The Shapiro-Wilk test is a test of normality. It is used to determine whether or not a sample comes from a normal distribution.
To perform a Shapiro-Wilk test in Python we can use the scipy.stats.shapiro() function, which takes on the following syntax:
scipy.stats.shapiro(x)
where:
- x: An array of sample data.
This function returns a test statistic and a corresponding p-value.
If the p-value is below a certain significance level, then we have sufficient evidence to say that the sample data does not come from a normal distribution.
This tutorial shows a couple examples of how to use this function in practice.
Example 1: Shapiro-Wilk Test on Normally Distributed Data
Suppose we have the following sample data:
from numpy.random import seed from numpy.random import randn #set seed (e.g. make this example reproducible) seed(0) #generate dataset of 100 random values that follow a standard normal distribution data = randn(100)
The following code shows how to perform a Shapiro-Wilk test on this sample of 100 data values to determine if it came from a normal distribution:
from scipy.stats import shapiro #perform Shapiro-Wilk test shapiro(data) ShapiroResult(statistic=0.9926937818527222, pvalue=0.8689165711402893)
From the output we can see that the test statistic is 0.9927 and the corresponding p-value is 0.8689.
Since the p-value is not less than .05, we fail to reject the null hypothesis. We do not have sufficient evidence to say that the sample data does not come from a normal distribution.
This result shouldn’t be surprising since we generated the sample data using the randn() function, which generates random values that follow a standard normal distribution.
Example 2: Shapiro-Wilk Test on Non-Normally Distributed Data
Now suppose we have the following sample data:
from numpy.random import seed from numpy.random import poisson #set seed (e.g. make this example reproducible) seed(0) #generate dataset of 100 values that follow a Poisson distribution with mean=5 data = poisson(5, 100)
The following code shows how to perform a Shapiro-Wilk test on this sample of 100 data values to determine if it came from a normal distribution:
from scipy.stats import shapiro #perform Shapiro-Wilk test shapiro(data) ShapiroResult(statistic=0.9581913948059082, pvalue=0.002994443289935589)
From the output we can see that the test statistic is 0.9582 and the corresponding p-value is 0.00299.
Since the p-value is less than .05, we reject the null hypothesis. We have sufficient evidence to say that the sample data does not come from a normal distribution.
This result also shouldn’t be surprising since we generated the sample data using the poisson() function, which generates random values that follow a Poisson distribution.
Additional Resources
The following tutorials explain how to perform other normality tests in various statistical software:
How to Perform a Shapiro-Wilk Test in R
How to Perform an Anderson-Darling Test in Python
How to Perform a Kolmogorov-Smirnov Test in Python