Inferences About the Skipped Correlation Coefficient: Dealing with Heteroscedasticity and Non-Normality
A common goal is testing the hypothesis that Pearson’s correlation is zero and typically this is done based on Student’s T test. There are, however, several well-known concerns. First, Student’s T is sensitive to heteroscedasticity. That is, when it rejects, it is reasonable to conclude that there is dependence, but in terms of making a decision about the strength of the association, it is unsatisfactory. Second, Pearson’s correlation is not robust: it can poorly reflect the strength of the association. Even a single outlier can have a tremendous impact on the usual estimate of Pearson’s correlation, which can result in a poor indication of the strength of the association among the bulk of the points. Numerous robust correlation coefficients have been proposed that deal with outliers among the marginal distributions, but these methods do not take into account the overall structure of the data in terms of dealing with outliers. A skipped correlation addresses this concern and methods for testing the hypothesis that this correlation is zero have been studied. However, there are serious limitations associated with one of these methods and extant studies regarding an alternative percentile bootstrap method do not address practical concerns reviewed in the paper. A minor goal is to report situations where this percentile bootstrap method can be unsatisfactory. The main result is that an alternative percentile bootstrap method performs well in simulations.
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