Introduction
A one-sample Wilcoxon signed rank test is applied when you are measuring values of a single variable that you are comparing to some test mean and when this variable is not normally distributed. In this blog entry, we’ll show you how to conduct a one-sample Wilcoxon signed rank test in Stata. You’ll also learn how to test for normalcy of distribution and create a 95% confidence interval graph for your data.
Create Data
First, we’ll create mock data, then we’ll show you how to test their normality, conduct a one-sample Wilcoxon signed rank test in Stata, and generate a 95% CI plot. Let’s assume we’re measuring IQ for 1,000 subjects.
set obs 1000
gen subj = _n
label variable subj "Subject"
gen iq_a = runiform(90,140)
gen iq = round(iq_a)
drop iq_a
label variable iq "IQ"
list in 1/30
Test for Normality
We’ll use the Shapiro-Wilk test to assess normality of IQ distribution in the sample, then create a histogram:
swilk iq
hist iq, freq scheme(s1color)
The null hypothesis for the Shapiro-Wilk test is normal distribution. The null hypothesis is rejected, W = .95838, p < .00001, so we cannot assume normal distribution (if the distribution had been normal, we could have attempted a one-sample t-test). The histogram demonstrates the non-normality of the distribution as well:
We can use sktest to separately assess for normality of skewness, kurtosis, and skewness and kurtosis:
sktest iq
Skewness is normal, but kurtosis and joint kurtosis and skewness are not.
The One-Sample Wilcoxon Signed Rank Test
Now let’s run the one-sample Wilcoxon signed rank test. We want to check if the sample median differs significantly from 105, so we type:
signrank iq = 105
By the way, you can get the sample median through:
sum iq, det
Here’s what we get after the signrank command:
Note that you get the asymptotic p value because of the large sample size, so you can also try:
signrank iq = 105, exact
We reject the null hypothesis that 105 is not significantly different from the sample median of 115, z = 17.05, p < .0001.
Graphic Support
Finally, let’s illustrate the sample mean and 95% CI:
ciplot iq, scheme(s1color)
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