Independent samples

A good example of a prescriptive approach to quality assessment is the protocol outlined in Figure 15.2, published by the Environmental Protection Agency (EPA) for laboratories involved in monitoring studies of water and wastewater. Independent samples A and B are collected simultaneously at the sample site. Sample A is split into two equal-volume samples, and labeled Ai and A2. Sample B is also split into two equal-volume samples, one of which, Bsf, is spiked with a known amount of analyte. A field blank. Dp, also is spiked with the same amount of analyte. All five samples (Ai, A2, B, Bsf, and Dp) are preserved if necessary and transported to the laboratory for analysis. 

Rhenium metal exhibits a very low paramagnetism which is field-iadependent and almost temperature-iadependent. In the range 79—471 K, magnetic susceptibiUty data for two independent samples were shown to correspond, when Tis ia Kelvin, to the following equations (5) ... 

Statistical errors of dynamic properties could be expressed by breaking a simulation up into multiple blocks, taking the average from each block, and using those values for statistical analysis. In principle, a block analysis of dynamic properties could be carried out in much the same way as that applied to a static average. However, the block lengths would have to be substantial to make a reasonably accurate estimate of the errors. This approach is based on the assumption that each block is an independent sample. 

As convenient as the method of flooding is, the data can be affected by a trace of a reactive impurity X, which may be minor with respect to B, but comparable to A. The observation purported to be the reaction between B and A may, in fact, be (or be altered by) an unsuspected reaction between X and A. The careful worker prepares an independent sample of B or shows that the rate remains invariant as B is repurified. 

Measurements are easy and cheap, that is a large number of measurements is available, either as many repeats on a small number of samples or as single determinations on a large number of independent samples. 

Modified from Tieman et al. [21]. Niimbers in parentheses represent the number of independent samples anal5rzed. 

One measure of the quality of an estimate of an average Is the confidence limits (or maximum probable error) for the estimate. For averages of Independent samples, the maximum probable error Is... 

The analytical procedure is checked by analyses of method blanlcs to assure that secondary contamination by the analytes to be determined is avoided or minimized. Because the water content of the CRM matrix to be analyzed may vary from one laboratory to another (dependent on the local humidity and temperature), the water content has to be determined. Accordingly, at least three independent samples are kept at I05°C for 2 h, then allowed to cool to ambient temperature in a desiccator and the water loss is determined. The certified values are generally reported on a dry mass basis. 

The linearity of the detector can be obtained by diluting the analyte stock solution and measuring the associated responses, while the linearity of the analytical method can be determined by making a series of concentrations of the analyte from independent sample preparations (weighing and spiking) [15]. It is also essential that the basic calibration linear curve be obtained by using independent samples, and not by using samples that have been prepared by dilution and injected into HPLC/GC, or spotted on one TLC plate. 

Straub RE et al. Susceptibility genes for nicotine dependence a genome scan and followup in an independent sample suggest that regions on chromosomes 2, 4, 10, 16, 17 and 18 merit further study. 

Independent confirmation of genetic association in independent samples/meta-analysis ... 

This procedure (based on sample variance and covariance) is referred to as the direct method of estimation of the covariance matrix of the measurement errors. As it stands, it makes no use of the inherent information content of the constraint equations, which has proved to be very useful in process data reconciliation. One shortcoming of this approach is that these r samples should be under steady-state operation, in order to meet the independent sampling condition otherwise, the direct method could give incorrect estimates. 

TRXF was used to determine the trace elements in samples of lecithin, insulin, procaine, and tryptophan in an attempt to develop elemental fingerprints that could be used to determine the origin of the sample [80]. It was reported that through the use of matrix-independent sample preparation and an internal standard, one could use TXRF to facilitate characterization of the samples without the need for extensive pretreatment. In another work, a study was made of the capability of TXRF for the determination of trace elements in pharmaceutical substances with and without preconcentration [81]. 

A semi-colon is used in the argument list to remind us that V is an independent (sample space) variable, while x and t are fixed parameters. Some authors refer to fyx (Vj x, f ) as the one-point, one-time velocity PDF. Here we use point to refer to a space-time point in the four-dimensional space (x, t). 

Tests for Several Central Values of Independent Samples... 

Bartlett test. H0 the variances of the data distributions are equal. Requirements normal distribution of all data sets, independent samples. 

Statistical Methods. Means of treatment groups for plasma retention of BSP, plasma osmolality, total plasma protein concentration and urine flow rates were compared by students t test for independent sample means (17). Plasma enzyme activity data were converted to a quantal form and analyzed by the Fischer Exact Probability Test (18). Values greater than 2 standard deviations (P < 0.05) from the control value were chosen to indicate a positive response in treated fish. 

The precision of the assay for nonreduced samples was demonstrated by the evaluation of six independent sample preparations on a single day (repeatability) and the analysis of independent sample preparations on three separate days by two different analysts (intermediate precision). The RSD values for the migration time were 0.9%. The RSD values for peak area percent of the main peak and the minor peaks in the profile were 0.6 and 12.6%, respectively. The higher variability observed with the minor peaks was determined to be primarily related to the sample heating during preparation for the analysis. These results demonstrate that the use of uncoated fused-silica capillaries in combination with a sieving matrix can provide adequate precision and analyte recovery. 

The samples (minimum four batches) included in the study should cover the expected normal variation of the process (target 3 sigma). If the batches used do not represent the full and normal process variation, the calculations are based on a historical value for process variation. The same batches are analyzed by multiple analysts (minimum 2) in different laboratories (minimum 3) using their own instruments, reagents, and solvents. Each analyst performs the entire method as described. Every sample should be analyzed at least twice (with independent sample preparation) in the same run. The replicates should also be blinded and randomly tested. 

TaIkowski, M. E., Mansour, H., Chowdari, K. V., et el(2006) Novel, replicated associations between dopamine Dj receptor gene polymorphisms and schizophrenia in two independent samples. Biol. Psychiatry. 60, 570-577. 

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