**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 R. 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 R, and generate a box plot. Let’s assume we’re measuring IQ for 1,000 subjects.

iq2 <- runif(1000, min=90, max=140)

iq <- round(iq2, digits = 0)

**Test for Normality**

We’ll use the Shapiro-Wilk test to assess normality of IQ distribution in the sample, then create a histogram:

shapiro.test(iq)

The null hypothesis for the Shapiro-Wilk test is normal distribution. The null hypothesis is rejected, *W* = .95266, *p *< .0001, 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:

hist(iq)

**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 is significantly different from a test value, mu. Let's pick 105 as our mu.

Now we enter the following code:

results <- wilcox.test(iq, mu = 105)

results

The null hypothesis is that the true location is equal to 105. Because *p *< .0001, we reject the null, meaning that the true location is significantly different from 105.

**Graphic Support**

Finally, let’s create a box plot from these data:

boxplot(iq,

main = "IQ",

ylab = "Number of people",

col="lightsteelblue1",

border="black"

)

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