Measures of central tendency, variability, and relative standing in nonnormal distributions: alternatives to the mean and standard score

Arch Phys Med Rehabil. 1988 Jun;69(6):406-9.


There are two major disadvantages to reporting test results in standardized scores such as z-scores or t-scores when describing individuals with disabilities. (1) Raw scores on many tasks from disabled individuals are notoriously nonnormal. They are asymmetric, in that they are skewed toward poor scores. (2) Low z-scores give a false impression of dysfunction because able-bodied subjects are often grossly overqualified for the application in question; they may have levels of strength or quickness several orders of magnitude greater than what is needed to do the assessment task. A recommended alternative is to describe the performance of disabled individuals using nonparametric statistics, and to report scores in boxplots, showing the extremes, the median, and the quartiles. Such points are easy to calculate and to interpret, and they are robust against outliers.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Disability Evaluation / methods*
  • Disabled Persons*
  • Humans
  • Rehabilitation
  • Statistics as Topic / standards*