feature vector associated.

1. What would be the best way of telling which of these features is significantly different between the groups?

2. Now imagine that some features have different distributions. All I know is that each feature is higher than 0 but it's basically unbounded. For example, F_0 in both groups is extremely large for both groups, say its value is around 1e6 while F_1 the values are around 1e2. Would it matter?

Someone suggested to do pairwise t-tests, like F_0_g1 with F_0_g2 and then do a bonferroni correction. But I don't really know if I am being correct or not.

Could anyone out there shine a light on this?

Background:

If anyone is interested. The groups I am trying to compare are indeed biological groups. And the features are what's called gene expression, F_n are genes. Genes are related to the function and morphology of diseases. So from a statistical point of view it is basically comparing two groups where each individual in each group has different features and there's a difference but the research questions always try to look for the details of these differences. In the biological world people tend to play a bit fast and lose with their statistics but I want to understand what I am doing.

• What is your sample size? Jan 30 at 13:38
• 800 in group one and 200 on group 2 Jan 30 at 13:46
• If your question is about RNA Seq, it would be more fitting for the Biology community. Jan 30 at 14:06
• @CaroZ the issue with this is that the application community rarely verifies that the data complies with the requirements of models. I am looking for more general solutions. There are similar problems in other fields and I would like to know more ways to tackle them taking into account data properties and different models. Jan 30 at 14:16
• RNASeq is pretty specific, there is no general cure against acquiring a huge amount of data and then struggling to analyse it. Jan 31 at 16:22