Sample replicate

The precision for an analysis in which the only source of variability is the analysis of replicate samples. 

An analysis, particularly a quantitative analysis, is usually performed on several replicate samples. How do we report the result for such an experiment when results for the replicates are scattered around a central value To complicate matters further, the analysis of each replicate usually requires multiple measurements that, themselves, are scattered around a central value. 

To determine which step has the greatest effect on the overall variance, both si, and si must be known. The analysis of replicate samples can be used to estimate the overall variance. The variance due to the method is determined by analyzing a standard sample, for which we may assume a negligible sampling variance. The variance due to sampling is then determined by difference. 

The solvent used was 5 %v/v ethyl acetate in n-hexane at a flow rate of 0.5 ml/min. Each solute was dissolved in the mobile phase at a concentration appropriate to its extinction coefficient. Each determination was carried out in triplicate and, if any individual measurement differed by more than 3% from either or both replicates, then further replicate samples were injected. All peaks were symmetrical (i.e., the asymmetry ratio was less than 1.1). The efficiency of each solute peak was taken as four times the square of the ratio of the retention time in seconds to the peak width in seconds measured at 0.6065 of the peak height. The diffusivities obtained for 69 different solutes are included with other physical and chromatographic properties in table 1. The diffusivity values are included here as they can be useful in many theoretical studies and there is a dearth of such data available in the literature (particularly for the type of solutes and solvents commonly used in LC separations). 

In their work on the precision of contemporary liquid chromatographic measurements, Scott and Reese (3) also evaluated the precision that could be expected from a computer measuring peak heights and peak areas. They again used twelve replicate samples and the results they obtained are shown in table 2. 

Product inhomogeneity (F) for replicate samples pulled from the same production lot would show up in sample means that scatter much more than the method repeatability (=A=). 

Samples must be representative of the environment in relation to study objectives and to permit comparison of data with appropriate standards, i.e. average concentrations, time-weighted exposures, peak concentrations, etc. Replicate samples may be advisable. 

The equation assumes that the cost of estimation error for an estimate based on n replicate samples is proportional to the mean squared error... 

These data are used to accept or reject a set of replicated samples. The replicates are usually duplicate samples. Therefore, the difference between the two values should lie within the critical range. If not, the sample Is rejected and the analyses rerun If possible. Discarding results should only be done after... 

FIGURE 3.7 MeHg concentration (ng/g dry weight) in sediment from 5 sites in the Florida Everglades. Box plots represent 5 replicate samples taken at 4 different times over 4 years. 

The sampling variance of the material determined at a certain mass and the number of repetitive analyses can be used for the calculation of a sampling constant, K, a homogeneity factor, Hg or a statistical tolerance interval (m A) which will cover at least a 95 % probability at a probability level of r - a = 0.95 to obtain the expected result in the certified range (Pauwels et al. 1994). The value of A is computed as A = k 2R-s, a multiple of Rj, where is the standard deviation of the homogeneity determination,. The value of fe 2 depends on the number of measurements, n, the proportion, P, of the total population to be covered (95 %) and the probability level i - a (0.95). These factors for two-sided tolerance limits for normal distribution fe 2 can be found in various statistical textbooks (Owen 1962). The overall standard deviation S = (s/s/n) as determined from a series of replicate samples of approximately equal masses is composed of the analytical error, R , and an error due to sample inhomogeneity, Rj. As the variances are additive, one can write (Equation 4.2) ... 

Replicate samples are collected to evaluate the measurement variability of held and laboratory procedures. When sampling a water source, replicate samples (two or more) should be collected sequentially. Select wells for replicate sampling that are known to have a measurable concentration of the compound of interest. 

Approximately eight pounds of fruit constituted each analytical sample 11, 14), the number of fruits per sample varied from ten to thirty. Fruits were selected at random from within a peripheral band around the tree 3 to 6 feet above the ground. Individual samples were constituted with fruits from six to eight trees and replicate samples were taken from different groups of trees. In some cases, samples of deciduous fruits were collected from three trees and additionally involved a portion of fruit from the upper quarter of the tree. Duplicate, or more generally triplicate, samples were utilized for analyses. All fruits for penetration studies were collected in paper bags, which were immediately stapled to ensure sample integrity. 

Bucholz KK, Li T-K, Hesselbrock V, Crowe R, Schuckit M, Porjesz B, Begleiter H, Reich T. Alcoholism susceptibility loci confirmation studies in a replicate sample and further mapping. Alcohol Clin Exp Res 2000 24 933-945. 

Fig. 2 Relative effects of rhamnetin, isorhamnetin and total extract from pollen of Phleum pratense on in vitro germination of pollen of Elytrigia repens. Data points are means and standard errors from 50 replicate samples.

Dissolution indicates the rate-limiting step for compound absorption when drugs are administered orally. The solubility of a pharmaceutical compound represents its maximum concentration in an aqueous buffer. Additional compound will not dissolve above this concentration. The solubility value is often heavily dependent upon pH and temperature and is typically measured at physiologically important pH levels and body temperature. The standards for dissolution testing are determined by the United States Pharmacopoeia (USP). Testing typically requires sampling of a solution at 15, 30, 45, and 60 min for immediate-release products. /./Pl.C is ideally suited for use in conjunction with USP apparatus types I or II and can rapidly analyze multiple time points or replicate samples. 

It may be possible to demonstrate a high degree of precision in a set of replicate analyses done at the same time and in such a situation the within batch imprecision would be said to be good. However, comparison of replicate samples analysed on different days or in different batches may show greater variation and the between batch imprecision would be said to be poor. In practice this may more closely reflect the validity of the analytical data than would the within batch imprecision. 

Several workers [ 1,29,66,67,104,146 -149] indicated that studying pollutants and/or SWM leachate migration profiles resulting from transport of pollutants with a test soil requires that replicate samples be subjected to leaching-column tests, where various pore volumes of the same solution are applied. 

Table I indicates the 95% confidence limits determined with a WSL high-flow rate olfactometer (1) and suggests various options (underlined) with respect to panel screening, panel size, number of replicate samples and dilution steps ...

Briefly, to assure quality assurance and quality control, samples are analyzed using standard analytical procedures. A continuing program of analytical laboratory quality control verifies data quality and involves participation in interlaboratory crosschecks, and replicate sampling and analysis. When applicable, it is advisable, even insisted upon by the EPA, that analytical labs be certified to complete the analysis requested. However, in many cases, time constraints often do not allow for sufficient method validation. Many researchers have experienced the consequences of invalid methods and realized that the amount of time and resources required to solve problems discovered later exceeds what would have been expended initially if the validation studies had been performed properly. 

Many corporate screening collections may inadvertently contain two or more samples of the same compound, for example, from different synthetic batches. Examining the results from a large number of such replicate samples can provide a useful way to assess the upper limit of variability in the primary assay. This represents an upper limit because other factors such as compound degradation can account for an unknown amount of the observed variability. Such replicate samples can also be filtered out if desired. 

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