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Introduction to design Olav M. Kvalheim Content • Making your data work twice • Effect of correlation on data interpretation • Effect of interaction on data interpretation Chemometrics/Infometrics Design of information-rich experiments and use of multivariate methods for extraction of maximum relevant information from data Making your data work twice What is Information? •A - mean value, no standard deviation given B C A •B - mean value with standard deviation given, large value of stand. dev. •C - mean value, low standard deviation Measurement strategy? A B Unknowns Calibration Weights Hotelling (1944) Ann. Math. Statistics 15, 297-306 The univariate weighing design Weigh A and B separately mA ± A mB ± B A = B= Precision is for both A and B The multivariate design Weigh A and B jointly to determine sum and difference: mA+ mB =S mA = ½S + ½D mB = ½S - ½D mA- mB =D A B 1 2 1 2 1 0.7 4 4 2 Precision for S Precision for D Precision is 0.7 for both A and B Univariate vs Bivariate strategy Precision in mAand mB Univariate Design Bivariate Design 0.7 Precision is improved by 30% by using a multivariate design with the same number of measurementsas for the univariate! Univariate vs Multivariate weighing With N masses to weigh, a multivariate design provides an 1 estimate of each mass with a precision N The larger the number of unknowns, the larger the gain in precision using a multivariate weighing design. Effect of correlation on data interpretation X1 X 2 Example • Process output is function of temperature and amount of catalyst Correlation between amount of catalyst and amount produced • Strong positive correspondence Correlation between Temperature and Produced amount • Weak positive correspondence Conclusion from correlation analysis • Increase amount of catalyst and temperature to increase production Result of test • Produced amount was lowered! Bivariate Regression Model • Produced amount = 300 • + 2.0 * Catalyst • - 0.5 * Temperature Correlation between temperature and amount of catalyst • Strong positive correspondence Solution to correlation problem • Multivariate Design - Change many process variables simultaneously according to experimental designs Effect of interaction on data interpretation X1X2 The task The yield of a chemical reaction is a function of temperature (t) and concentration (c). y = f (t,c) Optimise the yield for the reaction! Response surface in the presence of interaction Temperature, ºC 170 70 60 50 45 40 75 160 150 140 0.1 0.2 Concentration, M Efficiency of information extraction Information Multivariate design Univariate design (COST) Number of experiments Multivariate Design vs. Univariate Design • Correct Models Possible (Interactions) • Efficient Experimentation • Improved Precision/Information quality