ABSTRACT OBJECTIVE This study aims to propose a comprehensive alternative to the Bland-Altman plot method, addressing its limitations and providing a statistical framework for evaluating the equivalences of measurement techniques. This involves introducing an innovative three-step approach for assessing accuracy, precision, and agreement between techniques, which enhances objectivity in equivalence assessment. Additionally, the development of an R package that is easy to use enables researchers to efficiently analyze and interpret technique equivalences. METHODS Inferential statistics support for equivalence between measurement techniques was proposed in three nested tests. These were based on structural regressions with the goal to assess the equivalence of structural means (accuracy), the equivalence of structural variances (precision), and concordance with the structural bisector line (agreement in measurements obtained from the same subject), using analytical methods and robust approach by bootstrapping. To promote better understanding, graphical outputs following Bland and Altman's principles were also implemented. RESULTS The performance of this method was shown and confronted by five data sets from previously published articles that used Bland and Altman's method. One case demonstrated strict equivalence, three cases showed partial equivalence, and one showed poor equivalence.

The developed R package containing open codes and data are available for free and with installation instructions at Harvard Dataverse at https:

//doi.org/10.7910/DVN/AGJPZH. CONCLUSION Although easy to communicate, the widely cited and applied Bland and Altman plot method is often misinterpreted, since it lacks suitable inferential statistical support. Common alternatives, such as Pearson's correlation or ordinal least-square linear regression, also fail to locate the weakness of each measurement technique. It may be possible to test whether two techniques have full equivalence by preserving graphical communication, in accordance with Bland and Altman's principles, but also adding robust and suitable inferential statistics. Decomposing equivalence into three features (accuracy, precision, and agreement) helps to locate the sources of the problem when fixing a new technique.