B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 E. EvansEstimation of Random Deviations in Analytical Methods Using Analysis of Variance 1 Estimation of Random Deviations in Analytical Methods using Analysis of Variance Objectives Application of good experimental design Importance of replication and randomisation Use of F-tests and hypothesis testing Estimation of random deviations in an analytical method

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 E. EvansEstimation of Random Deviations in Analytical Methods Using Analysis of Variance 2 Experimental Design Fixed and random effects Factors and levels Replication Randomisation

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 E. EvansEstimation of Random Deviations in Analytical Methods Using Analysis of Variance 3 Analytical Methods Can be simple one-step procedures or involving multiple steps and complex manipulations Tend to be hierarchical in nature Difficult to estimate the relative variance contribution of each step

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 E. EvansEstimation of Random Deviations in Analytical Methods Using Analysis of Variance 4 Schematic of Hierarchical Extraction Method Extract with acetic acid for 30 min Centrifuge and separate supernatant Extract with hydroxylammonium chloride for 30 min Analyse supernatant using FAAS

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 E. EvansEstimation of Random Deviations in Analytical Methods Using Analysis of Variance 5 Experimental Design for Extraction of Zn

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 E. EvansEstimation of Random Deviations in Analytical Methods Using Analysis of Variance 6 The Statistical Model

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 E. EvansEstimation of Random Deviations in Analytical Methods Using Analysis of Variance 7 Breakdown of the Variance Contributions

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 E. EvansEstimation of Random Deviations in Analytical Methods Using Analysis of Variance 8 The Null Hypothesis H 0 "The extraction does not contribute significantly to the overall variance of the method".

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 E. EvansEstimation of Random Deviations in Analytical Methods Using Analysis of Variance 9 Testing the Null Hypothesis If P = the probability of rejecting H 0 when it is true then: P<0.001: very strong evidence against H 0 (i.e % confidence level). P<0.01:strong evidence against H 0 (i.e. 99 % confidence level). P<0.05:some evidence against H 0 (i.e. 95% confidence level). P>0.05:little or no evidence against H 0

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 E. EvansEstimation of Random Deviations in Analytical Methods Using Analysis of Variance 10 Randomised Order of Analysis

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 E. EvansEstimation of Random Deviations in Analytical Methods Using Analysis of Variance 11 Sample Data

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 E. EvansEstimation of Random Deviations in Analytical Methods Using Analysis of Variance 12 Results of ANOVA Factor E1E2(E1)Error DF 2618 SS MS F P Variance component % variance