Asymptotic confidence intervals for the Pearson correlation via skewness and kurtosis
| Autor: | Anthony J. Bishara, Thomas Nash, Jiexiang Li |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Psychometrics 050109 social psychology 01 natural sciences 010104 statistics & probability symbols.namesake Normality test Arts and Humanities (miscellaneous) Jarque–Bera test Statistics Confidence Intervals Humans Computer Simulation 0501 psychology and cognitive sciences 0101 mathematics General Psychology Mathematics 05 social sciences Reproducibility of Results Pearson distribution General Medicine Pearson product-moment correlation coefficient D'Agostino's K-squared test Sampling distribution Skewness Data Interpretation Statistical symbols Kurtosis Monte Carlo Method Algorithms |
| Zdroj: | British Journal of Mathematical and Statistical Psychology. 71:167-185 |
| ISSN: | 0007-1102 |
| Popis: | When bivariate normality is violated, the default confidence interval of the Pearson correlation can be inaccurate. Two new methods were developed based on the asymptotic sampling distribution of Fisher's z' under the general case where bivariate normality need not be assumed. In Monte Carlo simulations, the most successful of these methods relied on the (Vale & Maurelli, 1983, Psychometrika, 48, 465) family to approximate a distribution via the marginal skewness and kurtosis of the sample data. In Simulation 1, this method provided more accurate confidence intervals of the correlation in non-normal data, at least as compared to no adjustment of the Fisher z' interval, or to adjustment via the sample joint moments. In Simulation 2, this approximate distribution method performed favourably relative to common non-parametric bootstrap methods, but its performance was mixed relative to an observed imposed bootstrap and two other robust methods (PM1 and HC4). No method was completely satisfactory. An advantage of the approximate distribution method, though, is that it can be implemented even without access to raw data if sample skewness and kurtosis are reported, making the method particularly useful for meta-analysis. Supporting information includes R code. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Plný text