Gonzales VA, Ottenbacher KJ: Measures of central tendency in rehabilitation research: what do they mean? Am J Phys Med Rehabil 2001;80:141–146.
Measures of central tendency including the mean, median, and mode are commonly reported in rehabilitation research. It is believed that the relationship among the mean, median, and mode changes in a specific way when the distribution being analyzed is skewed. A number of widely used textbooks were reviewed to determine how the relationship among the mean, median, and mode is presented in the health sciences and rehabilitation literature. We report a potential misinterpretation of the relationship between measures of central tendency that was identified in several research and statistical textbooks on the subject of rehabilitation. The misinterpretation involves measures of central tendency derived from skewed unimodal sample distributions. The reviewed textbooks state or imply that in asymmetrical distributions, the median is always located between the mode and mean. An example is presented illustrating the fallacy of this assumption. The mean and median will always be to the right of the mode in a positively skewed unimodal distribution and to the left of the mode in a negatively skewed distribution; the order of the mean and median is impossible to predict or generalize. The assumption that the median always falls between the mode and mean in the calculation of coefficients of skewness has implications for the interpretation of exploratory and confirmatory data analysis in rehabilitation research.
From the School of Allied Health Sciences, University of Texas Medical Branch at Galveston, Galveston, Texas.
All correspondence and requests for reprints should be addressed to Kenneth J. Ottenbacher, PhD, SAHS 4.202, University of Texas Medical Branch at Galveston, 301 University Boulevard, Galveston, TX 77555-1028.
Supported, in part, by a postdoctoral fellowship from the National Institute on Disability and Rehabilitation Research, Department of Education, Advance Rehabilitation Research Training Program (H133P990001) (to Dr. Gonzales).