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Some theory behind a Wilcoxon Single Sample T-test

A Wilcoxon single sample t-test or one-sample Wilcoxon ranked test is a nonparametric version of a single sample T-test. However, where a t-test assumes normal distribution, the Wilcoxon does not. Therefore, if your data is particularly a) skewed, b) kurtotic or c) otherwise highly non-normal, and you want to test a single sample, this is the test for you.

In brief, instead of testing a hypothesis against a desired mean the Wilcoxon tests against a desired median. The test is defined as statistically significant if your median falls within the 95% confidence interval for your data. To determine whether this is the case, the data is ranked based on where it falls when the values are ordered. If you are conducting a test manually, you can find the rank of either end of the limit by approximating with a table. When you use Stata it calculates and tests an exact value for you. Once you have a rank for either end of the limit, you count in that many ranks in your data. These values represent the upper and lower end of your confidence interval and if your test value falls in that limit then the result is considered significant.