B Systematic Errors

Typical two-sample plot when (a) random errors are larger than systematic errors due to the analysts and (b) systematic errors due to the analysts are larger than the random errors. 

Cropley, J.B., Systematic Errors in Recycle Reactor Kinetic Studies, Chemical Engineeiing Piogiess, February 1987, 46-51. (Model building, experimental design)... 

Cox, D.C. Furman, W.B. Systematic error associated with apparatus 2 of the USP dissolution test V interaction of two tableted prednisone formulations with glass and plastic vessels. J. Pharm. Sci. 1984, 73, 1125-1127. 

Fig. 19 Core sampler with end-cap can be used for freely-flowing (e.g., granulated) materials that would escape from the sampling tube during removal from the bed without the end-cap. (A) Very little entrainment is visible after insertion, and (B) systematic errors are reduced.

Figure 19-10 Power functions for l2s control rule. A, Random error. B, Systematic error. (From Westgard JO, Groth T. Power functions for statistical control rules. Clin Chem 1979 25 863-9.)...

Partitioning of random error, systematic errors due to the analyst, and systematic error due to the method for (a) replicate analyses performed by a single analyst and (b) single determinations performed by several analysts. 

Analysis of the sample before and after the spike gave signals of0.456 for B and f.03 for sample Bsl- Considering these data, what is the most likely source of the systematic error ... 

Cullinan presented an extension of Cussler s cluster diffusion the-oiy. His method accurately accounts for composition and temperature dependence of diffusivity. It is novel in that it contains no adjustable constants, and it relates transport properties and solution thermodynamics. This equation has been tested for six very different mixtures by Rollins and Knaebel, and it was found to agree remarkably well with data for most conditions, considering the absence of adjustable parameters. In the dilute region (of either A or B), there are systematic errors probably caused by the breakdown of certain implicit assumptions (that nevertheless appear to be generally vahd at higher concentrations). 

The reliability factor B was 0276 after the first refinement and 0-211 after the fourth refinement. The parameters from the third and fourth refinements differed very little from one another. The final values are given in Table 1. As large systematic errors were introduced in the refinement process by the unavoidable use of very poor atomic form factors, the probable errors in the parameters as obtained in the refinement were considered to be of questionable significance. For this reason they are not given in the table. The average error was, however, estimated to be 0-001 for the positional parameters and 5% for the compositional parameters. The scattering power of the two atoms of type A was given by the least-squares refinement as only 0-8 times that of aluminum (the fraction... 

Equations (8.44) and (8.45) guarantee convergence to a canonical distribution only in the case of fixed B. Because B varies (i.e., the method uses information from momenta sampled in the past in determining the vector B), the evolution is not strictly Markovian. As a consequence, the correlations introduced can lead to the accumulation of systematic errors in the determination of configuration averages [77], However, these correlations can be broken if the update of B is not done each step, but with a lower updating frequency. This is analogous to other approximately Markovian procedures employed in MC simulations (e.g., update of the maximum displacements allowed for individual atoms [78]). 

Figure 38-1 Two-sample charts illustrating systematic errors for Methods A vs. B.

The systematic error contribution is larger for METHOD B than METHOD A. 

If you answered (b), perhaps you were thinking of the spread of values obtained from replicate measurements. While these do indeed form a range, one such range will relate to only one source of uncertainty and there may be several sources of uncertainty affecting a particular measurement. The precision of a measurement is an indication of the random error associated with it. This takes no account of any systematic errors that may be connected with the measurement. It is important to realize that uncertainty covers the effects of both random error and systematic error and, moreover, takes into account multiple sources of these effects where they are known to exist and are considered significant. 

The preceding analysis neglects the fact that for very fast follow-up reactions, transformation of B into C may take place within the solvent cage before separation of B and P (Scheme 2.14). The ensuing systematic error is an increasing function of kc but does not exceed +30 mV for rate constants as high as 1011 M-1 s-1.21 Typical examples concern the reductive cleavage of chloro- and bromobenzenes and pyridines.22... 

When the difference D between the results A and B is computed the systematic errors, which have the same magnitude and sign, will cancel. This leaves the difference of the two random error components, which do not necessarily cancel for a particular pair. 

Figure 4) No systematic error is present. The only error contribution is the result of random deviations in the results obtained for the two quality control samples, A and B. 

Possible difficulties in obtaining accurate retention data for physicochemical measurements should be recognized, however. The evaluation of to, the elution time of an "unretained peak (274) is often connected with systematic error and the measurement of the retention time of asymmetrical peaks may not be accurate. Moreover, no satisfactory methods are available for the precise evaluation of the phase ratio in the column. Consequently, the measurement of the equflibrium constant proper is beset with difficulties as discussed in Section VII.B. 

Systematic errors in analysis can usually be eliminated but true random errors are due to operations in an assay which are not completely controlled. A common type of random error arises from the acceptance of manufacturers tolerances for glassware. Table 1.2 gives the RSD values specified for certain items of grades A and B glassware. 

A next attempt involved fitting the experimental results of Table I to Eq. (Al). This 80-point least-squares fit led to K—49.4, a= 1.031, b=0.113, c = 0.537, d = 1.998, and tr = 0.02129 (5.2%), which reflected about the right dependence of P cPti on N b, Qub, and pa, but failed to reflect the predicted dependence on b (thereby leading to large values of K). Since a disproportionate number of the data points (75 of 80) were for explosives wherein Mtxb varied over the relatively narrow range 27.2-31.3, we feel that the dependency of P on Mt,rb may have been masked by the systematic errors in the measurements. It should be noted that if, as the results seem to show, exponents near 1.0 and 0.5 for jVwb and Q b realistically reflect the influences of these properties of the explosive on P, an exponent near 0.5 for M rb in Eq. (1) is necessary to introduce the buffering phenomenon discussed in the present series of papers. 

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