title: Correlating and predicting psychiatric symptom ratings: Spearman's r versus Kendall's tau correlation.
abstract: 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.
authors.affiliation: Mental Health Clinical Research Center, Department of Psychiatry, University of Iowa, Iowa City 52242, USA. stephan-arndt@uiowa.edu
authors.forename: S
authors.initials: S
authors.lastname: Arndt
authors.forename: C
authors.initials: C
authors.lastname: Turvey
authors.forename: N C
authors.initials: NC
authors.lastname: Andreasen
mesh_terms: D000328:Adult; D014150:Antipsychotic Agents / Q000009:adverse effects*; D010054:Brief Psychiatric Rating Scale; D004409:Dyskinesia, Drug-Induced / Q000175:diagnosis* / Q000209:etiology*; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D011237:Predictive Value of Tests; D011618:Psychotic Disorders / Q000175:diagnosis / Q000188:drug therapy / Q000453:epidemiology; D018709:Statistics, Nonparametric
chemical_list: D014150:Antipsychotic Agents