ERIC Number: EJ1073517
Record Type: Journal
Publication Date: 2015-Oct
Abstractor: As Provided
Reducing Bias and Error in the Correlation Coefficient Due to Nonnormality
Bishara, Anthony J.; Hittner, James B.
Educational and Psychological Measurement, v75 n5 p785-804 Oct 2015
It is more common for educational and psychological data to be nonnormal than to be approximately normal. This tendency may lead to bias and error in point estimates of the Pearson correlation coefficient. In a series of Monte Carlo simulations, the Pearson correlation was examined under conditions of normal and nonnormal data, and it was compared with its major alternatives, including the Spearman rank-order correlation, the bootstrap estimate, the Box-Cox transformation family, and a general normalizing transformation (i.e., rankit), as well as to various bias adjustments. Nonnormality caused the correlation coefficient to be inflated by up to +0.14, particularly when the nonnormality involved heavy-tailed distributions. Traditional bias adjustments worsened this problem, further inflating the estimate. The Spearman and rankit correlations eliminated this inflation and provided conservative estimates. Rankit also minimized random error for most sample sizes, except for the smallest samples (n = 10), where bootstrapping was more effective. Overall, results justify the use of carefully chosen alternatives to the Pearson correlation when normality is violated.
Descriptors: Research Methodology, Monte Carlo Methods, Correlation, Simulation, Measurement Techniques, Social Science Research, Statistical Analysis, Error Patterns, Statistical Inference, Sampling, Statistical Bias, Statistical Distributions
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Publication Type: Journal Articles; Reports - Research
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