Correlating and predicting psychiatric symptom ratings: Spearman's r versus Kendall's tau correlation

Simple correlations play a large role in the analysis of psychiatric data. They are used to predict outcome, validate new instruments, establish treatment efficacy and find symptom patterns. Researchers and data analysts often face a question about which correlation coefficient to use in a study but are often unaware of the strengths and weaknesses of the alternative correlation measures. The presence of outliers, nonconstant variance, skewed distributions and unequal n are common in psychiatric data and this poses severe problems for many classic statistical methods. We compare Pearson, Spearman and Kendall's correlation coefficients using a large sample of subjects with schizophrenia spectrum disorders who were evaluated with 7 different psychiatric rating scales. Samples sizes ranging from 8 to 50 were evaluated using bootstrapping methods. The criteria for evaluation of the correlations were the type I error rates, power, bias and confidence interval width. Pearson's r did not always control for false positives at the nominal rate and was often unstable. Spearman's r performed better than Pearson's but provided a biased estimate of the true correlation. Spearman's r was also difficult to interpret. Our results suggest that Kendall's tau(b) has many advantages over Pearson's and Spearman's r; when applied to psychiatric data, tau(b) maintained adequate control of type I errors, was nearly as powerful as Pearson's r, provided much tighter confidence intervals and had a clear interpretation.