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Point-biserial correlation is a statistical measure used to assess the strength and direction of the relationship between a binary (dichotomous) variable and a continuous variable. It is a specific type of correlation coefficient that quantifies the association between two variables when one of them is binary (taking on only two values, typically 0 and 1) and the other is continuous (taking on a range of values).

The point-biserial correlation coefficient is denoted by rpb or simply r, and its value can range from -1 to 1. The sign of the coefficient indicates the direction of the relationship:

• If rpb is positive (closer to 1), it suggests a positive relationship, meaning that as the binary variable increases (e.g., from 0 to 1), the continuous variable tends to increase as well.

• If rpb is negative (closer to -1), it indicates a negative relationship, meaning that as the binary variable increases, the continuous variable tends to decrease.

• If rpb is close to 0, it suggests little to no relationship between the two variables.

The point-biserial correlation coefficient is computed using the following formula:

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Where:

• M₁​ is the mean of the continuous variable for the group with the binary variable equal to 1.
• M₀​ is the mean of the continuous variable for the group with the binary variable equal to 0.
• p is the proportion of cases with the binary variable equal to 1.
• q is the proportion of cases with the binary variable equal to 0.
• N is the total number of cases.

Point-biserial correlation is often used in situations where you want to examine the relationship between a binary independent variable (e.g., gender) and a continuous dependent variable (e.g., test scores). It helps you determine if there's a significant association between the two variables and quantify the strength and direction of that association.

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The script below loads data from multiple folders, calculates point-biserial correlation coefficients between binary and continuous variables, identifies the best correlations for each folder, and calculates overall correlations for each folder, providing a summary of the relationships between variables within and across different folders. Code:
         
         
       Input:    
         
         
         
         
         
         
         
       Output:    
         

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