6.3 Partial Correlation

6.3 Partial Correlation#

Partial correlation is a statistical measure used to determine the relationship between two variables while controlling for the influence of one or more additional variables. Unlike a simple correlation, which assesses the direct association between two variables, partial correlation isolates the effect of confounding variables to better understand the true relationship.

Example: Partial Correlation with the Iris Dataset#

We will use the pingouin package for our partial correlation analysis and apply it to the famous Iris dataset, which provides data on the physical characteristics of the iris flower. Our goal is to investigate the relationship between petal length and petal width, while controlling for sepal length

# Import the necessary libraries
import seaborn as sns
import pingouin as pg

# Load the iris dataset
df = sns.load_dataset('iris')

# Compute the partial correlation between petal length and petal width,
# controlling for sepal length
partial_corr = pg.partial_corr(data=df,
                               x='petal_length',
                               y='petal_width',
                               covar='sepal_length')
print(partial_corr)

           n         r         CI95%         p-val
pearson  150  0.886316  [0.85, 0.92]  5.257543e-51

Interpreting the Results:#

The output includes several important metrics.

  • r (correlation coefficient): This value measures the strength and direction of the linear relationship between petal length and petal width, while controlling for sepal length. In this example, a result of 0.886 suggests a strong positive linear relationship between petal length and width after adjusting for sepal length.

  • CI95% (95% confidence interval): [0.85, 0.92] indicates the range within which the true partial correlation coefficient is likely to fall with 95% confidence. A narrower confidence interval suggests a more precise estimate of the correlation.

  • p-value: The p-value (5.26e-51) indicates the statistical significance of the correlation. A value close to 0 suggests that the observed correlation is statistically highly significant and unlikely to be due to random chance under the null hypothesis.

In conclusion, the partial correlation analysis confirms a strong positive linear relationship between petal length and petal width, independent of the effect of sepal length.

Summary

  • Partial correlation measures the relationship between two variables while controlling for the effect of a third variable.

  • The pingouin package offers a nice and easy way for calculating partial correlations.

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