Author(s): PUEO, B., HOPKINS, W.G., JIMENEZ-OLMEDO, J.M., Institution: UNIVERSITY OF ALICANTE, Country: SPAIN, Abstract-ID: 911

INTRODUCTION:
A neglected issue in reliability studies is the separation of standard (typical) error of measurement into its two components: technical error arising from the measuring device, and biological variability arising from the subjects. Estimation of these components would allow evaluation of the devices performance independent of subject variability. Such estimation is possible when subjects are measured simultaneously with two different or identical devices, followed by analysis with a mixed model (1). We have now developed an alternative analysis implemented with a spreadsheet, which we have validated by simulation. We have also demonstrated its practical application to real data consisting of jump-height measurements.
METHODS:
The basis of the spreadsheet is the analysis of the four pairs of change scores between the tests and devices. The standard deviations (SDs) representing technical errors and biological variability were derived with formulae in raw units, percent units (via log-transformation) and standardized units, and their confidence limits were derived with 1800 bootstrap samples (the maximum possible in the latest version of Excel). The spreadsheet analyses were reproduced in a SAS Studio program and compared with a mixed model. The program generated and analyzed 2000 datasets for chosen true (population) values of means and SDs simulating real data. These simulations allowed empirical derivation of factors to correct small-sample biases in the estimates of the SDs and in the coverage of their confidence intervals. For the practical application of the spreadsheet, 31 participants each performed two maximal countermovement jumps, with jump height measured simultaneously using a photoelectric system (Device A) and a jump mat (Device B).
RESULTS:
The spreadsheet produced precise estimates and accurate confidence-interval coverage, outperforming the mixed model for sample sizes as low as 10. Analysis of the jump-height data revealed typical errors of 5.6% (90% confidence interval 4.5 to 6.8%) and 7.1% (5.7 to 8.6%) for Devices A and B respectively, which consisted of biological variability of 5.4% (4.1 to 6.8%) combined with technical errors of 1.4% (-2.1 to 2.9%) and 4.5% (3.5 to 5.4%) for Devices A and B respectively. Using standardization with an external SD of 10% to assess magnitudes, the technical error for Device A made negligible contribution to its typical error, while the differences in technical and typical errors between Devices B and A were moderate and likely substantial. There was negligible mean bias in Device B relative to A (-0.6%, -1.6 to 0.6%).
CONCLUSION:
The spreadsheet provides accessible trustworthy analysis of reliability data taken simultaneously with two devices. The practical example highlights its relevance in contexts demanding precise measurement.
REFERENCE
1. Pueo et al., Int J Sports Physiol Perform, 2016
Funding: Generalitat Valenciana (grant number CIGE/2022/15).