Sampling bias, systematic

Note that the variance does not depend on the true value x, and the mean estimator x has the least variance. The finite sampling bias is the difference between the estimate x and the true value x, and represents the finite sampling systematic part of the generalized error... 

Accuracy is the degree of agreement of a measured value with the true value of the quantity under concern. Inaccuracy results from imprecision (random error) and bias (systematic error) in the measurement process. Bias can only be estimated from the results of measurements of samples of known composition. SRMs are ideal for use in such an evaluation (22). 

Svramping The introduction of a potential interferent to both calibration standards and the solution of the analyte in order to minimize the effect of the interferent in the sample matrix. Systematic error Errors that have a known source they affect measurements in one and only one way, and can, in principle, be accounted for. Also called determinate error or bias. 

This is a remarkably simple result but a few cautionary remarks are necessary. The MSA method has a great advantage in that, since the recovered spike and analyte from the sample are contained in the same sample extract solution, the volumes v and V are the same for both and thus do not appear explicitly in the final expression for Qa. An assumption that was glossed over in the derivation of Equation [8.66d] was that the reponse level to which the extrapolation should be done was indeed R = zero this is valid in the absence of any bias systematic errors (such as can arise if e.g., la 7 0). However, if any such error is present, extrapolation to a value of other than zero will be observed this possibility is considered later (see discussion leading to Equation [8.75]). 

The LTT plot (Figure 17.2) allows comparison of the pattern of diversification of extant taxa in the pleurocarpous mosses with the equivalent curves for the angiosperms and polypod ferns as calculated by Schneider et al. (2004). Note that the shape of these plots is susceptible to differences in the sampling strategy (Nee et al., 1994 Pybus and Harvey, 2(XX) Shaw et al., 2003). Issues of systematic sampling bias were not explored by Shaw et al. (2003), who concentrated instead on the effect of randomized incomplete sampling, allowing them to accept or reject different models of diversification rates. 

Bias As applied to sampling, bias refers to a systematic displacement, error, uncertainty, or mistake caused by a flaw in the sampling procedure. 

Bias—Systematic error that contributes to a difference between the mean and an accepted reference value. Since all organic solvents can contain nitrogen, an absolute statement of bias could not be determined from this study. Although, an estimate of bias was determined by spiking a single solvent (xylene) with three different concentrations of nitrogen. These three spiked samples were then analyzed as unknowns in the interlaboratory study (see Table 2). 

In general, when very few samples are available the force Fk(N) will not be an accurate approximation of d/l/d . Large variations in Fj (N) may lead to nonequilibrium effects and systematic bias of the calculation. Mathematically, this can be expressed by introducing a perturbation zLif fq, p, N), which is a function of the number of steps N. At N = 1 if we average over all possible initial configurations, abbreviated by subscript 0, we obtain... 

Perhaps the most challenging part of analyzing free energy errors in FEP or NEW calculations is the characterization of finite sampling systematic error (bias). The perturbation distributions / and g enable us to carry out the analysis of both the finite sampling systematic error (bias) and the statistical error (variance). 

As discussed in Sect. 6.1, the bias due to finite sampling is usually the dominant error in free energy calculations using FEP or NEW. In extreme cases, the simulation result can be precise (small variance) but inaccurate (large bias) [24, 32], In contrast to precision, assessing the systematic part (accuracy) of finite sampling error in FEP or NEW calculations is less straightforward, since these errors may be due to choices of boundary conditions or potential functions that limit the results systematically. 

Now consider the finite sampling systematic error. As discussed in Sect. 6.4.1, the fractional bias error in free energy is related to both the sample size and entropy difference 5e N exp(-AS/kB). With intermediates defined so that the entropy difference for each substage is the same (i.e., AS/n), the sampling length Ni required to reach a prescribed level of accuracy is the same for all stages, and satisfies... 

The section following shows a statistical test (text for the Comp Meth MathCad Worksheet) for the efficient comparison of two analytical methods. This test requires that replicate measurements be made on two different samples using two different analytical methods. The test will determine whether there is a significant difference in the precision and accuracy for the two methods. It will also determine whether there is significant systematic error between the methods, and calculate the magnitude of that error (as bias). 

There are four major types of sampling methods random, stratified, systematic, and cluster. Random is by far the most commonly employed method in toxicology. It stresses the fulfillment of the assumption of avoiding bias. When the entire pool of possibilities is mixed or randomized (procedures for randomization are presented in a later section), then the members of the group are selected in the order that are drawn from the pool. 

The notion representative is a composite property of the mean square error, which includes both the systematic (bias) and random part (statistical) of the sampling error [2] ... 

Define Quality Control, Quality Assurance, sample, analyte, validation study, accuracy, precision, bias, calibration, calibration curve, systematic error, determinate error, random error, indeterminate error, and outlier. 

In general, bias refers to a tendency for parameter estimates to deviate systematically from the true parameter value, based on some measure of the central tendency of the sampling distribution. In other words, bias is imperfect accuracy. In statistics, what is most often meant is mean-unbiasedness. In this sense, an estimator is unbiased (UB) if the average value of estimates (averaging over the sampling distribution) is equal to the true value of the parameter. For example, the mean value of the sample mean (over the sampling distribution of the sample mean) equals the mean for the population. This chapter adheres to the statistical convention of using the term bias (without qualification) to mean mean-unbiasedness. 

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