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Uses and Difference Between Point Biserial and Biserial Correlation in Research

Point Biserial Correlation Coefficient

The Point-Biserial Correlation is used to measure the relationship between a continuous variable and a dichotomous variable. It evaluates the relationship between two variables when one variable is binary and the other is continuous.

The formula of point biserial correlation is:

• M₁ = mean (for the entire test) of the group that received the positive binary variable (i.e. the “1”).

• M₀ = mean (for the entire test) of the group that received the negative binary variable (i.e. the “0”).

• S_n = standard deviation for the entire test.

• p = Proportion of cases in the “0” group.

• q = Proportion of cases in the “1” group.

Biserial Correlation Coefficient

Biserial correlation was introduced by Pearson in 1909. In biserial correlation one of the variables is dichotomous ordinal data and is continuous. It is a correlation between one or more quantitative variables, and one or more dichotomous variables.

The formula of biserial correlation is:

r_b = [(Y₁ – Y₀) * (pq/Y) ] /σ_y,

• Y₀ = mean score for data pairs for x=0,

• Y₁ = mean score for data pairs for x=1,

• q = proportion of data pairs for x=0,

• p = proportion of data pairs for x=1,

• σ_y = population standard deviation.

Difference Between Point Biserial and Biserial Correlation Coefficient

1. The point-biserial correlation is used when the variable is a true dichotomy and the biserial correlation is used with an artificial dichotomy.

2. In point biserial correlation one variable is continuous and the other variable is binary and in biserial correlation one variable is dichotomous or an artificially dichotomized variable.