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We have a couple sets of gene expression data (from microarrays) which we are examining to try and determine which sets of genes are significantly and similarly differentially expressed between two time points.

The first data set has triplicate measurements at each of the two relevant time points, and we have created a null distribution by taking the difference between measurements at the same time point for each gene (this yields 6 values that you might expect to see if the gene is not differentially expressed for each gene). We then calculate the p-value for a gene by finding the average of the difference between the measurements at the two time points and finding how many of the values in the null distribution are greater than this average (in absolute value - we are doing a two-tailed test) and dividing by the number of values in the null distribution.

I have seen this method suggested on this site (Calculating p-value from an arbitrary distribution) as a means of calculating p-values, but I have some misgivings. First, since the null distribution we have made is not continuous, several genes could be given the same p-value because their average differential expressions fall between two of the values in the null distribution, even if they are substantially different. Second, all genes with average differential expressions that lie outside the highest absolute value in the null distribution, however slightly, will be given a p-value of 0. Is there some way to form a continuous distribution from the discrete null distribution we have that would solve these problems? I have thought about fitting to a gaussian, but I'm not sure if that is appropriate.

Also, the second data set does not have triplicates, so we can't do the same analysis for it that we did for the first. The two datasets seem to have been measured on different scales, and after normalizing, standardizing, and scaling each of them to between 0 and 1, the peaks of the two distributions of differential expressions between the two time points do not quite line up. Does this mean it would be invalid to use the null distribution obtained from the first dataset to do p-value calculations for the second? Is there something we can do to make it valid?

Thank you for your time.

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