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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?

Thanks!

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)

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  • $\begingroup$ Without having original data, you must trust your distribution assumptions. But the sample sizes looks very large ... so if you are willing to trust the CLT (central limit theorem) you can just calculate z-scores, that is, treat as normal distributed. More critical will be: Can you really assume independence? Are the means from time series, what are they? You need to tell us! $\endgroup$ Jul 29 at 16:19
  • $\begingroup$ Thanks! I've amended the question to include more information about what these data represent, is there anything else crucial I'm missing? $\endgroup$
    – Absolome
    Jul 30 at 15:12

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