The Shapiro-Wilk test is a test of normality that assesses whether a sample is likely to originate from a normal distribution. Verifying normality of distribution is a requirement for running several of the well-known statistical tests such as Student’s t-test and ANOVA.

In this test, the null hypothesis H0 states that the sample comes from a normally distributed population.

The function to use in R is shapiro.test() and the syntax is shapiro.test(sample) where sample is the vector containing the data.

Let’s take an example where we measured the size of blue ground beetles (Carabus intricatus) at a given location. Here is the code for the vector containing the data:

# sample data
size <- c(25,22,28,24,26,24,22,21,23,25,26,30,25,24,21,27,28,23,25,24,20,22,24,23,22,24,20,19,21,22)

To visualize the distribution of the sample, we may use a Q-Q plot with a quantile-quantile line:

The rather good alignment of the dots in this plot shows that the distribution is close to normality, but this needs to be verified with a test.

Running the test

We use shapiro.test() the following way:

shapiro.test(size)

## 
##  Shapiro-Wilk normality test
## 
## data:  size
## W = 0.97168, p-value = 0.586

Apparently, the p-value is rather high, well over 0.05. The null hypothesis H0 is NOT rejected, meaning that the sample is very likely to be normally distributed.

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