Standard error of the laboratory

First we need to state some basic statistics, which is of crucial importance in the following sections. When determining a continuous variable such as fat or moisture content, etc. with a wet chemistry laboratory reference method, it is important to estimate the standard error of the laboratory reference method (SEL or Sref). Assume that there are A[l, 2,A] samples, each measured in M[l, 2,... y,... A/] replicates and that the average from the replicates is used in the multivariate NIR... 

Standard error of the laboratory reference method (Sret) as defined above. This error term is or should be easy to calculate. 

This study used beef samples spanning a relatively wide range of the components, for example, 1-23% fat (Table 7.3.4). The standard error of the laboratory reference method (SEL or S f) was 0.11% for moisture, 0.075% for protein, and 0.054% for fat. 

In the first study, a pilot plant grinder was used. Beef batches of 20 kg with ranges of 6.2-21.7% fat, 59.6-72.9% moisture, and 18.1-20.7% protein were analyzed. The grinder was equipped with several different plate hole diameters 4,8,13, and 19 mm. Spectra were taken with all four grinder plates. The standard error of the laboratory reference method (Sret) varied with the grinder plate hole diameter and was 0.12-0.24% for fat, 0.12-0.25% for moisture, and 0.07-0.10% for protein. 

Statistics Standard Error of the Laboratory (SEE) for Wet Chemical Methods Abbreviation(s) SEE... 

RMS = root mean square noise of the instrument. SEC = standard error of calibration for each constituent. SEA = standard error of analysis or the difference between analysis values from the same samples analyzed by NIR and the reference laboratory. SED = standard error of a difference. Factory SED = standard error of the difference between the same samples analyzed by the master and slave instrument at different times. H = standardized H statistic. SEE = standard error of the laboratory reference values. (This statistic can be either the difference between duplicates in one laboratory or the difference between the same samples analyzed by two different laboratories.) M SEE = standard error of blind duplicates in the master reference laboratory. 

Vitha, M. F. Carr, P. W. A Laboratory Exercise in Statistical Analysis of Data, /. Chem. Educ. 1997, 74, 998-1000. Students determine the average weight of vitamin E pills using several different methods (one at a time, in sets of ten pills, and in sets of 100 pills). The data collected by the class are pooled together, plotted as histograms, and compared with results predicted by a normal distribution. The histograms and standard deviations for the pooled data also show the effect of sample size on the standard error of the mean. 

Outlying variances, e.g. as reflected by a Cochran test, do reveal that some sets of data suffer insufficient precision compared to the other sets obtained by other laboratories. Such sets affect the final uncertainty of the certified value but not the certified value as such. The technical discussion should address the reason why a set of data lacks precision (day to day bias ) or why in one laboratory the reproducibility figure is much lower than for the rest of the participants (repeatability figure rather than reproducibility, selection of data, not fully independent measurements etc.). Sets of data are rejected if the standard error of the mean (s/n) exceeds the standard deviation of the distribution of all the laboratory mean values. It must be stressed that BCR has accepted and even promoted alternative methods of measurements in some certification exercises, in order to back-up trueness of certified values. Finally, such methods may have shown that their precision was too poor and were not used to calculate the certified value and its uncertainty. In such cases the results are made available to the user of the CRM through the certification report. 

Notes-, (a) Based on NHANES III (1988-1994) laboratory sample, weighted to national population, (b) Excluding patients with thyroid disease and goiter, (c) GM - Geometrlo means. Weighted geometric mean standard error of the mean (SEM) and 95% confidence Interval. 

The value of t for a given coefficient is equal to the value of the coefficient divided by the estimate of the standard error of that coefficient obtained from the regression data. It arises this way because the values of the dependent variable each contain a contribution from the random error in the reference laboratory, if another set of samples were to be used for the calibration, a different set of data would be used in the calibration, even if the data were taken from different aliquots of the same specimens. Then, when the calculations were performed, slightly different answers would result. It is possible to estimate from the data itself how much variation in the coefficients would result from this source. The estimate of the variation is called the standard error of the coefficient and Student s t is a coefficient divided by its standard error. 

The density determination may be carried out at the temperature of the laboratory. The liquid should stand for at least one hour and a thermometer placed either in the liquid (if practicable) or in its immediate vicinity. It is usually better to conduct the measurement at a temperature of 20° or 25° throughout this volume a standard temperature of 20° will be adopted. To determine the density of a liquid at 20°, a clean, corked test-tube containing about 5 ml. of toe liquid is immersed for about three-quarters of its length in a water thermostat at 20° for about 2 hours. An empty test-tube and a shallow beaker (e.g., a Baco beaker) are also supported in the thermostat so that only the rims protrude above the surface of the water the pycnometer is supported by its capillary arms on the rim of the test-tube, and the small crucible is placed in the beaker, which is covered with a clock glass. When the liquid has acquired the temperature of the thermostat, the small crucible is removed, charged with the liquid, the pycnometer rapidly filled and adjusted to the mark. With practice, the whole operation can be completed in about half a minute. The error introduced if the temperature of the laboratory differs by as much as 10° from that of the thermostat does not exceed 1 mg. if the temperature of the laboratory is adjusted so that it does not differ by more than 1-2° from 20°, the error is negligible. The weight of the empty pycnometer and also filled with distilled (preferably conductivity) water at 20° should also be determined. The density of the liquid can then be computed. 

Snow, especially its water-soluble fraction, is one of the most sensitive and informative indicators of mass-transfer in the chain air - soil - drinking water. Therefore analytical data on snow-melt samples were selected for inter-laboratory quality control. Inter-laboratory verification of analytical results estimated in all the groups have shown that relative standard errors for the concentrations of all the determined elements do not exceed (5-15)% in the concentration range 0.01 - 10000 microg/1, which is consistent with the metrological characteristics of the methods employed. All analytical data collected by different groups of analysts were tested for reliability and... 

A control is a standard solution of the analyte prepared independently, often by other laboratory personnel, for the purpose of cross-checking the analyst s work. If the concentration found for such a solution agrees with the concentration it is known to have (within acceptable limits based on statistics), then this increases the confidence a laboratory has in the answers found for the real samples. If, however, the answer found differs significantly from the concentration it is known to have, then this signals a problem that would not have otherwise been detected. The analyst then knows to scrutinize his or her work for the purpose of discovering an error. 

Assuming that only random errors affect the laboratory determinations of a given reaction enthalpy, the overall uncertainty interval associated with the mean value (ATH) of a set of n experiments is usually taken as twice the standard deviation of the mean (erm) ... 

The graph is obtained by plotting Y,- against Y, results for each of the ten laboratories. The axes are drawn such that the point of intersection is at the mean values for Y, and 7/. As a single method is used in the trial, the circle represents the standard deviation of the pooled Y and Y data. The plot shows the predominance of systematic error over random error. Ideally, for bias-free data (i.e. containing no systematic error) the points would be clustered around the mid-point with approximately equal numbers in each of the four quadrants formed by the axes. In practice the points lie scattered around a 45° line. This pattern has been observed with many thousands of collaborative trials. 

Fig. 7. A simulation of the Hamiltonian identification concept in Fig. 6 for a 10-state quantum system, with the observations being state populations. The data errors were taken as 1%. The closed loop optimal inversion was capable of finding a single experiment, which dramatically filtered out the data noise to produce Hamiltonian matrix elements with an order of magnitude better quality than that of the data noise. In contrast, a standard inversion involving 5000 observations gave significantly poorer results, including amplification of the laboratory noise.

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