Laboratory means, standard deviation

This hypothesis is tested by analysis of variance in which — apart from the already determined standard deviation within laboratories (Equation 3) — a so-called standard deviation of laboratory means (standard deviation between laboratories) figures as an important ingredient ... 

LABORATORY N MEAN STANDARD DEVIATION RELATIVE STANDARD DEVIATION... 

The first area covers laboratory analysis. Analysts can express results from data in a number of ways...mean, standard deviation, and range. The analysts can separate the error involved in various phases of an analytical problem. They can work on a single detection technique, which is univariate, or they can utilize more than one measuring technique, which is... 

The best indicator of the reliability of the assay is the precision, expressed as the mean and coefficient of variation (CV), of a series of analyses carried out on consecutive days (the between-run variation). In the authors laboratory the internal quality control samples were run in ten series of analyses over a 2-month period. The calculated mean, standard deviation and coefficient of variation are shown in Table 3.3.3. 

As a final exercise, retrieve the spreadsheet that we created in Chapter 3 for the gravimetric determination of chloride, which we called grav chloride.xls. Enter formulas into cells B12—B14 to compute the mean, standard deviation, and the RSD in parts per thousand of the percent chloride in the samples. In this example, multiply the relative standard deviation by 1000 in cell B14. Adjust the decimal point in the results to display the proper number of significant figures. The worksheet below shows the results. Save your worksheet so that you can use it as a model for making laboratory calculations. 

The styles of representation of the uncertainties also differ widely from laboratory to laboratory. Estimated standard deviations (e.s.d.) are often multiplied by a certain constant (2, 2.6 or 3). Several authors report "estimated limits of error" when they regard the probability of finding the geometric parameters outside the range as negligible. In general, the tables follow the styles reported by the authors and in each case define the meaning of the listed uncertainty, since it is considered to be inappropriate, if possible at all, to alter them into a uniform style. 

After exclusion of outlier according to Dixon, Grubb, and Cochran as presented in Ref. 5, the parameters (mean, standard deviation, etc.) are calculated. One-way analysis of variance and outlier tests are applied to estimate the components of variance, repeatability, and reproducibility parameters. In the evaluation report often several performance parameters are given, i.e., the arithmetic mean, geometric mean, consensus mean, mean of results from different groups of analyses, and so forth, and a histogram of all results at the very least. For the validation of each laboratory a performance score is calculated. 

Analysis of filtered Baltic Sea samples of about 0.5 pmol/L spiked to nominally I, 2 and 3/tmol/L ammonia and analysed in three independent analytical runs resulted in a mean standard deviation of 0.092 pmol/L or 2.7 % Hansen and Johannsen, unpublished). Similar results have been reported by Riley et al. (1972) and Solorzano (1969). The recent ICES intercomparison exercise (Aminot and Kirkwood, 1995) showed an overall relative standard deviation of more than 20 %, indicating that, despite good precision of ammonia measurements within one laboratory, the inter-laboratory precision is comparatively poor. This is probably due to the ease of contamination in preparations of zero water and standards as well as in the handling of samples for ammonia determinations. 

Different biological samples were analyzed via the ICP-IDMS approach depicted in Figure 8.8 and the results obtained were compared with those of an interlaboratory study in which 14 laboratories using various non-IDMS techniques participated. In this study, a silicon content of 5.3 + 1.0 pg (mean + standard deviation based on five independent analyses) was found for a homogeneous pork liver sample via ICP-IDMS, which agreed well with the result of the inter-laboratory study of 5.1 + 2.8 pg g (mean of the means of individual laboratories + corresponding standard deviation). In contrast to this agreement, the results for a spinach powder were 333 + 11 pg g for ICP-IDMS and 176 + 189 pg g for the inter-laboratory study. The reason for this extreme difference between the ICP-IDMS result and the mean value, and also for the unacceptable standard deviation in the inter-laboratory study, is the presence of considerable amounts of silicate in spinach. Many laboratories had not adequately dealt with this silicate portion due to analytical difficulties with and errors in the sample preparation. 

Figure 6 State-of-the-art determination of riboflavin in foods. Results of individual European laboratories for vitamin B2 determination (HPLC methods, except 7,8,16) in pork muscle (identical samples). Data represent the mean standard deviation of at least three separate determinations for each laboratory. (From Ref. 66.)...

XI.4.4.2 The standard deviation for repeatability for each sample was calculated from pair-wise (repeat pairs) variances pooled across the laboratories. The standard deviation for reproducibility was calculated from the variance of the mean values of each pair. This variance is equal to the sum of two variances, the variance a, due to differences between laboratories and the variance due to repeatability error a, divided by the number of replicates... 

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. 

In reality, the queue size n and waiting time (w) do not behave as a zero-infinity step function at p = 1. Also at lower utilization factors (p < 1) queues are formed. This queuing is caused by the fact that when analysis times and arrival times are distributed around a mean value, incidently a new sample may arrive before the previous analysis is finished. Moreover, the queue length behaves as a time series which fluctuates about a mean value with a certain standard deviation. For instance, the average lengths of the queues formed in a particular laboratory for spectroscopic analysis by IR, H NMR, MS and C NMR are respectively 12, 39, 14 and 17 samples and the sample queues are Gaussian distributed (see Fig. 42.3). This is caused by the fluctuations in both the arrivals of the samples and the analysis times. 

Confirmation of the results by at least one independent laboratory Lowest concentration at which an acceptable mean recovery is obtained with a relative standard deviation <20%... 

Selectivity and sensitivity of available instruments are tested in all laboratories in the initial step of validation. The crops used for fortification experiments and the concentration levels are identical in all laboratories. Recoveries are determined with all available detection techniques, but after discussion of the results each laboratory selects individually one valid result for each analyte-matrix-level combination. Only this result is used for the calculation of the final mean recovery and standard deviation. Typical criteria for the acceptance of methods are given in Table 11. 

The only information presently available on the national frequency distribution of indoor radon levels is a 1984 analysis by Nero at the Lawrence Berkley Laboratory (Nero et al., 1984). Using data from about 500 houses, Nero developed a frequency distribution of radon levels in U.S. single family houses. This distribution is characterized by a geometric mean of 0.9 pCi/L and a geometric standard deviation of 2.8. 

If the analytical method used by participants in the proficiency testing round has been validated by means of a formal collaborative trial, then the repeatability and reproducibility data from the trial can be used. The repeatability standard deviation gives an estimate of the expected variation in replicate results obtained in a single laboratory over a short period of time (with each result produced by the same analyst). The reproducibility standard deviation gives an estimate of the expected variation in replicate results obtained in different laboratories (see Chapter 4, Section 4.3.3 for further explanation of these terms). 

Both correlation and variance analysis results showed that the hypothesis on the linear correlation between inter-laboratory data and the homogeneity of the corresponding variances is true for all data sets, at the for 95% confidence level. Table 2 presents a typical example of such a comparison. Based on the detected property of homogeneous variances, root-mean-square standard deviation, S, for all melted snow samples was estimated S = 0.32 0.06 for 95% confidence level [3]. 

Mettler produce two automatic titrimeters the DL 40 GP memotitrator and the lower-cost DL 20 compact titrator. Features available on the DL 40GP include absolute and relative end-point titrations, equivalence point titrations, back-titration techniques, multi-method applications, dual titration, pH stating, automatic learn titrations, automatic determination of standard deviation and means, series titrations, correction to printer, acid balance analogue output for recorder and correction to the laboratory... 

Lee and Chau [66] have discussed the development and certification of a sediment reference material for total polychlorobiphenyls. Alford Stevens et al. [49] in an inter-laboratory study on the determination of polychlorobiphenyls in environmentally contaminated sediments showed the mean relative standard deviation of measured polychlorobiphenyl concentrations was 34%, despite efforts to eliminate procedural variations. Eganhouse and Gosset [67] have discussed the sources and magnitude of bias associated with the determination of polychlorobiphenyls in environmental sediments. Heilman [30] studied the adsorption and desorption of polychlorobiphenyl on sediments. 

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) ... 

A control sample is a sample for which the concentrations of the test analyte is known and which is treated in an identical manner to the test samples. It should ideally be of a similar overall composition to the test samples in order to show similar physical and analytical features. For instance, if serum samples are being analysed for their glucose content, the control sample should also be serum with a known concentration of glucose. A control sample will be one of many aliquots of a larger sample, stored under suitable conditions and for which the between batch mean and standard deviation of many replicates have been determined. It may be prepared within the laboratory or purchased from an external supplier. Although values are often stated for commercially available control samples, it is essential that the mean and standard deviation are determined from replicate analyses within each particular laboratory. 

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