correlation ratio: meaning, definition, pronunciation and examples
C2/TechnicalTechnical/Academic
Quick answer
What does “correlation ratio” mean?
A statistical measure of the degree of association (non-linear dependence) between two variables, typically one continuous and one categorical.
Audio
Pronunciation
Definition
Meaning and Definition
A statistical measure of the degree of association (non-linear dependence) between two variables, typically one continuous and one categorical.
In statistics, specifically in analysis of variance and regression, it is the square root of the ratio of the between-group variance to the total variance. It quantifies how much of the variability in a continuous dependent variable can be predicted from knowing the categories of an independent variable. It is also known as eta (η) or eta-squared (η²) in some contexts.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or use. Spelling conventions follow general BrE/AmE patterns (e.g., BrE 'analyse' vs. AmE 'analyze' in surrounding text).
Connotations
None; purely technical.
Frequency
Equally low frequency and confined to technical statistical discourse in both varieties.
Grammar
How to Use “correlation ratio” in a Sentence
The correlation ratio BETWEEN [continuous variable] AND [categorical variable] was high.We calculated the correlation ratio OF [dependent variable] ON [independent variable].Vocabulary
Collocations
Examples
Examples of “correlation ratio” in a Sentence
verb
British English
- To assess non-linearity, one can correlate the groups using the correlation ratio.
- We need to correlate the data via the correlation ratio method.
American English
- Researchers correlated the effects using the correlation ratio.
- The model correlates the variables with a correlation ratio.
adverb
British English
- The variables were correlated ratio-wise.
- The association was measured correlation-ratio-style.
American English
- They analyzed the data correlation-ratio-fashion.
- It was assessed correlation-ratio-method.
adjective
British English
- The correlation-ratio analysis revealed a strong non-linear link.
- We examined the correlation-ratio statistic.
American English
- The correlation-ratio approach is suitable here.
- A high correlation-ratio value was obtained.
Usage
Meaning in Context
Business
Extremely rare. Might appear in advanced market segmentation analysis or complex quality control modelling.
Academic
Primary context. Used in research papers, theses, and textbooks on statistics, psychology, education, and other social/behavioural sciences.
Everyday
Virtually never used.
Technical
Core context. Used by statisticians, data scientists, and researchers in methodology sections to report the strength of nonlinear relationships.
Vocabulary
Synonyms of “correlation ratio”
Strong
Neutral
Weak
Vocabulary
Antonyms of “correlation ratio”
Watch out
Common Mistakes When Using “correlation ratio”
- Using it to describe a linear relationship (use Pearson's r instead).
- Confusing the correlation ratio (η) with its square (η²).
- Applying it to two continuous variables without discretizing one (it's designed for categorical predictors).
FAQ
Frequently Asked Questions
No. R-squared (from linear regression) explains the proportion of variance in a continuous dependent variable explained by one or more continuous (or categorical) independent variables under a linear model. The correlation ratio (η²) explains variance from a categorical predictor without assuming linearity. In one-way ANOVA, η² and R² are numerically identical.
A correlation ratio (η) of 0.8 indicates a strong non-linear association. Its square (η² = 0.64) means that 64% of the variance in the continuous dependent variable can be predicted from (or is associated with) the categories of the independent variable.
No. The correlation ratio is defined as the square root of a ratio of variances, so it always ranges from 0 to 1. It measures the magnitude of association, not its direction.
Use the correlation ratio when your predictor (independent) variable is categorical (nominal or ordinal) and you want to measure how well it predicts a continuous outcome, especially if you suspect the relationship is not a straight line. Use Pearson's correlation for the linear relationship between two continuous variables.
A statistical measure of the degree of association (non-linear dependence) between two variables, typically one continuous and one categorical.
Correlation ratio is usually technical/academic in register.
Correlation ratio: in British English it is pronounced /ˌkɒr.əˈleɪ.ʃən ˈreɪ.ʃi.əʊ/, and in American English it is pronounced /ˌkɔːr.əˈleɪ.ʃən ˈreɪ.ʃoʊ/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “None applicable.”
Learning
Memory Aids
Mnemonic
Think CORRELATION (connection) RATIO (a fraction). It's the 'ratio' that tells you how much of one thing is connected to/can be explained by the categories of another thing.
Conceptual Metaphor
EXPLANATORY POWER IS A FRACTION (e.g., 'The correlation ratio tells us what fraction of the variation is explained by group membership.').
Practice
Quiz
What is the primary use of the correlation ratio?