I'm in a situation where I have two (equally long) lists of means, with sample sizes and stderr for each mean. The variance for these means are all variable and different, and so are the sample sizes. Here's an example of 3 random positions:
x1: [0.205404 0.164482 0.178328] x1_n: [284507 284690 283342] x1_stderr: [0.10421694 0.06447948 0.06529081] x2: [0.89220201 0.37634269 1.41769034] x2_n: [244332 250842 257166] x2_stderr: [0.0520862 0.02368293 0.04494423]
In which x1 and x2 are the lists of means, (x1/x2)_n are the lists of sample sizes, and (x1/x2)_stderr are the lists of standard errors.
I need to determine, for each position on these lists, whether the values at that position in either list are significantly different to a given confidence level or not. I can't simply compare the entire lists to each other as a whole, because what I'm looking for is where these two datasets are significantly different from each other (and where they are not). What I'd like to end up with is a list of boolean values that indicate whether any given position on these lists is significantly different (a 'True' value) or not (a 'False' value).
What would be a good way to go about testing these values, given that I already have values for standard error for each position and that I'm comparing only two means without knowing the underlying specific data values?
And, as a small followup- do I need to perform any sort of multiple testing corrections while I am testing these data for significance?
PS: I'm working with these values in Python, if that matters.
Edit (thanks kjetil b halvorsen): I should probably give more info about what these data represent:
x1 and x2 are two different RNAs, the values are information about specific positions in those RNAs. The RNAs are from the same gene, but in different species, and the measurements of x1 and x2 were taken independently of each other, and so I believe qualify as independent. I am trying to determine if the RNAs are significantly different from each other in this specific value at a single-base resolution.
n here represents sequencing depth for the reads at that base in the RNA (so the number of times we measured at that position)