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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.

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  • $\begingroup$ What is your sample size? $\endgroup$
    – Peter Flom
    Jan 30 at 13:38
  • $\begingroup$ 800 in group one and 200 on group 2 $\endgroup$ Jan 30 at 13:46
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    $\begingroup$ If your question is about RNA Seq, it would be more fitting for the Biology community. $\endgroup$
    – CaroZ
    Jan 30 at 14:06
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    $\begingroup$ @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. $\endgroup$ Jan 30 at 14:16
  • $\begingroup$ RNASeq is pretty specific, there is no general cure against acquiring a huge amount of data and then struggling to analyse it. $\endgroup$
    – CaroZ
    Jan 31 at 16:22

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It looks to me like you are trying to analyse RNAseq data, am I wrong ? You should not use t-tests. The distribution of read counts is usually negative binomial.

This is why DESeq2 would fit one glm per gene you have. You should read more about it here. You can specify the group as a factor, in order to have your answer to as to whether which genes are significantly up or downregulated according to the group.

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  • $\begingroup$ Yes this is what I need to do in a broad sense. Sounds very interesting thank you! In general people come with very high dimensional data and then hope that we'll know an easy way to find meaningful differences between groups, or even find the groups. It's all just quite confusing so this reference looks very interesting. Can you elaborate on how do I interpret the outputs of the glms to find which genes in fact contribute to the difference between groups? $\endgroup$ Jan 30 at 14:14
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    $\begingroup$ Yes, this is typical of RNASeq. If you have experience with any kind of glms, you will understand the output. Maybe give it a try and let us know if you need more information ? DeSEQ2 will literally fit on glm pr gene and tell you the log2 fold change in gene expression between the groups, as well as whether the difference is significant or not after correction for the (very) multiple comparisons. $\endgroup$
    – CaroZ
    Jan 30 at 14:16

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