The value of Bayes' theorem for interpreting abnormal test scores in cognitively healthy and clinical samples

The base rates of abnormal test scores in cognitively normal samples have been a focus of recent research. The goal of the current study is to illustrate how Bayes' theorem uses these base rates--along with the same base rates in cognitively impaired samples and prevalence rates of cognitive impairment--to yield probability values that are more useful for making judgments about the absence or presence of cognitive impairment. Correlation matrices, means, and standard deviations were obtained from the Wechsler Memory Scale--4th Edition (WMS-IV) Technical and Interpretive Manual and used in Monte Carlo simulations to estimate the base rates of abnormal test scores in the standardization and special groups (mixed clinical) samples. Bayes' theorem was applied to these estimates to identify probabilities of normal cognition based on the number of abnormal test scores observed. Abnormal scores were common in the standardization sample (65.4% scoring below a scaled score of 7 on at least one subtest) and more common in the mixed clinical sample (85.6% scoring below a scaled score of 7 on at least one subtest). Probabilities varied according to the number of abnormal test scores, base rates of normal cognition, and cutoff scores. The results suggest that interpretation of base rates obtained from cognitively healthy samples must also account for data from cognitively impaired samples. Bayes' theorem can help neuropsychologists answer questions about the probability that an individual examinee is cognitively healthy based on the number of abnormal test scores observed.