B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 1 Basic Course Experiments to Demonstrate Intercomparisons (1) Description of underlying experiments (2) Statistical evaluation of data (3) Teaching material for subsequent tutorials

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 2 Experimental volumetric method: titration of aliquots (25 mL) of an aqueous solution of NaOH (c  0.01 mol L -1 ) with a standard solution of H 2 SO 4 (c 1 = 0.1 mol L -1,c 2 = mol L -1 ) employing a manual 50 mL-burette each student analyzes aliquots of the same solution each student repeats the titration three times with each standard solution  six titrations per student the results are handed out to supervisors via tables containing the consumed volume of standard solution

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 3 Statistical Data Evaluation: Formation of Classes set of 54 experiments histogram Gaussian normal distribution? V/(10 -2 mL) N

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 4 Statistical Data Evaluation: the Probability Function cumulative frequency V/10 -2 mL N

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 5 Statistical Data Evaluation: the Probability Function normalized cumulative frequency x P(x)

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 6 Normal Probability Plot ,5 99,999 P(V) V/mL special graph paper:normal probability paper straight line  normal distribution

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 7 Probability =  (z, ,  ) Density of probability =  (x, ,  ) Distribution function Probability Equation: Mathematical Description

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 8 The Gaussian Distribution Function two parameters:  = maximum  = spread In most cases repeated measurements of a single quantity are normally distributed (after elimination of outliers).

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 9 Calculation of Estimates from Experimental Data arithmetic mean = estimate of  = sum of all measurements; n = number of measurements standard deviation s = estimate of  relative standard deviation (RSD) = (s/ )  100 

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 10 The RSD is a measure of the precision of a method. The precision of a method can be improved by variation of experimental parameters. Influence of Experimental Parameters on Standard Deviation (manual 50 mL-burette) Concentration of standard solution: c 1 = 0.1 mol L -1 c 2 = mol L mL25.71 mL s0.118 mL0.249 mL RSD3.67 %0.97% N5454

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 11 Improving Precision by Repeated Measurements 18 students, each student performed three titrations (N=54)  arithmetic mean of three results c0.1 mol L mol L mL25.70 mL s0.118 mL0.249 mL RSD3.66 %0.97% 3.22 mL25.70 mL s M mL0.215 mL RSD M 2.68 %0.84% The RSD is a measure of the precision of a method. The precision of a method can be improved by forming the arithmetic mean of the results of repeated measurements.

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 12 Standard Deviation of the Mean mean of a sample of measurements  estimate of the true value  in case of no systematic deviation:  = quantity to be measured standard error of the mean = standard deviation of the mean s M

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 13 Normal Distribution with Different Spread

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 14 Analyzing the Measurement Uncertainty (1) random deviation: volume uncertainty volumetric flask, volume uncertainty burette, reading uncertainty volumetric flask, reading uncertainty burette (dominating when using not-appropriate standard solution), individual uncertainties (2) systematic deviation: i.e. uncertainty of concentration of standard solution, cannot be reduced by forming the arithmetic mean of the results of repeated measurements

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 15 Definition: Precision Precision = closeness of agreement between independent test results obtained under stipulated conditions (ISO , 1993) high precision  low standard deviation low precision  large standard deviation estimate of the precision does not consider the deviation of the arithmetic mean of a series of results from the true value precision can be estimated if the true value is not known

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 16 Definition: Accuracy Accuracy = closeness of agreement between the result of a measurement and the true value of the measurand (International vocabulary.....,1984) accuracy is not only given by the spread of a normal distribution, but also by the deviation of the arithmetic mean of a series of results from the true value accuracy can only be determined if the true value is known

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 17 Confidence Limits of the Mean confidence interval = range within, with given probability, the true value lies confidence limits = extreme values of the confidence range t is a factor that depends both on the degree of confidence required and the degrees of freedom (n - 1) The confidence limit is a measure of the precision of a result. The precision of a result can be improved by repeated analysis.

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 18 Confidence Limits of the Mean

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 19 Presentation of Analytical Results (1) Possibilities of presentation (1) as estimate of the quantity measured, s as estimate of the precision (2) as estimate of the quantity measured, 95% confidence limit as estimate of the precision of the measurement no universal convention  the form used has to be stated, n has to be given No quantitative experimental value is of any value unless it is accompanied by an estimate of the uncertainty involved in its measurement.

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 20 arithmetic mean three significant figures Presentation of Analytical Results (2) The number of significant figures given indicates the precision of a value. significant figures: all digits which are certain plus the first uncertain one In our case result of titration: c(NaOH) = mol L -1 ( mol L -1 ) n = 54 number of measurements standard deviation

B. Neidhart, W. Wegscheider (Eds.): Quality in Chemical Measurements © Springer-Verlag Berlin Heidelberg 2000 U. PyellBasic Course Experiments to Demonstrate Intercomparisons 21 Summary Learning objectives statistical deviation  systematic deviation Gaussian normal distribution, statistical evaluation of data improving the precision of a method presentation of data