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Interpreting the correlation coefficient when one of the variables is discrete
D R Appleton1, A J Rugg-Gunn, A F Hackett
1Department of Medical Statistics, Dental School, University of Newcastle-upon-Tyne, England.
Journal of Dental Research
|November 1, 1986
Summary
Discretizing continuous data reduces correlation coefficients. Researchers found that measurement error, decreased slope, and fewer data points significantly lower correlation, especially with few discrete scores.
Area of Science:
- Statistics
- Data Analysis
Background:
- Correlation coefficients measure linear association between variables.
- Discretization transforms continuous data into discrete categories, potentially altering statistical relationships.
Purpose of the Study:
- To investigate the impact of data discretization on correlation coefficients.
- To quantify the reduction in correlation due to dichotomization and a simulated continuous-to-counting variable model.
Main Methods:
- Theoretical calculation of correlation reduction from dichotomizing bivariate normal variables.
- Computer simulations modeling a continuous variable with measurement error generating a counting variable.
Main Results:
- Dichotomization significantly reduces the correlation coefficient compared to underlying continuous variables.
- Simulations showed decreased correlation with increased measurement error, decreased slope, and fewer counts.
- Correlation reduction was pronounced when using only a few discrete scores (e.g., four or five).
Conclusions:
- Interpreting correlation coefficients requires caution when variables are discretized, especially with limited discrete scores.
- Discretization inherently attenuates correlation, necessitating careful consideration in statistical analyses.
- The study highlights the importance of understanding data transformation effects on correlation estimates.