# How to perform an analysis of covariance (ANCOVA) (in Python, using pingouin)

## Task

Recall that covariates are variables that may be related to the outcome but are unaffected by treatment assignment. In a randomized experiment with one or more observed covariates, an analysis of covariance (ANCOVA) addresses this question: How would the mean outcome in each treatment group change if all groups were equal with respect to the covariate? The goal is to remove any variability in the outcome associated with the covariate from the unexplained variability used to determine statistical significance.

Related tasks:

- How to do a one-way analysis of variance (ANOVA)
- How to compare two nested linear models
- How to conduct a mixed designs ANOVA
- How to conduct a repeated measures ANOVA

## Solution

The solution below uses an example dataset about car design and fuel consumption from a 1974 Motor Trend magazine. (See how to quickly load some sample data.)

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from rdatasets import data
df = data('mtcars')

Let’s use ANCOVA to check the effect of the engine type (0 = V-shaped, 1 = straight, in the variable `vs`

) on the miles per gallon when considering the weight of the car as a covariate. We will use the `ancova`

function from the `pingouin`

package to conduct the test.

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from pingouin import ancova
ancova(data=df, dv='mpg', covar='wt', between='vs')

Source | SS | DF | F | p-unc | np2 | |
---|---|---|---|---|---|---|

0 | vs | 54.228061 | 1 | 7.017656 | 1.292580e-02 | 0.194839 |

1 | wt | 405.425409 | 1 | 52.466123 | 5.632548e-08 | 0.644024 |

2 | Residual | 224.093877 | 29 | NaN | NaN | NaN |

The $p$-value for each variable is in the `p-unc`

column.

The $p$-value for the `wt`

variable tests the null hypothesis, “The quantities `wt`

and `mpg`

are not related.” Since it is below 0.05, we reject the null hypothesis, and conclude that `wt`

is significant in predicting `mpg`

.

The $p$-value for the `vs`

variable tests the null hypothesis, “The quantities `vs`

and `mpg`

are not related if we hold `wt`

constant.” Since it is below 0.05, we reject the null hypothesis, and conclude that `vs`

is significant in predicting `mpg`

even among cars with equal weight (`wt`

).

Note: Unfortunately, a two-factor ANCOVA is not possible in pingouin. However, a model with more than one covariate is possible, as you can provide a list as the `covar`

parameter when calling `ancova`

.

Content last modified on 24 July 2023.

See a problem? Tell us or edit the source.

Contributed by Krtin Juneja (KJUNEJA@falcon.bentley.edu)