Statistical testing for significant difference in means across multiple groups

Question

I apologize in advance for the redundancy of my post (I've seen many other posts asking almost the same thing), but I am not familiar with statistical terminology which makes efficiently searching past posts difficult. Also, the nature of my data is slightly different than other examples and I'm unsure whether or not that makes the answers applicable to my scenario.

I have a dataset of genetic expression values for several genes, across many different human tissues. This is what it looks like:

  gene      tissue1    tissue2   
1 gene_A     170.20     466.25
2 gene_B       6.50       9.05
3 gene_C      16.40      17.75
4 gene_D      13.90      30.50
5 ...

Each value in the tissue columns is actually an average of several samples but I do not have data for those individual samples.

I want to determine which genes have the most statistically significant difference in expression between tissue1 and tissue2. Which statistical test is most appropriate here? What cautions should I keep in mind with that test?

Answer 1

I think there is not enough information for the test of significance you want to do. As you said, we don't have information about the individual samples (sample size, variance, etc.). Besides, I think the expression "most statistically significant difference" is not appropriate. If we are talking about interpreting p-values, it is better to say statistically significant or not. If you had the information, you could have run a series of t-tests for the significance of difference (of means) between tissues for each gene, then calculated effect sizes (e.g., Cohen's ds) and compared them (after adjusting for the bias). At this point, I can only think of reporting the magnitude of difference between tissues for each gene.

Answer 2

This is not possible. The best you can do is compute the difference in means for each gene, but in a new tissue sample this difference may be of a different size.

This means there is a variance attached to the difference in means and you would need to know (or estimate) the size of this variance to be able to identify the genes with the strongest effect size (or lowest p-values, for example).

I can think of one helpful alternative analysis. You could try to cluster the genes into $k$ groups based on the two tissue samples. This would help you to identify groups of genes that on average differ.