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Estimating Winsorized correlations in a univariate or bivariate random effects model
Author(s) -
Wilcox Rand R.
Publication year - 1994
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1994.tb01030.x
Subject(s) - intraclass correlation , bivariate analysis , statistics , mathematics , normality , outlier , econometrics , univariate , correlation , random effects model , multivariate normal distribution , sample size determination , copula (linguistics) , context (archaeology) , multivariate statistics , meta analysis , reproducibility , medicine , paleontology , geometry , biology
A well‐known result is that slight departures from normality can have a large effect on the usual correlation coefficient rendering the magnitude of the correlation difficult to interpret and potentially misleading. In the context of a random effects model, which is the focus of attention in this paper, this means that effect size, as measured by the intraclass correlation, might be small due to outliers or heavy‐tailed distributions rather than a lack of differences among the groups being compared. Similarly, a large intraclass correlation might be due to trivial shifts away from normality which would become small if an adjustment for non‐normality were made. Moreover, this problem has to do with the effects of non‐normality on population parameters, not just statistics, so problems can arise even with large sample sizes. This follows almost immediately from results in Tukey (1960), and it is briefly illustrated here. One approach to this problem is to use a Winsorized analogue of the intraclass correlation. This paper suggests three ways the Winsorized intraclass correlation might be estimated and compares them via simulations. A bivariate generalization of the random effects model is also considered, and two methods of estimating the group‐level correlation are described and compared. Alternatives to Winsorization are also discussed.