Indeterminate errors evaluation

Evaluating Indeterminate Error Although it is impossible to eliminate indeterminate error, its effect can be minimized if the sources and relative magnitudes of the indeterminate error are known. Indeterminate errors may be estimated by an appropriate measure of spread. Typically, a standard deviation is used, although in some cases estimated values are used. The contribution from analytical instruments and equipment are easily measured or estimated. Indeterminate errors introduced by the analyst, such as inconsistencies in the treatment of individual samples, are more difficult to estimate. 

To evaluate the effect of indeterminate error on the data in Table 4.1, ten replicate determinations of the mass of a single penny were made, with results shown in Table 4.7. The standard deviation for the data in Table 4.1 is 0.051, and it is 0.0024 for the data in Table 4.7. The significantly better precision when determining the mass of a single penny suggests that the precision of this analysis is not limited by the balance used to measure mass, but is due to a significant variability in the masses of individual pennies. 

We can evaluate the impact of indeterminate error due to instrumental noise on the information obtained from transmittance measurements. The following discussion apphes to UV/ VIS spectrometers operated in regions where the hght source intensity is low or the detector sensitivity is low and to IR spectrometers where noise in the thermal detector is signihcant. 

A variety of statistical methods may be used to compare three or more sets of data. The most commonly used method is an analysis of variance (ANOVA). In its simplest form, a one-way ANOVA allows the importance of a single variable, such as the identity of the analyst, to be determined. The importance of this variable is evaluated by comparing its variance with the variance explained by indeterminate sources of error inherent to the analytical method. 

The vector u is an n+m dimensional vector which can be partitioned into two vectors the n-dimensional vector x of measured parameters and the m-dimensional vector of unmeasured ones. Some of the unmeasured variables can be evaluated from the measurement of the others variables using the balance equations, and some not. Thus, the unmeasured parameters may be classified as "determinable" or "indeterminable". On the other hand, some of the elements of vector x of measured variables can be computed from the balances and the rest of the measured parameters. Such measured variables will be called "overdetermined". The rest of the elements of vector x will be called "just determined". Measurement of x is denoted by x, and the difference of any measured system parameter and its true value is called the "error" denoted by 6, i.e. 

It is evident from this example that, though the evaluation of the electrochemical parameters Ic and Be is very good, this method for the numerical determination of the solution resistance introduces an unacceptable error in the calculation of R,. But this indetermination does not depend on the numerical method that has been adopted because the values of Ic and Be are reproduced very faithfully. This aspect is very important because it shows that the accuracy of a technique should be assessed by examining some cases in which all the parameters are known. 

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