Background: Bland and Altman plot method is a widely cited graphical approach to assess equivalence of quantitative measurement techniques. It has been widely applied, however often misinterpreted by lacking of inferential statistical support. We aim to develop and distribute a statistical method in R in order to add robust and suitable inferential statistics of equivalence. Methods: Three nested tests based on structural regressions are proposed to assess the equivalence of structural means (accuracy), equivalence of structural variances (precision), and concordance with the structural bisector line (agreement in measurements of data pairs obtained from the same subject) to reach statistical support for the equivalence of measurement techniques. Graphical outputs illustrating these three tests were added to follow Bland and Altman's principles of easy communication. Results: Statistical p-values and robust approach by bootstrapping with corresponding graphs provide objective, robust measures of equivalence. Five pairs of data sets were analyzed in order to criticize previously published articles that applied the Bland and Altman's principles, thus showing the suitability of the present statistical approach. In one case it was demonstrated strict equivalence, three cases showed partial equivalence, and one case showed poor equivalence. Package containing open codes and data is available with installation instructions on GitHub for free distribution. Conclusions: Statistical p-values and robust approach assess the equivalence of accuracy, precision, and agreement for measurement techniques. Decomposition in three tests helps the location of any disagreement as a means to fix a new technique.