Shapiro Test

The Shapiro Test is a statistical test that is used to test the hypothesis of a normal distribution. It compares the distribution of the data with a normal distribution.

The null hypothesis assumes that the data are normally distributed. If the p-value is below the significance level (below 0.05), then the null hypothesis is rejected.

In such a case, we can argue that the data is not normally distributed (the alternative hypothesis is accepted).

Let's run the Shapiro Test for the first columns from the control and test groups at the same time:


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# Import libraries 
import pandas as pd
from scipy.stats import shapiro

# Read .csv files
df_control = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/c3b98ad3-420d-403f-908d-6ab8facc3e28/ab_control.csv', delimiter=';')
df_test = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/c3b98ad3-420d-403f-908d-6ab8facc3e28/ab_test.csv', delimiter=';')

# Do the Shapiro test for the control sample
stat_control, p_control = shapiro(df_control['Impression'])
print('Control group: ')
print('Stat: %.4f, p-value: %.4f' % (stat_control, p_control))

# Define the distribution form
if p_control > 0.05:
  print('Control group is likely to normal distribution')
else:
  print('Control group is NOT likely to normal distribution')
  
# Do the Shapiro test for the test sample
stat_test, p_test = shapiro(df_test['Impression'])
print('Test group: ')
print('Stat: %.4f, p-value: %.4f' % (stat_test, p_test))

# Define the distribution form
if p_test > 0.05:
  print('Control group is likely to normal distribution')
else:
  print('Control group is NOT likely to normal distribution')

Great! We got two results.

The higher the Statistic value, the more evidence is found in favor of a normal distribution. The p-value in both groups is high (greater than 0.05), which means we accept the null hypothesis.

Both columns are normally distributed.

Note
If we have more than 5 000 observations, it is better to use the Kolmogorov-Smirnov test. Its use is similar to the Shapiro test.

Everything was clear?

Thanks for your feedback!

Section 2. Chapter 7