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Sampling variance

Random errors Relative standard deviation Robust variance Samples and populations Standard deviation of the mean (standard error of the mean)... [Pg.74]

A more objective method is to investigate the Gelman-Rubin diagnostics for chain convergence. This procedure is automated within WinBUGS. This method compares the between-chains and within-chain variability in a similar spirit to an analysis of variance. Samples are required from at least two chains that are started... [Pg.143]

Variance (sample), s2 The square of the sample standard deviation. (Section 2.4.2)... [Pg.9]

Estimation of variance. The variance is normally estimated by the following formula of the empirical variance/sample variance (note that the sample mean X is determined from the same set of data as the sample variance itself) ... [Pg.406]

We suppose that a measurement signal is a mix of r (unknown) independent sources Sj with variance cf. A detector give p> r measurement signals /W/t obtained with several frequencies. The relations between sources and measurement signals are supposed to be linear, but the transfer matrix T is unknown. If we get n >p>r samples m i) of measurement signals, mix of n... [Pg.364]

Once numerical estimates of the weight of a trajectory and its variance (2cr ) are known we are able to use sampled trajectories to compute observables of interest. One such quantity on which this section is focused is the rate of transitions between two states in the system. We examine the transition between a domain A and a domain B, where the A domain is characterized by an inverse temperature - (3. The weight of an individual trajectory which is initiated at the A domain and of a total time length - NAt is therefore... [Pg.275]

It is an estimation of the unknown true value p of an infinite population. We can also define the sample variance s as follows ... [Pg.192]

The values of x and s vary from sample set to sample set. However, as N increases, they may be expected to become more and more stable. Their limiting values, for very large N, are numbers characteristic of the frequency distribution, and are referred to as the population mean and the population variance, respectively. [Pg.192]

So basic is the notion of a statistical estimate of a physical parameter that statisticians use Greek letters for the parameters and Latin letters for the estimates. For many purposes, one uses the variance, which for the sample is s and for the entire populations is cr. The variance s of a finite sample is an unbiased estimate of cr, whereas the standard deviation 5- is not an unbiased estimate of cr. [Pg.197]

The t test can be applied to differences between pairs of observations. Perhaps only a single pair can be performed at one time, or possibly one wishes to compare two methods using samples of differing analytical content. It is still necessary that the two methods possess the same inherent standard deviation. An average difference d calculated, and individual deviations from d are used to evaluate the variance of the differences. [Pg.199]

Confidence limits for an estimate of the variance may be calculated as follows. Eor each group of samples a standard deviation is calculated. These estimates of cr possess a distribution called the ) distribution ... [Pg.202]

The F statistic describes the distribution of the ratios of variances of two sets of samples. It requires three table labels the probability level and the two degrees of freedom. Since the F distribution requires a three-dimensional table which is effectively unknown, the F tables are presented as large sets of two-dimensional tables. The F distribution in Table 2.29 has the different numbers of degrees of freedom for the denominator variance placed along the vertical axis, while in each table the two horizontal axes represent the numerator degrees of freedom and the probability level. Only two probability levels are given in Table 2.29 the upper 5% points (F0 95) and the upper 1% points (Fq 99). More extensive tables of statistics will list additional probability levels, and they should be consulted when needed. [Pg.204]

It is possible to compare the means of two relatively small sets of observations when the variances within the sets can be regarded as the same, as indicated by the F test. One can consider the distribution involving estimates of the true variance. With sj determined from a group of observations and S2 from a second group of N2 observations, the distribution of the ratio of the sample variances is given by the F statistic ... [Pg.204]

The fact that each sample variance is related to its own population variance means that the sample variance being used for the calculation need not come from the same population. This is a significant departure from the assumptions inherent in the z, r, and statistics. [Pg.204]

Note the difference between the equation for a population s variance, which includes the term n in the denominator, and the similar equation for the variance of a sample (the square of equation 4.3), which includes the term - 1 in the denominator. The reason for this difference is discussed later in the chapter. [Pg.73]

Defining the sample s variance with a denominator of n, as in the case of the population s variance leads to a biased estimation of O. The denominators of the variance equations 4.8 and 4.12 are commonly called the degrees of freedom for the population and the sample, respectively. In the case of a population, the degrees of freedom is always equal to the total number of members, n, in the population. For the sample s variance, however, substituting X for p, removes a degree of freedom from the calculation. That is, if there are n members in the sample, the value of the member can always be deduced from the remaining - 1 members andX For example, if we have a sample with five members, and we know that four of the members are 1, 2, 3, and 4, and that the mean is 3, then the fifth member of the sample must be... [Pg.80]

The probabilistic nature of a confidence interval provides an opportunity to ask and answer questions comparing a sample s mean or variance to either the accepted values for its population or similar values obtained for other samples. For example, confidence intervals can be used to answer questions such as Does a newly developed method for the analysis of cholesterol in blood give results that are significantly different from those obtained when using a standard method or Is there a significant variation in the chemical composition of rainwater collected at different sites downwind from a coalburning utility plant In this section we introduce a general approach to the statistical analysis of data. Specific statistical methods of analysis are covered in Section 4F. [Pg.82]

Let s consider the following problem. Two sets of blood samples have been collected from a patient receiving medication to lower her concentration of blood glucose. One set of samples was drawn immediately before the medication was administered the second set was taken several hours later. The samples are analyzed and their respective means and variances reported. ITow do we decide if the medication was successful in lowering the patient s concentration of blood glucose ... [Pg.82]

A manufacturer s process for analyzing aspirin tablets has a known variance of 25. A sample of ten aspirin tablets is selected and analyzed for the amount of aspirin, yielding the following results... [Pg.87]

The variance for the sample of ten tablets is 4.3. A two-tailed significance test is used since the measurement process is considered out of statistical control if the sample s variance is either too good or too poor. The null hypothesis and alternative hypotheses are... [Pg.87]

Percent of overall variance (So) due to the method as a function of the relative magnitudes of the standard deviation of the method and the standard deviation of sampling (Sm/Ss). The dotted lines show that the variance due to the method accounts for 10% of the overall variance when Ss= 3 xs . [Pg.180]

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. [Pg.181]

The following data were collected as part of a study to determine the effect of sampling variance on the analysis of drug animal-feed formulations.2... [Pg.181]

The data on the left were obtained under conditions in which random errors in sampling and the analytical method contribute to the overall variance. The data on the right were obtained in circumstances in which the sampling variance is known to be insignificant. Determine the overall variance and the contributions from sampling and the analytical method. [Pg.181]

Solving for n allows us to calculate the number of particles that must be sampled to obtain a desired sampling variance. [Pg.187]


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See also in sourсe #XX -- [ Pg.142 , Pg.182 ]




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Among-samples variance

Generalized Sample Variance

Pooled sample variance

Predictor variables sample variance

Sample preparation variance

Sample variance

Sample variance

Variance during sample preparation

Variance of sampling

Variance sample size

Within-samples variance

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