Sample increments, estimation

A statistically valid sampling plan requires careful design emd execution so that generalizations based on mathematical probability can be drawn from a small number of test portions. Guidelines are given for estimation of the minimum number and size of sample increments needed to achieve a given level of confidence in chemical analyses. 

A second factor to consider in a valid sampling plan is the collection of enough individual sample increments to ensure that heterogeneity on a large scale does not bias the results. Estimation of this number can be made straightforwardly if the component of interest is distributed... 

The number of individual sample increments needed to achieve a given level of confidence in the analytical results is estimated by... 

In order to estimate the measurement and sampling variances when the halofugi-none concentration in chicken liver is determined, four sample increments were taken from different parts of the liver and three replicate measurements were made on each. The following results were obtained (mg kg ) ... 

The overall random error of an analytical process, expressed as the variance v, can be regarded as the sum of two other variances, that due to sampling x), and that due to the remaining measurement components of the process sb. These variances are estimates of the corresponding population variances cr" and its components (tT and <75. The overall standard deviation s is calculated as usual from single measurements on each of h sample increments, and the confidence limits of the true mean value of the population 11 are obtained from ... 

To obtain some idea as to the actual vertical penetration of TCDD in those areas contaminated by dispersion, three sample points were selected near the farm road which was sprayed in 1971. At each point a single sample was collected from each of three depths, viz, at the 0- to 2-, 2- to 4-, and 4- to 6-inch depths, using clean knives and spoons. The selection of a 2-inch increment was based upon the estimated removal on a single pass by a qualified operator of earth-moving machinery. The resulting data are as follows ... 

If the material being sampled consists of discrete particles such that an average particle mass can be calculated, then still another method is useful. In this procedure the constants and B of Equation 5 are obtained from the intraclass correlation coefficient between pairs of small, single-increment samples of equal mass, the increments of each pair being collected near each other and the pairs distributed over the population under study. The value of r can be estimated from the relation ... 

Whenever increment/sample masses are not identical, estimation of the total lot mass, Al must be done as a weighted mean from the analytical results, lest an additional IWE be introdnced. 

Willan AR. Analysis, sample size, and power for estimating incremental net health benefit for clinical trial data. Control Clin Trials 2001 22 228-37. 

The method of standard addition is the least widely used method of quantitation, but it is used to ensure that the calibration standards experience the same matrix effects as the sample constituents. In this method, the sample is analyzed first in order to estimate the concentration of the solute(s) of interest. Several different, known concentrations of the solute(s) of interest are then added to portions of the sample, to provide approximate incremental increases in detector response. Each portion of the sample is then reanalyzed. The principle of the method is that the extra signal produced by the addition of the standards is proportional to the original signal. The method is applicable only when a known straight-line relationship has been established between the instrument response and the analyte concentration.18... 

Sampling is an important part of estimates of blending quality. In most cases, scientists do not have mixing problems, but actually have sampling problems.8 Ideally, a powder for testing should be sampled when it is in motion and the whole of the stream of powder should be taken for many short increments of time instead of... 

An estimate of the extent of base-pair mismatch between hybridized DNA strands can be made by measuring the thermal stability of the reassociated duplexes. Place hybridized filters in fresh incubation buffer and heat at 5° increments to 90°. At each 5° increase, remove a small sample of the buffer and count. Controls are reassociated homologous DNAs. The amount of nucleotide mispairing has been estimated at 1% for each degree the Tm of the heterologous duplex is lowered (Arm).2 31... 

NaCl solution. In one set of experiments, the slurry was titrated with 0.1 normal NaOH solution in one cm increments to a pH of about 10. The samples of this set are referred to as the "slurry" samples (titration of the calcined zeolite - NaCl solution slurry). In another set of experiments, the calcined zeolite - NaCl solution slurry was filtered, the filter cake washed with about 100 cnP distilled water, and the combined filtrates were titrated with 0.1 N NaOH solution, again to a pH of about 10. The samples of this latter set are referred to as the "filtrate" samples (the zeolite being removed by filtration prior to titration of the filtrate). In addition to the manual titrations, automated potentiometric titration curves were obtained with a Metrohm E636 Titroprocessor, which has an estimated pH measurement accuracy of 0.001 pH unit and an estimated volumetric addition accuracy of 0.001 cm ... 

In this primer, we will use the noun sample in a very specific way. A sample will mean the physical material in total that is taken for analysis from the lot. It may consist of severai increments (individual physical portions) that may be combined and measured or measured separately and statistically averaged. The measurement from the sample will mean either the chemical or physical measurement of interest on the sample itself (the total material composited from different physical increments) or else the statistical average of the separate chemical or physical measurements on the different physical increments. In other words, the measurement from the sample will mean the value obtained from the sampling procedure or protocol and subsequent chemical and/or physical analysis that is used to estimate the true lot value. 

Entropy evaluations from published cryothermal data on the lanthanide (III) oxides are summarized in Table II with an indication of the lowest temperature of the measurements and the estimated magnetic entropy increments below this temperature. Their original assignment of crystalline field levels from thermal data still appears to be in good accord with recent findings e.g., 17). Unfortunately, measurements on these substances were made only down to about 8°K. because the finely divided oxide samples tend to absorb the helium gas utilized to enhance thermal equilibration between sample and calorimeter. 

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