Testing the Significance of a Correlation With Nonnormal Data: Comparison of Pearson, Spearman, Transformation, and Resampling Approaches

It is well known that when data are nonnormally distributed, a test of the significance of Pearson's r may inflate Type I error rates and reduce power. Statistics textbooks and the simulation literature provide several alternatives to Pearson's correlation. However, the relative performanc...

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Bibliographic Details
Published in:Psychological methods 2012-09, Vol.17 (3), p.399-417
Main Authors: Bishara, Anthony J., Hittner, James B.
Format: Article
Language:English
Subjects:
Alternatives
Biological and medical sciences
Data Interpretation, Statistical
Fundamental and applied biological sciences. Psychology
Linear Models
Monte Carlo Method
Nonlinear Dynamics
Permutations
Power
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Psychometrics. Statistics. Methodology
Rank Difference Correlation
Sample Size
Simulation
Statistical Correlation
Statistical Distributions
Statistics as Topic - methods
Statistics, Nonparametric
Statistics. Mathematics
Textbooks
Transformation
Type I Errors
Type II Errors
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Summary:It is well known that when data are nonnormally distributed, a test of the significance of Pearson's r may inflate Type I error rates and reduce power. Statistics textbooks and the simulation literature provide several alternatives to Pearson's correlation. However, the relative performance of these alternatives has been unclear. Two simulation studies were conducted to compare 12 methods, including Pearson, Spearman's rank-order, transformation, and resampling approaches. With most sample sizes (n ≥ 20), Type I and Type II error rates were minimized by transforming the data to a normal shape prior to assessing the Pearson correlation. Among transformation approaches, a general purpose rank-based inverse normal transformation (i.e., transformation to rankit scores) was most beneficial. However, when samples were both small (n ≤ 10) and extremely nonnormal, the permutation test often outperformed other alternatives, including various bootstrap tests.
ISSN:1082-989X
1939-1463
DOI:10.1037/a0028087