# How to compare a new measurement against an existing null distribution?

I have a dataset that describes the distances between two identical genes in two replicate experiments (gene a in rep1 vs gene a in rep 2). Let us assume that due to biological variation, the distance between the genes of two replicates should be small, but not necessarily zero. Thus from what I can understand, this dataset would represent a null distribution.

I want to use these samples of observations to get an idea of what constitutes a 'non-significant' distance between two genes.

Ultimately, I want to be able to take two different genes, calculate their distance, and estimate how 'significant' the resulting distance metric is (e.g. is the distance similar to the to those in my replicate dataset or is it very different).

What is a reasonable approach to do this type of analysis / hypothesis testing?

EDIT:

I have carried out a series of biological experiments where the output of the experiment is a N x N matrix of counts. I then created a custom distance metric that takes in two rows of counts and calculates the 'difference' between them (I will call this difference metric D). I calculated D for all pairwise comparisons and now have an array of difference metrics D called D_array.

My assumption based on biology is that the majority of D in D_array represent that there is no significant difference between the two rows of counts and only the >= 95% interval of D metrics actually represent real differences between two rows of counts. Let us assume that this is true, even if it doesn't make sense.

So this means if D_array = [0, 1, 2, 3, 4 ... 99] (100 metrics) then only a D score of 95-99 are actually representative of a real difference between two rows of counts.

Note: D_array is not representative of my data. My actual data actually has a distribution of values like this (black line represents the mean): https://i.stack.imgur.com/XFFY4.jpg

Given D_array I want to be able to determine whether a newly calculated distance value D' is "significant" based on my previous data: the distribution of my D_array. Ideally, I would like to provide some sort of metric of 'significance' such as a p-value. By significance I mean the probability / significance of having gotten a result as extreme as D'.