I'm predicting that certain genes (n=20) are more GC rich than expected in all protein-coding genes. How can I test this hypothesis efficiently?
I generated the same number of random genes (also n=20) and calculated GC content for them. After using the t-test (2-tailed, two-sample unequal variance) it shows a significant P < 0.005 result. But I'm not sure that I can interpret it with high confidence.
You could try a permutation test. These are a kind of non-parametric statistical test which involve creating your own null distribution from your data.
Your hypothesis $H_{1}$ in this case, is that your gene set has a higher GC content than expected by chance. Similarly, your null hypothesis, $H_{0}$ is that there is there is no difference between your set a random set of gene from the population. You are interested in a p-value, which simply asks what the probability of obtaining a test result at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct.
So thus to obtain a p-value and take say, 1000 random samples of protein-coding genes and calculate their GC content to obtain a null distribution. Then to obtain a p-value that your gene set has a higher GC content than expected under the null, take the proportion of the null distribution greater than your gene set.
I feel you should be comparing your 20 genes against all other protein coding genes in the same organism.
A statistical test comparing the proportion of GC nucleotides in your sample to the rest may be the one to use.
