Multivariate normative comparisons

In neuropsychological evaluations and single case research generally a number of tests are administered, since the interest is not in a single, but in multiple characteristics of a patient. The typical problem is to decide whether or not a patient is different from normal controls with respect to one or more of these characteristics. Consideration of each characteristic separately entails an increased risk of a false positive decision (a wrongful decision that the patient is abnormal, or a type 1 error). From a statistical point of view this calls for a multivariate analysis. In this paper, we propose two approaches to perform normative comparisons for such multivariate data: Bonferroni corrected univariate comparisons and a multivariate comparison. Both approaches allow for the testing of unidirectional (two-sided) as well as directional (one-sided) hypothesis, i.e. the hypothesis that a patient deviates in a negative sense from the norm. Monte Carlo simulations were performed to check if the type I error of both approaches is adequately controlled, and to investigate the power of both approaches to detect deviation from the norm. The results indicate that the type I error rate of both approaches is correct, even in small samples. The results also indicate that the power is higher for the univariate approach if the normative sample size is very small (i.e. just exceeds the number of tests administered). In larger samples, the multivariate comparison has in general increased power. We illustrate both approaches with a clinical example of patients with Parkinson disease, who received deep brain stimulation to alleviate motor symptoms, and who were neuropsychologically evaluated to detect possible cognitive side effects.