Standard deviation in sampling

The peel strength standard deviation in samples 1,2,2a, 3, and 4 is 3-8%, while in sample 5 it is 20-22%. If this is taken into consideration, one can see that the adhesion of PMDA-ODA to silicon dioxide with APS is not affected by the presence of fluorine, neither is it affected by the change in peel ambient RH as shown in Fig. 4. 

Few populations, however, meet the conditions for a true binomial distribution. Real populations normally contain more than two types of particles, with the analyte present at several levels of concentration. Nevertheless, many well-mixed populations, in which the population s composition is homogeneous on the scale at which we sample, approximate binomial sampling statistics. Under these conditions the following relationship between the mass of a randomly collected grab sample, m, and the percent relative standard deviation for sampling, R, is often valid. ... 

In Example 7.6 we found that an analysis for the inorganic ash content of a breakfast cereal required a sample of 1.5 g to establish a relative standard deviation for sampling of 2.0%. How many samples are needed to obtain a relative sampling error of no more than 0.80% at the 95% conhdence level ... 

The sampling constant for the radioisotope " Na in a sample ( homogenized human liver has been reported as approximate 35 g. (a) What is the expected relative standard deviation fo sampling if f.O-g samples are analyzed (b) How many f.O-g samples need to be analyzed to obtain a maximum sampling error of 5% at the 95% confidence level ... 

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...

Analysis of Corexit 9527. Corexit 9527 in natural waters can be analyzed. The method is based on the formation of a Z>w(ethylenediamine) copper(II) complex, extraction of the complex into methylisobutylketone, and atomic absorption spectroscopy [1564]. The method is suitable for a concentration range of 2 to 100 mg/liter, with a precision as low as 5% relative to standard deviation for samples in the middle- to high range. Only a small sample volume (10 ml) is required. The sensitivity may be substantially increased for trace analysis by increasing the sample volume. 

UNC denotes the uncertainty level at which M should be given (in our case 5 %). In the following example we have calculated the minimum sample mass required to obtain a 5 % relative standard deviation in repetitive measurements for Pb in IAEA-338, lichen distribution of results normal... 

The sample standard deviation, s, provides an estimate of the population standard deviation, a. The (n — 1) term in equations (6.4) and (6.6) is often described as the number of degrees of freedom (frequently represented in statistical tables by the parameter v (Greek letter, pronounced nu ). It is important for judging the reliability of estimates of statistics, such as the standard deviation. In general, the number of degrees of freedom is the number of data points (n) less the number of parameters already estimated from the data. In the case of the sample standard deviation, for example, v = n — 1 since the mean (which is used in the calculation of s) has already been estimated from the same data. 

Applied potential Using a sample of type 316 stainless steel with a high content of molybdenum, the CPT was determined with an apphed potential in the range of -t400 to +800 mV/SCE (Fig. 23). It can be seen that the transition between the potential-dependent CPT and the potential-independent CPT is at about 550-600 mV/SCE, and that the standard deviation in CPT measurements decreases as the applied potential is increased (from about 5°C at low potentials and down to about 0.5°C at 800 mV/SCE). 

Table II Calculation by Visman Equation of Number of Samples Required for Determination of Dieldrin with a Sampling Uncertainty of 50% Relative Standard Deviation in Test Data of Table I, Using Pairs of Large Cores Taken Perpendicular to Spray-Track Direction.

Differences in measurement methods include analyzer systems based both on the same and on different measurement principles. The average standard deviation in the performance of different chemiluminescent ozone instruments that are sampling the same ambient air both with and without an added ozone concentration of 0.(X)2-0.5 ppm is 6-10%. Field studies comparing an ultraviolet monitor with several chemiluminescent monitors showed correlation coefficients for hourly averages of 0.80-0.95 between various pairs of instruments. Hourly averages for about 500 pairs of values at ambient ozone concentrations of 0.005-0.100 ppm showed deviations of 3-23% between the average values for paired instruments. 

Samples were excited with 30-ps 600-nm excitation flashes (< 100 11J 1.5-2 mm diameter) at 5 Hz. The maximum standard deviation in AA was typically 0.005. Rps. sphaeroides reaction centers (36) and polyvinyl alcohol (PVA) films (17) were prepared as described previously. 

Fig. 1. Thirty molecules (open and solid circles) are grouped into five clusters in a two-dimensional chemical space. In A, the original, unsealed variables are used, whereas the variables are scaled to have unit sample standard deviations in B. The lines connect each molecule to its cluster center. Solid circles denote the compounds chosen at random open circles are unselected compounds.

The cyanide sensor developed by the authors group is based on the formation of an addition product between cyanide ion and pyridoxal-5-phosphate, and its subsequent retention in the sensor (a fluorimetric flow-cell packed with QAE-Sephadex resin). The eluent is not injected, but merged with a stream of 0.05 M HCl after the reactor that is used both to acidify the complex and elute it after measurement. The calibration graph for the target analyte was linear from 50 ng/mL to 3.0 pg/mL, and the relative standard deviation and sample throughput were 1.4% (for 2 pg CN7mL) and... 

The standard deviation in the sample is denoted s or sd The standard deviation in the population is denoted a... 

For the determination of the intralaboratory repeatability of the DR CALUX bioassay for sediment samples, two sediment extracts were analyzed 10 times. Each analysis was performed in triplicate. As a prerequisite for a correct triplicate analysis, the percentage standard deviation in the triplicate determination should be below 15%. This is in accordance with the harmonized quality criteria for eell-based bioassay analyses of PCDDs/PCDFs in feed and food as formulated by Behnisch et al. (Behnisch et al, 2001 a) and as detailed in European Union directive 2002/69/ EC and direetive 2002/70/EC. The repeatability for the low-2,3,7,8-TCDD-content sediment... 

Fig. 3. Relation between the minimum number of units in a sample require for sampling errore (relative standard deviations in percentage) of 0.1 and 1 % (y-axis) and the overall composition of a sample (x-axis), for mixtures having two types of particles with a relative difference in composition ranging from 100 to 10% Reprinted wiA permission from W. E. Harris, B. Kratochvil, Analytical Chemistry, 46 (1974), p. 314. Copyright 1974 American Chemical Society...

When we are dealing with samples rather than populations, we cannot use the standard normal deviate, Z, to make predictions since this requires knowledge of the population mean and variance or standard deviation. In general, we do not know the value of these parameters. However, provided the sample is a random one, its mean 5 is a reliable estimate of the population mean p, and we can use the central limit theorem to provide an estimate of o. This esti mate, known as the standard error of the mean, is given by ... 

When comparing the means from two independent sampies we use the unpaired or two-sample t-test. If the numj)er of observations, means and standard deviations in the respective samples are nl, 1, si and n2, s2, then ... 

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