Lucia et al. (4) examined the stability of target heart rate values for training. The authors are to be congratulated for managing to recruit world class athletes for their study and performing a comprehensive analysis of the data. In their analysis, Lucia et al. (4) examined whether there were any systematic changes over the study period with analysis of variance. They also attempted to describe the individual random variability in target heart rates by employing the “95% limits of agreement” (95% LOA) method, most recently discussed by Bland and Altman (2).
We would like to comment on the way Lucia et al. (4) interpreted the LOA analysis. It was stated in the results section that “The heart rate values recorded at VT2 were in close agreement throughout the study because more than 90% of data points were within the LOA.” This statement gives the impression that test-retest variability is judged as being acceptable if 95% of the data used to calculate the 95% LOA are within those same 95% LOA. It is fully expected that about 95% of the sample differences from any repeatability study are within the 95% LOA calculated from that same sample; the LOA are descriptive statistics (reference limits) that are, by definition, designed to cover 95% of differences. This erroneous interpretation of LOA has been made in other studies (3,5) and obviously guarantees acceptable repeatability for any test-retest data.
Atkinson and Nevill (1) warned against the above error in interpretation and discussed the appropriate use of 95% LOA in making decisions about repeatability. In brief, the LOA can be thought to represent the difference between two tests for 95% of individuals in a population. The assumptions for this inference to the population of interest are that the population data are normally distributed and the sample size is not so small as to make the estimate of the population LOA imprecise (2). The researcher is meant to make an inferential statement about the variability that is present and discuss the practical impact of that variability on typical uses of the measurement tool.
Lucia et al. (4) found that the standard deviation of differences was about ± 8 beats·min-1 for their target heart rate measurements, which gives LOA of about ± 16 beats·min-1 (assuming the systematic changes between tests are negligible and that the errors are uniform). From these LOA, one can be reasonably certain (P = 0.95) that any elite cyclist would show test-retest variability no greater than ± 16 beats·min-1. Ideally, confidence limits would be calculated for the precision of the population LOA (1,2). The important point is that the researcher uses the LOA information to assess whether the expected individual variability would impact on the proposed uses of the test (e.g., whether the described individual random variability would lead to unwarranted changes being made in a subject’s training loads).
Greg Atkinson, Ph.D.
Alan M. Nevill, Ph.D.
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2. Bland, J. M., and D. G. Altman. Measuring agreement in method comparison studies. Stat. Methods Med. Res. 8: 135–160, 1999.
3. de Jong, J. S., P. J. van Diest, and J. P. A. Baak. In response (Letter). Lab. Invest. 75: 756–758, 1996.
4. L ucia , A., J. H oyos , M. P erez , J. L. and C hicharro . Heart rate and performance parameters in elite cyclists: a longitudinal study. Med. Sci. Sports Exerc.
5. Lucia, A., O. Sanchez, A. Carvajal, and J. L. Chicharro. Analysis of aerobic-anaerobic transition in elite cyclists during incremental exercise with the use of electromyography. Br. J. Sports Med. 33: 178–185, 1999.