The following examples show how to perform three different t-tests using a pandas DataFrame:

• Independent Two Sample t-Test
• Welch’s Two Sample t-Test
• Paired Samples t-Test

Example 1: Independent Two Sample t-Test in Pandas

An is used to determine if two population means are equal.

For example, suppose a professor wants to know if two different studying methods lead to different mean exam scores.

To test this, he recruits 10 students to use method A and 10 students to use method B.

The following code shows how to enter the scores of each student in a pandas DataFrame and then use the function from the SciPy library to perform an independent two sample t-test:

import pandas as pd
from scipy.statsimport ttest_ind

#create pandas DataFrame
df = pd.DataFrame({'method': ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A',
                              'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'],
                   'score': [71, 72, 72, 75, 78, 81, 82, 83, 89, 91, 80, 81, 81,
                             84, 88, 88, 89, 90, 90, 91]})

#view first five rows of DataFrame
df.head()

  method  score
0      A     71
1      A     72
2      A     72
3      A     75
4      A     78

#define samples
group1 = df[df['method']=='A']
group2 = df[df['method']=='B']

#perform independent two sample t-test
ttest_ind(group1['score'], group2['score'])

Ttest_indResult(statistic=-2.6034304605397938, pvalue=0.017969284594810425)

From the output we can see:

• t test statistic: –2.6034
• p-value: 0.0179

Since the p-value is less than .05, we reject the null hypothesis of the t-test and conclude that there is sufficient evidence to say that the two methods lead to different mean exam scores.

Example 2: Welch’s t-Test in Pandas

is similar to the independent two sample t-test, except it does not assume that the two populations that the samples came from have .

To perform Welch’s t-test on the exact same dataset as the previous example, we simply need to specify equal_var=False within the ttest_ind() function as follows:

import pandas as pd
from scipy.statsimport ttest_ind

#create pandas DataFrame
df = pd.DataFrame({'method': ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A',
                              'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'],
                   'score': [71, 72, 72, 75, 78, 81, 82, 83, 89, 91, 80, 81, 81,
                             84, 88, 88, 89, 90, 90, 91]})

#define samples
group1 = df[df['method']=='A']
group2 = df[df['method']=='B']

#perform Welch's t-test
ttest_ind(group1['score'], group2['score'], equal_var=False)

Ttest_indResult(statistic=-2.603430460539794, pvalue=0.02014688617423973)

From the output we can see:

• t test statistic: –2.6034
• p-value: 0.0201

Example 3: Paired Samples t-Test in Pandas

A is used to determine if two population means are equal in which each observation in one sample can be paired with an observation in the other sample.

For example, suppose a professor wants to know if two different studying methods lead to different mean exam scores.

To test this, he recruits 10 students to use method A and then take a test. Then, he lets the same 10 students used method B to prepare for and take another test of similar difficulty.

Since all of the students appear in both samples, we can perform a paired samples t-test in this scenario.

The following code shows how to enter the scores of each student in a pandas DataFrame and then use the function from the SciPy library to perform a paired samples t-test:

import pandas as pd
from scipy.statsimport ttest_rel

#create pandas DataFrame
df = pd.DataFrame({'method': ['A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'A',
                              'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'],
                   'score': [71, 72, 72, 75, 78, 81, 82, 83, 89, 91, 80, 81, 81,
                             84, 88, 88, 89, 90, 90, 91]})

#view first five rows of DataFrame
df.head()

  method  score
0      A     71
1      A     72
2      A     72
3      A     75
4      A     78

#define samples
group1 = df[df['method']=='A']
group2 = df[df['method']=='B']

#perform independent two sample t-test
ttest_rel(group1['score'], group2['score'])

Ttest_relResult(statistic=-6.162045351967805, pvalue=0.0001662872100210469)

From the output we can see:

• t test statistic: –6.1620
• p-value: 0.0001

Since the p-value is less than .05, we reject the null hypothesis of the paired samples t-test and conclude that there is sufficient evidence to say that the two methods lead to different mean exam scores.

Additional Resources

The following tutorials explain how to perform other common tasks in Python: