Relative standard deviation samples

The relative standard deviation for sampling, Sj r, is obtained by dividing equation... 

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. ... 

Determine Ks and the amount of sample needed to give a relative standard deviation for sampling of 2.0%. Predict the percent relative standard deviation and the absolute standard deviation if samples of 5 g are collected. 

To determine Ks we need to know the average mass of the cereal samples and the relative standard deviation for the %(w/w) ash. The average mass of the five cereal samples is 1.0007 g. The average %(w/w) ash and the absolute standard deviation are, respectively, 1.298% and 0.03194. The percent relative standard deviation, therefore, is... 

The amount of sample needed to give a relative standard deviation of 2%, therefore, is... 

If we use 5.00-g samples, then the expected percent relative standard deviation is... 

When the target population is segregated, or stratified, equation 7.5 provides a poor estimate of the amount of sample needed to achieve a desired relative standard deviation for sampling. A more appropriate relationship, which can be applied to both segregated and nonsegregated samples, has been proposed. ... 

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 ... 

Each of the f2 samples had a nominal weight of O.f g. Determine the approximate value for fQ, and the mass of sample needed to achieve a percent relative standard deviation of 2%. 

Precision For absorbances greater than 0.1-0.2, the relative standard deviation for atomic absorption is 0.3-1% for flame atomization, and 1-5% for electrothermal atomization. The principal limitation is the variation in the concentration of free-analyte atoms resulting from a nonuniform rate of aspiration, nebulization, and atomization in flame atomizers, and the consistency with which the sample is heated during electrothermal atomization. 

Precision When the analyte s concentration is well above the detection limit, the relative standard deviation for fluorescence is usually 0.5-2%. The limiting instrumental factor affecting precision is the stability of the excitation source. The precision for phosphorescence is often limited by reproducibility in preparing samples for analysis, with relative standard deviations of 5-10% being common. 

Precision For samples and standards in which the concentration of analyte exceeds the detection limit by at least a factor of 50, the relative standard deviation for both flame and plasma emission is about 1-5%. Perhaps the most important factor affecting precision is the stability of the flame s or plasma s temperature. For example, in a 2500 K flame a temperature fluctuation of +2.5 K gives a relative standard deviation of 1% in emission intensity. Significant improvements in precision may be realized when using internal standards. 

Precision The precision of a gas chromatographic analysis includes contributions from sampling, sample preparation, and the instrument. The relative standard deviation due to the gas chromatographic portion of the analysis is typically 1-5%, although it can be significantly higher. The principal limitations to precision are detector noise and the reproducibility of injection volumes. In quantitative work, the use of an internal standard compensates for any variability in injection volumes. 

What mass of carbon is needed to give a percent relative standard deviation of 1.0% for the activity of a sample if counting is limited to 1 h How long must the radioactive decay from a 0.50-g sample of carbon be monitored to give a percent relative standard deviation of 1 % for the activity ... 

What is the estimated relative standard deviation for the results of a collaborative study in which the sample is pure analyte (100% w/w analyte) Repeat for the case in which the analyte s concentration is 0.1% w/w. 

A newly proposed method is to be tested for its singleoperator characteristics. To be competitive with the standard method, the new method must have a relative standard deviation of less than 10%, with a bias of less than 10%. To test the method, an analyst performs ten replicate analyses on a standard sample known to contain 1.30 ppm of the analyte. The results for the ten trials are... 

A class of analytical students is asked to analyze a steel sample to determine the %w/w Mn. (a) Given that the steel sample is 0.26% w/w Mn, estimate the expected relative standard deviation for the class results, (b) The actual results obtained by the students are... 

A study was conducted to measure the concentration of D-fenfluramine HCl (desired product) and L-fenfluramine HCl (enantiomeric impurity) in the final pharmaceutical product, in the possible presence of its isomeric variants (57). Sensitivity, stabiUty, and specificity were enhanced by derivatizing the analyte with 3,5-dinitrophenylisocyanate using a Pirkle chiral recognition approach. Analysis of the caUbration curve data and quaUty assurance samples showed an overall assay precision of 1.78 and 2.52%, for D-fenfluramine HCl and L-fenfluramine, with an overall intra-assay precision of 4.75 and 3.67%, respectively. The minimum quantitation limit was 50 ng/mL, having a minimum signal-to-noise ratio of 10, with relative standard deviations of 2.39 and 3.62% for D-fenfluramine and L-fenfluramine. 

Investigated is the influence of the purity degree and concentration of sulfuric acid used for samples dissolution, on the analysis precision. Chosen are optimum conditions of sample preparation for the analysis excluding loss of Ce(IV) due to its interaction with organic impurities-reducers present in sulfuric acid. The photometric technique for Ce(IV) 0.002 - 0.1 % determination in alkaline and rare-earth borates is worked out. The technique based on o-tolidine oxidation by Ce(IV). The relative standard deviation is 0.02-0.1. 

As the result of the performed investigations was offered to make direct photometric determination of Nd microgram quantities in the presence of 500-fold and 1100-fold quantities of Mo and Pb correspondingly. The rare earth determination procedure involves sample dissolution in HCI, molybdenum reduction to Mo (V) by hydrazine and lead and Mo (V) masking by EDTA. The maximal colour development of Nd-arsenazo III complex was obtained at pH 2,7-2,8. The optimal condition of Nd determination that was established permit to estimate Nd without separation in solution after sample decomposition. Relative standard deviations at determination of 5-20 p.g of Nd from 0,1 g PbMoO are 0,1-0,03. The received data allow to use the offered procedure for solving of wide circle of analytical problems. 

The complex of the following destmctive and nondestmctive analytical methods was used for studying the composition of sponges inductively coupled plasma mass-spectrometry (ICP-MS), X-ray fluorescence (XRF), electron probe microanalysis (EPMA), and atomic absorption spectrometry (AAS). Techniques of sample preparation were developed for each method and their metrological characteristics were defined. Relative standard deviations for all the elements did not exceed 0.25 within detection limit. The accuracy of techniques elaborated was checked with the method of additions and control methods of analysis. 

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...

The accuracy and precision of the determinations were investigated. Recovery was found to be 101 2.0% for a range of volumetrically mixed samples and the relative standard deviation (RSD), for a standard injected 23 times over a period of 4.5 months, was found to be 1.1%. It should be noted that the performance of a method for samples based on standard materials may not be attainable when real samples are being determined and further method development may be required. 

Thus, one can be far from the ideal world often assumed by statisticians tidy models, theoretical distribution functions, and independent, essentially uncorrupted measured values with just a bit of measurement noise superimposed. Furthermore, because of the costs associated with obtaining and analyzing samples, small sample numbers are the rule. On the other hand, linear ranges upwards of 1 100 and relative standard deviations of usually 2% and less compensate for the lack of data points. 

The relative standard deviation of the determination was found to be 0.5% (photometer) resp, 0.7% (HPLC ) for samples and references. 

Figure 4.22. Correlation of assay values for components A and B, for three dosage levels of A, with 10 samples per group. The comer symbols indicate the 10% specification limits for each component. For manual injection (left panel) only relative standard deviations of 1-2% are found, but no correlation. Automatic injection (right panel) has a lower intrinsic relative standard deviation, but the data are smeared out along the proportionality line because no internal standard was used to correct for variability of the injected volume. The proportionality line does not go through the comers of the specification box because component B is either somewhat overdosed (2.4%). analytical bias, or because an interference results in too high area readings for B. The...

Successful use of modern liquid chromatography in the clinical laboratory requires an appreciation of the method s analytical characteristics. The quantitative reproducibility with respect to peak height or peak area is quite good. With a sample loop injector relative standard deviations better than 1% are to be expected. The variability of syringe injection (3-4% relative standard deviation) requires the use of an internal standard to reach the 1% level (2,27). 

All the analytical data are from the same laboratory consequently, interlaboratory analytical variation is not a factor. The intralaboratory variation for that laboratory was 9.1 percent (i.e., the relative standard deviation based on repetitive analyses of performance evaluation samples). 

The data presented In Figures 2, 3, and 4 are from five different laboratories However, the samples from any one method In each segment were sent to the same contractor thus. Interlaboratory analytical variation Is not a factor In the data columns, but It may be a factor In the data rows The estimated Interlaboratory and Intralaboratory relative standard deviations for TCDD concentrations of 2 to 12 ppb range from 9 to 18 percent and 5 to 13 percent, respectively ... 

Fig. 4.3 Relative standard deviation (J sd) [%] over sample mass [mg] for Pb in IAEA 393, Algae. Each data point represents at least 20 individual measurements (Sonntag and Rossbach 1997).

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... 

Repeatability is defined as precision under conditions where independent test results are obtained with the same method on identical test material in the same laboratory by the same operator using the same equipment within short intervals of time. The replicate analytical portion for testing can be prepared from a common field sample containing incurred residues. This approach is used extremely rarely. Normally, repeatability is estimated by the relative standard deviation ofrecoveries, which should be lower than 20% per commodity and fortification levels according to SANCO/825/00. In justified cases, higher variability can be accepted. 

The limit of detection (LOD) is an important criterion of the efficiency of an analytical method. It is characterized by the smallest value of the concentration of a compound in the analytical sample. The detectable amount of anilide compounds is in the range 0.01-0.5 ng by GC and 0.1 ng by HPLC. The limit of quantitation (LOQ) ranges from 0.005 to 0.01 mg kg for vegetables, fruits and crops. The recoveries from untreated plant matrices with fortification levels between 10 and 50 times the LOD and the LOQ are 70-120%. The relative standard deviation (RSD) at 10-50 times the level of the LOD and LOQ are <10 % and <20%, respectively. 

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