Reproducibility error

Figure 2. Model vs. natural system inputs, outputs, and errors. (Reproduced with permission from Ref. 2.)...

Second, there is no unique scheme of data interpretation. The process of inference always remains arbitrary to some extent. In fact, all the existing DDT data combined still allow for an infinite number of models that could reproduce these data, even if we were to disregard the measurement uncertainties and take the data as absolute numbers. Although this may sound strange, it is less so if we think in terms of degrees of freedom. Let us assume that there are one million measurements of DDT concentration in the environment. Then a model which contains one million adjustable parameters can, in principle, exactly (that is, without residual error) reproduce these data. If we included models with more adjustable parameters than observa-... 

Fig. 13. Temperature dependence of the fraction of RNase-A in the denatured form as estimated by (O) sedimentation and ( ) viscosity. Solvent 0.15 M KC1 pH 2.8 phthalate buffer. The size of the circles is an approximate estimate of experimental error. Reproduced from Holcomb and Van Holde (261).

Using a ring-disk probe (also called inverse SORS) in backscattered geometry we have been able to reach bone about 6 mm below the skin [60]. Mineral/matrix ratios are accurately (<4% relative error) reproduced if a protocol for optimizing the ring/disk spacing is followed [62]. 

Figure 2.17 System aberrations of the X-ray diffractometer due to axial-divergence and flat-specimen errors. (Reproduced with permission from R. Jenkins and R.L. Snyder, Introduction to X-ray Powder Diffractometry, John Wiley Sons Inc., New York. 1996 John Wiley Sons Inc.)...

Figure 8. The interaction energies of the 7t-(H20)M complexes. The energies have been evaluated at the MP2/aug-cc-pVDZ level and have been corrected for both zero point vibrational energies and basis set superposition errors. (Reproduced by permission of American Institute of Physics [136])...

The initial requirements for the determination of statistical significance have been addressed by recent improvements in the experiment acquisition process. Systematic errors, reproducibility concerns, and bias in the data acquisition process (see Sections 4.3 and 4.4) have been minimized... 

Fig. 137. Di rect analysis of BNRM H-3A steel A/ith an accuracy better than 5%. All sample by a single laser ablation pulse and experimental concentrations were determined ICP-TOF-MS. All elements at concentrations to A/ithin 16% error. (Reproduced A/ith greater than 0.5% by mass A/ere measured permission from Ref. [680].)...

The error attributed to the determination of the NHV (calorimetric measurement, determination of hydrogen content, and final calculation) is satisfactory with a repeatability of 0.3% and a reproducibility of 0.4%. 

This work allows the optimization of the testing conditions in order to minimize human error in the inteipretation and obtaining of an reproducible and clear anomaly spectrum. 

There are several variations of this method. The PRDDO/M method is parameterized to reproduce electrostatic potentials. The PRDDO/M/FCP method uses frozen core potentials. PRDDO/M/NQ uses an approximation called not quite orthogonal orbitals in order to give efficient calculations on very large molecules. The results of these methods are fairly good overall, although bond lengths involving alkali metals tend to be somewhat in error. 

There are many more error correction methods, which are reviewed in detail by Duch and Diercksen. They also discuss the correction of other wave functions, such as multireference methods. In their tests with various numbers of Be atoms, the correction most closely reproducing the full Cl energy is... 

The parameters in the original parameterization are adjusted in order to reproduce the correct results. These results are generally molecular geometries and energy differences. They may be obtained from various types of experimental results or ah initio calculations. The sources of these correct results can also be a source of error. Ah initio results are only correct to some degree of accuracy. Likewise, crystal structures are influenced by crystal-packing forces. 

These partial rate factors have been recalculated from the experimental data of Dewar and Urch. Their reported values for diphenylmethane are not seriously discrepant with the values now given, but this is not so for the values for fluorene. As given, and copied in the literature, the values were /j = 2040 / = 60 fi = 944. There are consequent errors in table 8 and figs. 16 (reproduced as fig. 9. i of this volume) and 32 of ref. 22. 

The precision of a result is its reproducibility the accuracy is its nearness to the truth. A systematic error causes a loss of accuracy, and it may or may not impair the precision depending upon whether the error is constant or variable. Random errors cause a lowering of reproducibility, but by making sufficient observations it is possible to overcome the scatter within limits so that the accuracy may not necessarily be affected. Statistical treatment can properly be applied only to random errors. 

Collaborative testing provides a means for estimating the variability (or reproducibility) among analysts in different labs. If the variability is significant, we can determine that portion due to random errors traceable to the method (Orand) and that due to systematic differences between the analysts (Osys). In the previous two sections we saw how a two-sample collaborative test, or an analysis of variance can be used to estimate Grand and Osys (or oJand and Osys). We have not considered, however, what is a reasonable value for a method s reproducibility. 

Hydrogen bond geometries may be reproduced or predicted fairly weH with reasonable, but sometimes underestimated heavy atom—heavy atom distances radial dependence of the hydrogen bond may be in error. 

Accuracy and Interpretation of Measured pH Values. The acidity function which is the experimental basis for the assignment of pH, is reproducible within about 0.003 pH unit from 10 to 40°C. If the ionic strength is known, the assignment of numerical values to the activity coefficient of chloride ion does not add to the uncertainty. However, errors in the standard potential of the cell, in the composition of the buffer materials, and ia the preparatioa of the solutioas may raise the uacertaiaty to 0.005 pH unit. 

Estimations based on statistics can be made for total accuracy, precision, and reproducibility of results related to the sampling procedure being applied. Statistical error is expressed in terms of variance. Total samphng error is the sum of error variance from each step of the process. However, discussions herein will take into consideration only step (I)—mechanical extraction of samples. Mechanical-extracdion accuracy is dependent on design reflecding mechanical and statistical factors in carrying out efficient and practical collection of representative samples S from a bulk quantity B,... 

The possibility of preconcentration of selenium (IV) by coprecipitation with iron (III) hydroxide and lanthanum (III) hydroxide with subsequent determination by flame atomic absorption spectroscopy has been investigated also. The effect of nature and concentration of collector and interfering ions on precision accuracy and reproducibility of analytical signal A has been studied. Application of FefOH) as copreconcentrant leads to small relative error (less than 5%). S, is 0.1-0.2 for 5-100 p.g Se in the sample. Concentration factor is 6. The effect of concentration of hydrochloric acid on precision and accuracy of AAS determination of Se has been studied. The best results were obtained with HCl (1 1). 

While SCREEN.DAT should still reproduce the correct results, it will be easier to work with the file if the original input does not contain any errors. 

Systematic error, as stated above, can be eliminated— not totally, but usually to a sufficient degree. This elimination process is called calibration. Calibration is simply a procedure where the result of measurement recorded by an instrument is compared with the measurement result of a standard. A standard is a measuring device intended to define, to represent physically, to conserve, or to reproduce the unit of measurement in order to transmit it to other measuring instruments by comparison. There are several categories of standards, but, simplifying a little, a standard is an instrument with a very high accuracy and can for that reason be... 

A more difficult criterion to meet with flow markers is that the polymer samples not contain interferents that coelute with or very near the flow marker and either affect its retention time or the ability of the analyst to reproducibly identify the retention time of the peak. Water is a ubiquitous problem in nonaqueous GPC and, when using a refractive index detector, it can cause a variable magnitude, negative area peak that may coelute with certain choices of totally permeated flow markers. This variable area negative peak may alter the apparent position of the flow marker when the flow rate has actually been invariant, thereby causing the user to falsely adjust data to compensate for the flow error. Similar problems can occur with the elution of positive peaks that are not exactly identical in elution to the totally permeated flow marker. Species that often contribute to these problems are residual monomer, reactants, surfactants, by-products, or buffers from the synthesis of the polymer. 

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