Assessing the accuracy of analytical methods using linear regression with errors in both axes

In this paper, a new technique for assessing the accuracy of analytical methods using linear regression is reported. The results of newly developed analytical methods are regressed against the results obtained using reference methods. The new test is based on the joint confidence interval for the slope and the intercept of the regression line, which is calculated taking the uncertainties in both axes into account. The slope, intercept, and variances which are associated with the regression coefficients are calculated with bivariate least-squares regression (BLS). The new technique was validated using three simulated and five real data sets. The Monte Carlo method was applied to obtain 100 000 data sets for each of the initial simulated data sets to show the correctness of the new technique. The application of the new technique to five real data sets enables differences to be detected between the results of the joint confidence interval based on the BLS method and the results of the commonly used tests based on ordinary least-squares or weighted least-squares regression.