Spread of results

Figure 1.22. The null and the alternate hypotheses Hq resp. Hi. The normal distribution probability curves show the expected spread of results. Since the alternate distribution ND(/tb, a might be shifted toward higher or lower values, two alternative hypotheses Hi and H are given. Compare with program HYPOTHESIS. Measurement B is clearly larger than A, whereas S is just inside the lower CL(A).

Figure 2 shows the spread of results for two different physiological and dosimetric models, even though a standardized exposure situation is assumed (OECD/NEA, 1983). 

The values quoted in Table 4.3 refer to the spread of results expected when a given sample is analysed in a number of separate laboratories. For repeat analyses carried out by one operator in a single laboratory, the coefficient of variation (%CV) would typically be one half to two thirds of the values shown in Table 4.3. For within-laboratory reproducibility (intermediate precision), the %CV should not be greater than the reproducibility %CV for the given concentration in Table 4.3. 

Why is the spread of the results from a number of laboratories likely to be larger than the spread of results obtained from one laboratory ... 

Relative measures of the spread of data are often used, particularly where, for example, the spread of results seems to increase with analyte concentration. The relative standard deviation (RSD) is a measure of the spread of data in comparison to the mean of the data ... 

Single crystals of zinc were broken106 by two cleavage and one tensile method. The 7 was about 100,400, and 575 erg/cm2, respectively, for these three arrangements. Also this wide spread of results is easier to reconcile with the new than with the Griffith theory. 

The standard uncertainty of a measurement result tells about the spread of results (dispersion) that would be expected given the basis on which it was estimated. It has the properties of a standard deviation, and with the appropriate degrees of freedom, a probability of finding a particular result can be calculated. The concept is illustrated in figure 6.1. 

Figure 6.1. An illustration of the concept of dispersion of measurement results. Upper panel results that might be obtained by multiple bona fide measurements. Each result is represented by a cross. Lower panel The spread of results expressed as a normal probability density based on a single result and knowledge of the measurement uncertainty.

While thousands of analyses of archaeological bronzes have been reported in the literature, the basis for comparing them, especially those from different laboratories, is shaky. A round-robin project of chemical analyses was attempted to improve the situation. Two ancient bronze objects were milled to a fine powder, sieved, and mixed to a homogeneous mass. Samples of 500 mg each drawn randomly from this mass were circulated, and results were returned from 21 laboratories. Forty-eight elements were analyzed some laboratories did only one element, some did as many as 42. The coefficient of variance (or relative standard deviation) ranges from 4% for Cu up to over 200% for some trace elements. The results are tabulated, and methods are suggested to narrow the spread of results in the next run of this program. 

In almost all cases our relative standard deviations are higher than Morrisons. This shows that we have a greater spread of results. 

Flanagan, working with USGS standard rocks (pieces of the Westerly Granite), shows an 11% relative standard deviation for Fe (in an amount around 1% ) much less than our value of 31-49% (12). The manganese determinations he reports have a relative standard deviation of 43%, again better than our 74% and 88%. We also have a greater spread of results than his. 

Fig. 4. Electrophoretic mobilities (Ug)of natural (untreated) - curve A - and treated particles as a function of salinity (S°/°<>) for two sets of samples from Keithing Burn (KB 1 open symbols - 31 March 1982 KB 2 closed symbols - 30 dune 1982). Shaded area B indicates the spread of results from other estuaries (redrawn from Fig. 3 of Hunter and Liss 1979). Curve D - suspended particles centrifuged and resuspended in UV- oxidized sample supernatant and then UV-oxidized. Curve C - natural samples (particles plus supernatant) UV-oxidized. Curve E - sample supernatant UV-oxidized to form new particles (UV-PPT). Several UV-PPT samples from KB2 were centrifuged and the particles resuspended in their original untreated sample supernatant. The resulting changes in Ug are indicated by the dashed lines (asterisks - final values). Keithing Burn suspended matter is mostly composed of iron oxides (after Loder and Liss, 1985).

Different carbon fibers were analyzed, which explains the spread of results. 

Precision is defined as the closeness of agreement between independent test results obtained under stipulated conditions . The precision of an analytical method is evaluated by making repeat independent measurements on identical samples to determine the spread of results. 

It is often necessary to estimate the spread of results obtained in different laboratories. A laboratory needs to show that the results from an analytical method are reproducible. Reproducibility is similar to repeatability except that the analyses are carried out on identical samples under reproducibility conditions e.g. different operator, different apparatus, different laboratory, long interval of time). Reproducibility limit is similar to repeatability limit except that the results are obtained under reproducibility conditions. 

Coning and quartering a paste [30] has been used for preparing samples down to about 20 mg in weight but the efficiency of the method is operator dependent. Lines [31] compared three methods of sampling powder prior to Coulter analysis and found a spread of results of +6% with cone and quartering, 3.25% with random selection and 1.25% with cone and quartering a paste. 

The CCSD results of Salek et al (2005) and the MCSCF results of Luo et al (1993) compute the frequency dependence as an intrinsic part of the correlated calculation. The work of Sim et alP (1993) and Reiss et al. (2005) takes the static value obtained at the MP2 level and scales it using the RPA method to get the frequency dependence. Luo et alP (1993) also report the result of an RHF/RPA calculation where the frequency dependence is the natural extension of the RHF method. The plotted points are at the four readily available laser frequencies that have been used in almost all experimental work. The most popular of these has been the YAG frequency corresponding to 1.17 eV or 1064 nm. At this frequency the spread of results ranges from about 1550 to 2600 au. If only the two fully frequency-dependent correlated calculations are considered the range is from about 1700 to 2600 au. Salek et al, using the CCSD method find that as the frequency is increased from zero to 1.17 eV, increases from 1736 to 2667 au and Luo et al, using MCSCF, from 1373 to 1898 au. 

Table 5 shows the experimental specific refractivities, K X) = n(l) l]/ p, and the average polarizability as calculated from equation (1) at a number of frequencies for liquid and vapour phases. The values of the specific refractivity of the vapour have been obtained from the Cauchy dispersion formula of Zeiss and Meath.39 In this paper the authors assess the results of a number of experimental determinations of the refractive index of water vapour and its variation with frequency. Even after some normalization of the data to harmonize the absolute values from different determinations there is a one or two percent spread of results at any one wavelength. Extrapolation of the renormalized data for five independent sets of data leads to zero frequency values of K(7.) within the range (2.985-3.013) x 10-4 m3 kg 1, giving, via equation (1), LL — 9.63 0.10 au. Extrapolation of the earlier refractive index data of Cuthbertson and Cuthbertson40 by Russell and Spackman41 from 8 values of frequency between 0.068 and 0.095 au, leads to a zero frequency value, of y.i, 1,(0) = 9.83 au. While the considerable variation between the raw experimental data reported in different determinations is cause for some uncertainty, it appears that the most convincing analysis to date is that of... 

Table 5.8 Results of analysis of Conostan 20 oil blend spiked with the listed metals. The results in brackets are scatter for six measurements and symbol a is used to denote the spread of results over six measurements...

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