Sample variability

The standard deviation as defined relates to the repeatability of measurements on the same sample. When many samples are taken from a large population, sampling variability and population variability terms have to be added to Eq. (1.6) and the interpretation will reflect this. 

The objective of sediment and water sampling is to obtain reliable information about the behavior of agrochemicals applied to paddy fields. Errors or variability of results can occur randomly or be due to bias. The two major sources of variability are sediment body or water body variability and measurement variability . For the former, a statistical approach is required the latter can be divided into sampling variability, handling, shipping and preparation variability, subsampling variability, laboratory analysis variability, and between-batch variability. ... 

Notice that the results from one of the time points of the kinetic analysis may be used for the Group 1 values, assuming that day-to-day and sample-to-sample variability is minimal and that the time used for the remaining groups is the same as that of the Group 1 sample. From the ANOVA will be obtained not only information about the best temperature and pH, but also an indication of whether pH and temperature interact with one another. Further ANOVA or kinetic analysis can help to pinpoint the optimal yield as a function of all of the variables. 

Competitive PCR (cPCR) has emerged as the best strategy for controlling the sam-ple-to-sample variability of PCR. In cPCR different templates of similar lengths and with the same primer binding sequences are coamplified in the same tube. This ensures identical thermodynamics and amplification efficiency for both templates. The amount of one of the templates must be known and, after amplification, products of both templates must be distinguishable and separately quantifiable. 

A later analysis (Emhart et al. 1987) related PbB levels obtained at delivery (maternal and cord blood) and at 6 months, 2 years, and 3 years of age to developmental tests (MDI, PDI, Kent Infant Development Scale [KID], and Stanford-Binet IQ) administered at 6 months, 1 year, 2 years, and 3 years of age, as appropriate. After controlling for covariates and confounding risk factors, the only significant associations of blood lead with concurrent or later development were an inverse association between maternal (but not cord) blood lead and MDI, PDI, and KID at 6 months, and a positive association between 6-month PbB and 6-month KID. The investigators concluded that, taken as a whole, the results of the 21 analyses of correlation between blood lead and developmental test scores were "reasonably consistent with what might be expected on the basis of sampling variability," that any association of blood lead level with measures of development was likely to be due to the dependence of both PbB and... 

In terms of confidence limits the two Grand Means can be written as 38.5 + 6.4 mg/m2 for the EC plot and 49.9 + 32.7 mg/m for the GF plot at the 90 level. This statement emphasizes the extent to which sampling variability can affect the confidence with which an analytical result is known. Unless the sampling program is designed to measure and identify the source of the variability much effort towards improvement of the quality of the chemical analyses can be wasted (4). The difficulty of improving the sampling procedures to reduce the variability is illustrated by calculation of the number of samples that would have to be analyzed to obtain estimates known to have an uncertainty less than 10 at the 90 confidence level (4). This would require 106 analyses from the EC plot and 2140 from the GF. Both sample sizes... 

SIMCA can be applied to the problem of classification when attempting to correlate measurable effect variables with composition of the classified samples. In correlation analyses one may wish to determine how other sample variables, such as sediment composition, organic content, lipid concentration, etc., influence the composition of measured residues or concentrations of PCBs. 

Weight fraction each Aroclor in sample variable 1-4 Variables 5-73 are fractional concentration of each PCB isomer Variable 74 designates total PCB concentrationin sample... 

We found that it is necessary to run several sets of differential display primers prior to an analysis of the distribution of differential display bands. This allows for a comparison between different independent reactions using different PCR primers to assess the quality of individual cDNA samples and discriminate between sample-to-sample variability and potential positive bands that are consistently found in different repUcates. The presence or absence of a specific band in lanes corresponding to independent experimental samples indicates a reproducible difference in the relative amount of cDNA in a given sample, which should reflect differences in mRNA levels. However, the interpretation of the differential display results is not always straightforward. For example, a thick band can reflect quantitative differences in the initial concentration of a specific cDNA between samples or can represent comigration of two bands. Replication of the PCR reactions for samples that have differences in banding pattern will eliminate a significant number of false positive differential display differences. Also, in some cases, it may be informative to alter the electrophoresis conditions to maximize resolution of a band of interest prior to isolation, reamplification, and further analysis of potential positive bands. 

Sample variabilities and the measurement error must be considered (risk analysis, cf. Section I.C) to avoid that an analyte signal yo will be measured outside the calibrated range. Thus, the range shall be chosen a little wider than the expected range of analyte concentrations. 

The study published by Hennessey et al. (46) concluded that proteomic profiles of frozen samples were consistent in the absence of microdissection. However, several critical points need to be considered first, the fact that proteomic profiles did not change between biologic replicates might simply mean that the intra-sample variability of the selected proteins was probably low, so that regardless of where the sample was taken the tumor looked the... 

More generally, whatever statistic we are interested in, there is always a formula that allows us to calculate its standard error. The formulas change but their interpretation always remains the same a small standard error is indicative of high precision, high reliability. Conversely a large standard error means that the observed value of the statistic is an unreliable estimate of the true (population) value. It is also always the case that the standard error is an estimate of the standard deviation of the list of repeat values of the statistic that we would get were we to repeat the sampling process, a measure of the inherent sampling variability. 

A single evaluation set is the simplest and most rapid validation scheme. A fraction—usually between 50% and 90% of the total number—of the available samples constitutes the training set, while the remaining objects form the evaluation set. The subdivision may be arbitrary, random, or performed by way of a uniform design, such as the Kennard and Stone and the duplex algorithm (Kermard and Stone, 1969 Snee, 1977), which allows two subsets to be obtained that are imiformly distributed and representative of the total sample variability. 

Categories N. of samples Variables N. of selected features Methods Classification ability [%] Ref. 

However, Am and Cm tend to be more available than Pu to the rats examined (Fig. 4) although the differences are not significant when sample variability is considered. Evidence for Am enrichment in the field may in fact be totally obscured by biological variability. Field studies at the Nevada Test Site with cattle exemplify this problem. When 5 tissue types from up to 20 animals which had grazed on contaminated soil were examined for Pu and Am, Pu/Am ratios varied by almost 2 orders of magnitude (31). 

Strictly, there should be a correction for the effect of fringing but this is not normally considered significant. It is not usually possible to obtain very great precision in measurements of high resistivity and results are never quoted beyond two significant figures. Often, between sample variability is such that two materials would be considered really significantly different only if their resistivities differed by a factor of 10. 

Poor reproducibility. Compromised reproducibility is most likely due to something other than the RAS, such as variability of food sample, variability of the sampling method, or inconsistent application of the methodology. However, poor reproducibility can result from the RAS apparatus if there are leaks or blockages of the flow or if the unit is not properly cleaned. 

P.J. Wangersky, Particulate organic carbon sampling variability, Limnol. Oceanogr. 19 (1974) 980-984. 

The particle size of the Pu disseminated in the N.T.S. trials is not known, but it was probably relatively large. Hardy noted that replicate samples of soil analysed for Pu gave unusually disparate results, probably on account of sampling variability related to particle size. 

Sample variability is a critical issue in prospective application. For optical technologies, variations in tissue optical properties such as absorption and scattering coefficients can create distortions in measured spectra. This section provides a brief overview of techniques to correct turbidity-induced spectral and intensity distortions in fluorescence and Raman spectroscopy, respectively. In particular, photon migration... 

Errors originating from inherent sample variability... 

They have a much more powerful effect on data relevancy and validity than errors originating from sample or population variability. In fact, a thoughtfully conducted planning process takes into account the population variability at the project site, and errors originating from sample variability are controlled by the proper implementation of the field sampling procedures. 

Precision Error from sample variability Error from population variability Measurement error Field and laboratory procedure error... 

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