I'm trying to find an appropriate statistical test to compare the following distributions. I have about 7 million continuous x values, with 3 continuous y values for every x value (from 3 biological replicates). The y values for each x value can be assumed to follow a Gaussian distribution.
The idea is to calculate how "alike" the three graphs are, find a "likeness factor", and subsequently remove data points associated with low x values, and finally recalculate the new "likeness factor".
Is there a statistical test, either parametric or non-parametric, that can be used for this type of analysis? Would it be possible to calculate p values with this test?
Please let me know if I need to provide more information.
to conclude that two samples come from the same distribution you need to test for similar variances (Fisher's F test) and means (t test). You can also do multivariate and nonparametric. But the idea is for them to have similar variances as well as means.
I believe you can also use the "coefficient of overlap" for your purpose, which gives you a measure of the similarity between two distribution patterns.
https://www.jstor.org/stable/20696577?seq=1#metadata_info_tab_contents
As I understand, these graphs are not the histograms of x values, there are only points (x,y) marked on graph. If so, I think that you have two ways. You can use the two-dimensional chi-squared test (as in the one-dimentional case, you should divide your universal set on (rectangular) bins) or you can divide you data into some groups (with respect to x) and use one-way within-subject ANOVA. I would recommend the first way, because the second way is not so accurate as the first one. I think, it can be possible to construct the analogue of the chi-squared test for contingency tables (to check three samples for uniformity simultaneously), but, I think, this work is not very easy.
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