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SystematicErrors

SystematicErrors - SystematicErrors The follow ing material...

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SystematicErrors The following material is from Skoog, Holler & Crouch, Principles of Instrumental Analysis, 6 th ,Thomson Brooks/Cole, Canada, 2007, 967 - 988, unless otherwise attributed. "Every physical measurement is subject to a degree of uncertainty that, at best, can only be decreased to an acceptable level. The determination of the magnitude of this uncertainty is often difficult and requires additional effort, ingenuity, and good judgment on the part of the observer. Nevertheless, evaluation of the uncertainty in analytical data is a task that cannot be neglected because a measurement of totally unknown reliability is worthless." ( ( Skoog & West, Analytical Chemistry, 4 th , Saunders College Publishing, PA, 1982, 25.) Precision and Accuracy Two terms are widely used in discussions of the reliability of data: precision and accuracy. Precision Precision describes the reproducibility of results, that is, the agreement between numerical values for two or more replicate measurements, or measurements that have been made in exactly the same way. Generally, the precision of an analytical method is readily obtained by simply repeating the measurement. Three terms are widely used to describe the precision of a set of replicate data: standard deviation, variance, and coefficient of variation. These terms have statistical significance. Accuracy Accuracy describes the correctness of an experimental result expressed as the closeness of the measurement to the true or accepted value. Accuracy is expressed in terms of either absolute error or relative error. The absolute error E of the mean (or average) of a small set of replicate analyses is given by the relationship Equation 1 E = - x i where x i is the true or accepted value of the quantity being measured. Often, it is useful to express the accuracy in terms of the relative error E r , where Equation 2 We will be concerned with two types of errors, random errors, often called indeterminate errors, and systematic errors, often called determinant errors. We will give random error the symbol E d and systematic error the symbol E s . The error in the mean of a set of replicate measurements is then the sum of these two types of errors: Equation 3 E = E d + E s Systematic or Determinant Errors Systematic errors have a definite value and an assignable cause and are of the same magnitude for replicate measurements made in the same way. Systematic errors lead to bias in measurement results. Bias is illustrated by the two curves in Figure 2, which show the frequency distribution of replicate results in the analysis of identical samples by two methods that have random errors of identical size. Method A has no bias so that the mean µ A is the true value. Method B has a bias that is given by Equation 5 Bias = µ B µ A
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Note that bias affects all of the data in a set and that it bears a sign. Systematic errors are of three types: instrumental, personal, and method.
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