Comparing regression relationships: application to chemically modified electrodes

When developing new chemically modified electrodes (CMEs), as currently done in this laboratory, attention is always paid to carefully evaluate their experimental performances [1-3]. This is especially needed after some tentative modifications of experimental conditions. Comparing regression relationships (RRs), usually obtained by ordinary least square regression, may help in deciding the right direction towards the optimization of electrode performances. This implies evaluating if significant differences exist between slopes and/or intercepts of RRs, hence if experimental differences arise only by inevitable random errors or not. In practice, the necessary tests should allow verifying if the considered regression relationships come from the same RRs population from which the actual samples are drawn. It was suggested that such a kind of comparisons can be performed by specific Student’s t-tests [4]. The flow chart for comparing two RRs is presented in the figure. H0: b1=b2 H0: not rejected H0: rejected 1 Compute common slope 2 H0: a1=a2 END H0: not rejected H0: rejected 1 Compute common END regression relationship 2 END (regression lines are significantly different) (regression lines are parrallel) Figure: Flow chart for the regression of two RRs; b: slopes; a: intercepts. Comparing more that two RRs is also possible by similar tests [4]. The matter is presented with the help of specifically developed Mathcad worksheets. Some examples are described by using simulated results as well as results relevant to CMEs developed in this laboratory. [1] E. Desimoni, Analyst, 124 (1999) 1191-1196 [2] E. Desimoni, B. Brunetti, Anal. Chim. Acta, 655 (2009) 30-37 [3] E. Desimoni, B. Brunetti, Accred. Qual. Assur., 17 (2012) 635-637 [4] J.H. Zar, Biostatistical analysis, 5th Ed., Prentice Hall, Inc., Upper Saddle River, New Jersey, US, 2010