Measures of central tendency in rehabilitation research: What do they mean?

V. A. Gonzales, Kenneth Ottenbacher

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)141-146
Number of pages6
JournalAmerican Journal of Physical Medicine and Rehabilitation
Volume80
Issue number2
DOIs
StatePublished - 2001

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Textbooks
Rehabilitation
Health
Research
Rehabilitation Research

Keywords

  • Averages
  • Measurement
  • Skewness
  • Statistics

ASJC Scopus subject areas

  • Rehabilitation
  • Health Professions(all)
  • Orthopedics and Sports Medicine
  • Physical Therapy, Sports Therapy and Rehabilitation

Cite this

Measures of central tendency in rehabilitation research : What do they mean? / Gonzales, V. A.; Ottenbacher, Kenneth.

In: American Journal of Physical Medicine and Rehabilitation, Vol. 80, No. 2, 2001, p. 141-146.

Research output: Contribution to journalArticle

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