Quality of Life Research

, Volume 16, Issue 5, pp 815–822

The mathematical relationship among different forms of responsiveness coefficients

  • G. R. Norman
  • Kathleen W. Wyrwich
  • Donald L. Patrick
Original Paper

DOI: 10.1007/s11136-007-9180-x

Cite this article as:
Norman, G.R., Wyrwich, K.W. & Patrick, D.L. Qual Life Res (2007) 16: 815. doi:10.1007/s11136-007-9180-x



Little consensus exists regarding the most appropriate measure of responsiveness. While most indices are variants on Cohen’s effect size, the mathematical relationships among these indices have not been elucidated. Consequently, the health-related quality of life (HRQL) literature contains many publications in which a variety of different indices are computed and differences among them noted. These differences are completely predictable when the underlying analytical form of each coefficient is explicated.


In this paper, we begin with a mathematical analysis of the variance components underlying an observed change score. From this, we determine analytically the relationships among the more commonly used indices of responsiveness.


Based on this analysis, we conclude that Cohen’s effect size and the Standardized Response Mean are the two most appropriate measures, as each provides unique information and each best captures an important relation between treatment effect and variability in response. However, the latter should be interpreted with caution, as under some circumstances, any measure based on variability in change scores can give misleading information. On this basis, we recommend that future analysis of responsiveness be restricted to the Cohen effect size to ensure interpretability and comparability with treatment effects in other domains.


Responsiveness HRQL Equivalence Mathematics 

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  • G. R. Norman
    • 1
  • Kathleen W. Wyrwich
    • 2
  • Donald L. Patrick
    • 3
  1. 1.Department of Clinical Epidemiology and Biostatistics, MDCL 3519McMaster UniversityHamiltonCanada
  2. 2.Department of Research MethodologySaint Louis UniversitySt. LouisUSA
  3. 3.Department of Health ServicesUniversity of WashingtonSeattleUSA

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