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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

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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

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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

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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

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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

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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

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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

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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".

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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. 99.9 % 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

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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

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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

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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 674.171928.9115.71 MS 337.09321.490.87 F 1.05368.35 P 0.4070.000 Variance component 1.734106.8710.873 % variance 1.697.60.8

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