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 independent two sample t-test 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 ttest_ind() function from the SciPy library to perform an independent two sample t-test:
import pandas as pd
from scipy.stats import 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
Welch’s t-test is similar to the independent two sample t-test, except it does not assume that the two populations that the samples came from have equal variance.
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.stats import 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
Since the p-value is less than .05, we reject the null hypothesis of Welch’s t-test and conclude that there is sufficient evidence to say that the two methods lead to different mean exam scores.
Example 3: Paired Samples t-Test in Pandas
A paired samples t-test 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 ttest_rel() function from the SciPy library to perform a paired samples t-test:
import pandas as pd
from scipy.stats import 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:
How to Perform a Chi-Square Test of Independence in Python
How to Perform a One-Way ANOVA in Python
How to Perform Fisher’s Exact Test in Python