Shapiro-Wilk Test in Python
Introduction
The Shapiro-Wilk test is a statistical test used to determine whether a dataset follows a normal distribution. It is based on the null hypothesis that the population is normally distributed. This test is commonly used in many fields, including finance, biology, and social sciences, to assess the normality assumption before applying certain statistical techniques.
In this article, we will explore how to perform the Shapiro-Wilk test using Python and understand its interpretation.
Shapiro-Wilk Test in Python
To perform the Shapiro-Wilk test in Python, we can use the shapiro() function from the scipy.stats module. First, let's install the necessary package using pip:
pip install scipy
Once installed, we can import the required function and proceed with the test. Suppose we have a dataset called data that we want to test for normality:
from scipy import stats
data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
stat, p = stats.shapiro(data)
print("Test Statistic:", stat)
print("p-value:", p)
The shapiro() function returns two values: the test statistic and the p-value. The test statistic is a measure of how well the data fits the normal distribution, and the p-value represents the probability of obtaining the observed data if the null hypothesis of normality is true.
Interpretation
Once we have performed the Shapiro-Wilk test, we can interpret the results based on the p-value. Here are some guidelines:
- If the p-value is greater than the significance level (commonly set at 0.05), we fail to reject the null hypothesis and conclude that the data is normally distributed.
- If the p-value is less than the significance level, we reject the null hypothesis and conclude that the data is not normally distributed.
Let's add the interpretation to our code:
alpha = 0.05
if p > alpha:
print("Data follows a normal distribution (fail to reject H0)")
else:
print("Data does not follow a normal distribution (reject H0)")
In our example, suppose the test statistic is 0.977 and the p-value is 0.784. Since the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the data follows a normal distribution.
Conclusion
The Shapiro-Wilk test is a powerful tool to assess the normality assumption of a dataset. By performing this test, we can determine whether the data follows a normal distribution, which is crucial for applying certain statistical techniques. Python provides a convenient and easy-to-use function in the scipy.stats module to perform the Shapiro-Wilk test. Remember, the interpretation of the test results is based on the p-value and the significance level.
