How to Perform a Two-Way ANOVA in Python

Last Updated : 28 Feb, 2022

Two-Way ANOVA: Two-Way ANOVA in statistics stands for Analysis of Variance and it is used to check whether there is a statistically significant difference between the mean value of three or more that has been divided into two factors. In simple words, ANOVA is a test conducted in statistics and it is used to interpret the difference between the mean value of at least three groups. The main objective of a two-way ANOVA is to find out how two factors affect a response variable and to find out whether there is a relation between the two factors on the response variable.

Syntax to installs pandas and NumPy libraries in the system:

pip3 install numpy pandas

Performing a Two-Way ANOVA in Python:

Let us consider an example in which scientists need to know whether plant growth is affected by fertilizers and watering frequency. They planted exactly 30 plants and allowed them to grow for six months under different conditions for fertilizers and watering frequency. After exactly six months, they recorded the heights of each plant centimeters. Performing a Two-Way ANOVA in Python is a step by step process and these are discussed below:

Step 1: Import libraries.

The very first step is to import the libraries installed above.

Python3

# Importing libraries 
import numpy as np 
import pandas as pd

Step 2: Enter the data.

Let us create a pandas DataFrame that consist of the following three variables:

fertilizers: how frequently each plant was fertilized that is daily or weekly.
watering: how frequently each plant was watered that is daily or weekly.
height: the height of each plant (in inches) after six months.

Example:

Python3

# Importing libraries 
import numpy as np 
import pandas as pd 
  
# Create a dataframe 
dataframe = pd.DataFrame({'Fertilizer': np.repeat(['daily', 'weekly'], 15), 
                          'Watering': np.repeat(['daily', 'weekly'], 15), 
                          'height': [14, 16, 15, 15, 16, 13, 12, 11, 14,  
                                     15, 16, 16, 17, 18, 14, 13, 14, 14,  
                                     14, 15, 16, 16, 17, 18, 14, 13, 14,  
                                     14, 14, 15]}) 

Step 3: Conduct the two-way ANOVA:

To perform the two-way ANOVA, the Statsmodels library provides us with anova_lm() function. The syntax of the function is given below,

Syntax:

sm.stats.anova_lm(model, type=2)

Parameters:

model: It represents model statistics

type: It represents the type of Anova test to perform that is { I or II or III or 1 or 2 or 3 }

Python3

# Importing libraries 
import statsmodels.api as sm 
from statsmodels.formula.api import ols 
  
# Performing two-way ANOVA 
model = ols( 
    'height ~ C(Fertilizer) + C(Watering) +\ 
    C(Fertilizer):C(Watering)', data=df).fit() 
sm.stats.anova_lm(model, typ=2) 

Step 4: Combining all the steps.

Example:

Python3

# Importing libraries 
import statsmodels.api as sm 
from statsmodels.formula.api import ols 
  
# Create a dataframe 
dataframe = pd.DataFrame({'Fertilizer': np.repeat(['daily', 'weekly'], 15), 
                          'Watering': np.repeat(['daily', 'weekly'], 15), 
                          'height': [14, 16, 15, 15, 16, 13, 12, 11, 
                                     14, 15, 16, 16, 17, 18, 14, 13,  
                                     14, 14, 14, 15, 16, 16, 17, 18, 
                                     14, 13, 14, 14, 14, 15]}) 
  
  
# Performing two-way ANOVA 
model = ols('height ~ C(Fertilizer) + C(Watering) +\ 
C(Fertilizer):C(Watering)', 
            data=dataframe).fit() 
result = sm.stats.anova_lm(model, type=2) 
  
# Print the result 
print(result) 

Output:

Output

Interpreting the result:

Following are the p-values for each of the factors in the output:

The fertilizer p-value is equal to 0.913305
The Watering p-value is equal to 0.990865
The Fertilizer * Watering: p-value is equal to 0.904053

The p-values for water and sun turn out to be less than 0.05 which implies that the means of both the factors possess a statistically significant effect on plant height. The p-value for the interaction effect (0.904053) is greater than 0.05 which depicts that there is no significant interaction effect between fertilizer frequency and watering frequency.

Suggest improvement

How to Perform a Shapiro-Wilk Test in Python

How to Create a Pie Chart in Seaborn?

Share your thoughts in the comments