A review of the satatistical considerations involved in the treatment of isotope dilution calibration data

The use of linear regression analysis for the reduction of isotope dilution data is reviewed. The calculation of linear regression statistics is based upon four assumptions: zero variance in the independent variable, equal variance for all values of the dependent variable, linearity and continuity. Unfortunately, isotope dilution data often violate one or more of these assumptions, which results in the calculation of an inaccurate calibration line. The inaccuracies can be avoided through careful inspection of the data, including analyses of variance and linearity. Large differences in the variances of the dependent variable require the use of a weighted linear regression. Nonlinearity necessitates either discarding data in the nonlinear portion of the calibration or the calculation and use of atom % excess and dilution instead of the sample isotope ratios.