4 Replies to “How to Calculate Correlation Between Continuous & Categorical Variables”

1. Hi,

   I really like this statistic! thank you! could you share the python library of this point-biserial correlation, please?

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2. how to perform a correlation between qualitative variable with multiple categories (more than 2) and continuous one ?

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   1. Hi Aalaa…To perform a correlation analysis between a qualitative variable with multiple categories (more than 2) and a continuous variable, you can follow these approaches depending on the nature of the qualitative variable and the type of insights you seek:

      —

      ### 1. **One-Way ANOVA (Analysis of Variance)**
      – **Use case**: Tests whether the means of the continuous variable differ significantly across the categories of the qualitative variable.
      – **Procedure**:
      1. Use the qualitative variable as the grouping variable.
      2. Conduct a one-way ANOVA to test the relationship.
      3. Interpret the F-statistic and p-value.
      – **Python Example**:
      “`python
      from scipy.stats import f_oneway

      # Example data
      continuous_data = [10, 15, 20, 25, 30, 35]
      category_data = [‘A’, ‘A’, ‘B’, ‘B’, ‘C’, ‘C’]

      # Split continuous data by categories
      group_a = [10, 15]
      group_b = [20, 25]
      group_c = [30, 35]

      # Perform one-way ANOVA
      f_stat, p_value = f_oneway(group_a, group_b, group_c)
      print(“F-statistic:”, f_stat)
      print(“p-value:”, p_value)
      “`

      —

      ### 2. **Point-Biserial or Categorical Regression**
      If you want to calculate the strength of association between a categorical variable with more than 2 levels and a continuous variable:
      1. Encode the categorical variable using one-hot encoding or dummy encoding.
      2. Perform regression to see the relationship.

      —

      ### 3. **Eta-Squared**
      – **Use case**: A measure of association strength that works for categorical vs. continuous data.
      – **Procedure**:
      1. Perform an ANOVA.
      2. Calculate Eta-squared (\( \eta^2 \)):
      \[
      \eta^2 = \frac{SS_{between}}{SS_{total}}
      \]
      where \(SS_{between}\) is the sum of squares between groups and \(SS_{total}\) is the total sum of squares.

      —

      ### 4. **Correlation Ratio (η or Eta)**
      – **Use case**: Measures the association between a categorical variable and a continuous variable.
      – **Procedure**:
      1. Calculate the variance within each group of the categorical variable.
      2. Compare the variance explained by the groups to the total variance.
      – **Python Example**:
      “`python
      import numpy as np
      import pandas as pd

      # Example data
      df = pd.DataFrame({
      ‘Category’: [‘A’, ‘A’, ‘B’, ‘B’, ‘C’, ‘C’],
      ‘Values’: [10, 15, 20, 25, 30, 35]
      })

      def eta_squared(data, categories, values):
      groups = data.groupby(categories)[values]
      overall_mean = data[values].mean()
      ss_between = sum(groups.size() * (groups.mean() – overall_mean)**2)
      ss_total = sum((data[values] – overall_mean)**2)
      return ss_between / ss_total

      eta = eta_squared(df, ‘Category’, ‘Values’)
      print(“Eta-squared:”, eta)
      “`

      —

      ### 5. **Visualization**
      Sometimes visual inspection can provide better insights:
      – Use **boxplots** to visualize the distribution of the continuous variable across categories.
      “`python
      import seaborn as sns
      import matplotlib.pyplot as plt

      sns.boxplot(x=’Category’, y=’Values’, data=df)
      plt.show()
      “`

      —

      ### Which Method to Choose?
      – Use **ANOVA** if you are interested in whether the mean differences are statistically significant.
      – Use **Eta-squared** or **correlation ratio** for a measure of effect size or association strength.
      – Use **regression** if you are incorporating the relationship into a predictive model.

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3. Hola ¿cómo puedo calcularlo en Stata?

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