I have two vectors of normalized data values representing two paired conditions ("methylation" and "expression"). A scatterplot of my data looks like this:
I'd like to know if I am using the Wilcoxon signed-rank test correctly in order to answer some questions. Specifically, I would like to identify those data points whose difference differs significantly from the median.
The p-value that
wilcox.test() reports in R suggests that the alternative hypothesis is true (that the median of the difference of the two conditions is not zero, or that H0 fails):
> wilcox.test(mtx$methylation_difference_normalized, mtx$expression_difference_normalized, alternative = "two.sided", paired = TRUE, exact = FALSE, correct = TRUE, conf.int = TRUE, conf.level = 0.95) V = 57049625, p-value < 2.2e-16 alternative hypothesis: true location shift is not equal to 0 95 percent confidence interval: 0.2722975 0.3382661 sample estimates: (pseudo)median 0.3250247
Assuming this is the case, is the confidence interval that is reported usable for identifying points in the scatterplot which are significant?
Given this result, for example, can I simply take the (absolute?) difference of any pair of observations, and if that difference falls outside this interval, do I identify that data point as statistically significant?
Failing that, is there another test I should be using instead to accomplish the same task?