# Is the Wilcoxon paired rank test appropriate for this data?

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?

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The p-value the wilcox.test() reports states the probability of finding data as extreme or more extreme than yours, IF the null hypothesis is true, nothing else. Specifically, it does not suggest "that the alternative hypothesis is true". I'm sorry for being a little pedantic, but it's important to be clear on exactly what statistical significance means. – gung Nov 1 '12 at 23:32
if that difference falls outside this interval, do I identify that data point as statistically significant? Statistical tests usually are about all data points as a whole because they test hypotheses about populations. How do you imagine each separate point to refer to a population on its own? – ttnphns Nov 2 '12 at 9:12