Definition

1. Noun:
   • A statistical measure of association: The phi coefficient is an index that quantifies the relationship between two binary variables, meaning both variables have only two possible, ordered categories (e.g., yes/no, success/failure, male/female). It is a special case of the Pearson correlation coefficient for 2x2 contingency tables.

Usage Examples

• Noun:
  • The researcher calculated the phi coefficient to assess the association between treatment (drug/placebo) and outcome (improved/not improved).
  • A phi coefficient of +0.8 indicates a strong positive relationship between the two binary variables.

Advanced Usage

• "Phi coefficient of association": A more formal term emphasizing its purpose to measure association.
  • The phi coefficient of association was used due to the dichotomous nature of the survey responses.

Variants and Related Words

• Phi (n): A common abbreviated form for the phi coefficient.
  • The phi for that contingency table was statistically significant.
• Matthews correlation coefficient (MCC) (n): A more general term often used synonymously with the phi coefficient, especially in machine learning for binary classification.
  • For evaluating the classifier, the Matthews correlation coefficient (phi coefficient) is more informative than accuracy.

Synonyms

• Phi correlation coefficient: A synonymous full name.
• Mean square contingency coefficient: A related historical term.

Related Phrases

• To compute the phi coefficient: The action of calculating this statistic.
  • The next step is to compute the phi coefficient from the frequency table.
• The magnitude of the phi coefficient: Refers to the absolute value of the coefficient, indicating the strength of the relationship.
  • The magnitude of the phi coefficient suggested a moderate association.

Notes on Application

• Interpretation: Like a correlation, its value ranges from -1 to +1. A value of 0 indicates no association, +1 indicates a perfect positive association, and -1 indicates a perfect negative association between the binary categories.
• Limitation: The phi coefficient is specifically designed for 2x2 tables. For larger contingency tables, other measures like Cramér's V are used.

Noun

1. an index of the relation between any two sets of scores that can both be represented on ordered binary dimensions (e.g., male-female)