Standard deviation of sampling

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 . 

Figure 7.28. Static mixer in laminar flow reduction in relative standard deviation of samples indicating improvement in mixture quality with increasing number n of elements traversed...

For example, if a maximum error of 5 ppm is desired for the average concentration of a particular chemical with 95% confidence and the standard deviation of sample results is 10 ppm, then... 

The required sample weight, w, for a relative standard deviation of sampling of 1% at a confidence level of 68% is given by ... 

A river is analyzed for its loading of adsorbable organohalogen compounds (AOX). Twenty samples are taken at the same time and location. Each sample has an AOX value of 20 rg L 1 with a standard deviation of sampling ss = 2.0 pg L. Each analytical determination has a standard deviation. v, - 1.0 pg L 1. 

Population standard deviation—standard deviation of sample—s ... 

If the sample is representative, then the second consideration is how artefacts of randomly choosing the samples lead to random variation in the estimate of statistics of interest, such as the mean or standard deviation of sample distribution of interindividual variability. While it is often assumed that a small sample of data is not or could not be representative, this is a common misconception. The issue of representativeness is one of study design and sampling strategy. If one has a representative sample, even if very small, then conventional statistical methods can be used to make inferences regarding sampling distributions of statistics, such as... 

Mean and standard deviation of samples from each plant in the container on a dry weight basis different superscripts within colums denote significcant differences (P<0.01)... 

EXAMPLE 27-5 If the standard deviation of sampling strata is 0.07, that of sampling within strata is 0.10, and that of a single determination is 0.21, and if the relative costs are in the ratio 4/2/1, calculate the optimum sampling scheme and minimum cost that will give an overall standard deviation of the mean of 0.08. 

We can rearrange Equation 8-5 to calculate the relative standard deviation of sampling,... 

The variance in the sampling does have a significant effect on the overall measurement variance at the 95% level as determined by ANOYA. The standard deviation of sampling is 0.52% and the standard deviation of the analysis is 0.33% protein. The estimated standard deviation of single random samples is 0.61% protein. 

Among the broad possibilities to characterize homogeneity, up to now, the mixing indices based on the standard deviation of sample concentrations have remained the most frequently used quality indicators. One of them was defined by Rose [2, 3], as... 

In Eq. (1), So is the standard deviation of sample concentrations before mixing, which generally corresponds to totally segregated state. Therefore, in segregated state M = 0, and in perfectly mixed state M = 1. It has to be noticed that this is not an absolute exact method to characterize the degree of homogeneity in a mixture, because, in case of finite size particles, the standard deviation s and, therefore, the value of M depends on the number of particles in a sample [8]. 

In a conventional mixing process, the maximum achievable degree of mixedness corresponds to a completely random arrangement of different particles. Based on the cissumption that the particle size of an individual comjjonent is identical, Lacey [9,10] has demonstrated that the minimal possible standard deviation of sample concentrations for a binary mixture can be expressed as... 

Some important mixing indices based on the variance or standard deviation of sample concentration. ... 

---