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One-way ANCOVA

tags: #statistics/inferential/anova/one_way

Running One-Way ANCOVA

Option 1: pingouin

We can run a one-way ANCOVA using the ancova() function from pingouin module:

from pingouin import ancova

To run one-way ANCOVA with one covariate:

# Run ANCOVA analysis with one covariate 
ancova(dv='dependent_variable', between='independent_variable', covar='covariate', data=df)

To run a one-way ANCOVA with more than one covariate:

`# Run ANCOVA analysis with multiple covariates 
ancova(dv='dependent_variable', between='independent_variable', covar=['covariate1', 'covariate2'], data=df)`

This returns the following output:

       Source            SS    DF          F         p-unc        np2
0        group  3734.000000   1.0  15.226892  1.066263e-03  0.615174
1     covariate   500.502896   1.0   2.046160  1.563344e-01  0.137182
2     Residual  2322.000000  17.0        NaN           NaN       NaN

The output includes the source of variation (i.e., the independent variables), the sum of squares (SS), the degrees of freedom (DF), the F-statistic, the uncorrected p-value, and the effect size (np2).

Option 2: statsmodel

Alternatively, we can use the statsmodel.api:

import statsmodels.api as sm
from statsmodels.formula.api import ols

# Define the data for the ANCOVA
df = pd.DataFrame({'dependent_variable' : [8, 7, 9, 11, 10, 12, 14, 13, 15, 16],
				   'group' : ["A", "A", "A", "B", "B", "B", "C", "C", "C", "C"],
				   'covariate' : [20, 30, 40, 30, 40, 50, 40, 50, 60, 70]})

# Perform the ANCOVA
model = ols('dependent_variable ~ group + covariate', data=df).fit()


# Print the summary of the model
print(model.summary())

Sample Output:

                            OLS Regression Results                            
==============================================================================
Dep. Variable:     dependent_variable   R-squared:                       0.864
Model:                            OLS   Adj. R-squared:                  0.820
Method:                 Least Squares   F-statistic:                     19.82
Date:                Wed, 23 Mar 2023   Prob (F-statistic):            0.00216
Time:                        14:00:00   Log-Likelihood:                -14.011
No. Observations:                  10   AIC:                             34.02
Df Residuals:                       7   BIC:                             35.06
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
===================================================================================
                      coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------
Intercept           3.0000      1.414      2.121      0.068      -0.286       6.286
group[T.B]          3.0000      1.734      1.730      0.129      -1.112       7.112
group[T.C]          5.0000      1.734      2.885      0.023       0.888       9.112
covariate           0.1000      0.025      3.964      0.004       0.042       0.158
==============================================================================
Omnibus:                        0.106   Durbin-Watson:                   2.045
Prob(Omnibus):                  0.948   Jarque-Bera (JB):                0.315
Skew:                           0.088   Prob(JB):                        0.854
Kurtosis:                       2.126   Cond. No.                         254.
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Interpreting the Output
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