Definition

Noun: - A statistical measure of association: The biserial correlation coefficient is a specific type of correlation coefficient used to measure the strength and direction of the relationship between two variables when one variable is continuous (many-valued) and the other is artificially dichotomous (has two categories, but is assumed to underlie a continuous, normally distributed variable).

Usage

This term is used primarily in the fields of statistics, psychometrics, and educational testing to quantify the relationship between a continuous measure (e.g., test scores, height, reaction time) and a dichotomized variable (e.g., pass/fail, yes/no, group membership where the dichotomy represents an underlying continuum).

Examples

• In a research context:
  • The researcher calculated the biserial correlation coefficient to assess the relationship between total exam score (continuous) and the dichotomized item response (correct/incorrect).
  • A high biserial correlation coefficient between the aptitude test and program completion suggests the test is a good predictor.

Advanced Usage

• Point-Biserial vs. Biserial Correlation: It is crucial to distinguish this from the point-biserial correlation coefficient. The biserial correlation is used when the dichotomous variable is dichotomized from a normal distribution (e.g., splitting a continuous score at a median to create "high" and "low" groups). The point-biserial is used when the dichotomy is or (e.g., gender, alive/dead).
• Interpretation: Like other correlation coefficients, its value ranges from -1.0 to +1.0, where values closer to the extremes indicate a stronger relationship.

Variants and Related Words

• Biserial correlation (n): A common shortened form for the biserial correlation coefficient.
• Point-biserial correlation coefficient (n): A related but distinct measure for a naturally dichotomous variable.
• Correlation coefficient (n): The general class of statistical measures to which the biserial correlation belongs.

Synonyms

• Biserial correlation
• Biserial r (informal, in statistical notation)

Notes on Usage

• This is a specialized technical term. In general writing, it is often replaced with a description like "the correlation between a continuous variable and a dichotomous one."
• The formula for the biserial correlation coefficient involves the ordinate (height) of the standard normal distribution at the point of dichotomy, which differentiates it computationally from the point-biserial formula.

Noun

1. a correlation coefficient in which one variable is many-valued and the other is dichotomous