A regression method for the power-duration relationship when both variables are subject to error

Eur J Appl Physiol. 2020 Apr;120(4):765-770. doi: 10.1007/s00421-020-04314-8. Epub 2020 Feb 20.


Purpose: The power-duration relationship has been variously modelled, although duration must be acknowledged as the dependent variable and is supposed to represent the only source of experimental error. However, there are certain situations, namely extremely high power outputs or outdoor field conditions, in which the error in power output measurement may not remain negligible. The geometric mean (GM) regression method deals with the assumption that also the independent variable is subject to a certain amount of experimental error, but has never been utilized in this context.

Methods: We applied the GM regression method for the two- and three-parameter critical power models and tested it against the usual weighted least square (WLS) procedure with our previous published data.

Results: There were no significant differences between parameter estimates of WLS and GM. Bias and limit of agreements between the two methods were low, while correlation coefficients were high (0.85-1.00).

Conclusions: GM provided equivalent results with respect to WLS in fitting the critical power model to experimental data and for its conceptual characteristics must be preferred wherever concerns on the precision of P measurement are present, such as for in-field power meters.

Keywords: Curve fitting; Cycling; Hyperbolic model; Model II nonlinear regression; Reduced major axis regression; Sport.

Publication types

  • Evaluation Study

MeSH terms

  • Physiology / methods*
  • Regression Analysis*