Reducing Bias and Error in the Correlation Coefficient Due to Nonnormality
| Autor: | James B. Hittner, Anthony J. Bishara |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Statistics::Theory
Correlation coefficient Applied Mathematics media_common.quotation_subject Article Pearson product-moment correlation coefficient Education symbols.namesake Bootstrapping (electronics) Sample size determination Statistics Developmental and Educational Psychology symbols Econometrics Probability distribution Point estimation Applied Psychology Rankit Normality Mathematics media_common |
| Zdroj: | Educational and Psychological Measurement. 75:785-804 |
| ISSN: | 1552-3888 0013-1644 |
| DOI: | 10.1177/0013164414557639 |
| Popis: | 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 +.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. |
| Databáze: | OpenAIRE |
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