Standard deviation precision

Thus, the calculated value of F (1.87) is less than the tabulated value therefore the methods have comparable precisions (standard deviations) and so the t-test can be used with confidence. 

Sample Recovery (ASTA Heat Units) Precision (Standard Deviations) ... 

What is the difference between precision, standard deviation, and uncertainty ... 

Our method of choice to quantify recombinant antibodies produced in PER.C6 cells is that of analytical protein A chromatography (APAC). This method is automated, rapid (total run time of 3.8 min), precise (standard deviation <5%), and sensitive (quantitation limit 25pgmL ), and generally outperforms ELISA methods, except for sensitivity. 

Analytical methods should be validated or verified, and the accuracy as well as the precision (standard deviations) should be recorded. The tests for related compounds or products of decomposition should be validated to demonstrate that they are specific to the product being examined and are of adequate sensitivity. 

Statements that an exponent has been determined with a precision (standard deviation) of, for example, a = 0.002 are suspect. Sometimes all this means is that the experimenter has plotted all the measured points, weighted them equally, and used a linear least-squares program to evaluate the best value of the slope and its standard deviation the reported is then not a limiting value, but an average value, and the a may be nearly meaningless. The actual uncertainty may be far larger, as more precise measurements and more careful analysis may show.f... 

The squares standard deviations can be weighted according to their relative importance (for example Oj can be divided by a characteristic value of the corresponding variable X ). It is important to realize here that the standard deviations O themselves are (due to possible reconciliation) complex functions of the selection of directly measured quantities and of their precision (standard deviations). The objective function (12.2.3) is thus strongly nonlinear. 

There is only one reported set of field data that compares measurements by a spectrum analyzer device and a standard laboratory analysis procedure (McKnight et al, 1989). A laboratory study was also carried out at NIST similar to the one described for lead-specific analyzers. In the laboratory study, the counting time was selected so that the precision (standard deviation) of individual replicate measurements of the same sample of g)fpsum wallboard was about 0.1 mg/cm2 the results are given as follows ... 

The shear viscosity is a tensor quantity, with components T] y, t],cz, T)yx> Vyz> Vzx> Vzy If property of the whole sample rather than of individual atoms and so cannot be calculat< with the same accuracy as the self-diffusion coefficient. For a homogeneous fluid the cor ponents of the shear viscosity should all be equal and so the statistical error can be reducf by averaging over the six components. An estimate of the precision of the calculation c then be determined by evaluating the standard deviation of these components from tl average. Unfortunately, Equation (7.89) cannot be directly used in periodic systems, evi if the positions have been unfolded, because the unfolded distance between two particl may not correspond to the distance of the minimum image that is used to calculate the fore For this reason alternative approaches are required. 

The breadth or spread of the curve indicates the precision of the measurements and is determined by and related to the standard deviation, a relationship that is expressed in the equation for the normal curve (which is continuous and infinite in extent) ... 

An analytical procedure is often tested on materials of known composition. These materials may be pure substances, standard samples, or materials analyzed by some other more accurate method. Repeated determinations on a known material furnish data for both an estimate of the precision and a test for the presence of a constant error in the results. The standard deviation is found from Equation 12 (with the known composition replacing /x). A calculated value for t (Eq. 14) in excess of the appropriate value in Table 2.27 is interpreted as evidence of the presence of a constant error at the indicated level of significance. 

Precision is a measure of the spread of data about a central value and may be expressed as the range, the standard deviation, or the variance. Precision is commonly divided into two categories repeatability and reproducibility. Repeatability is the precision obtained when all measurements are made by the same analyst during a single period of laboratory work, using the same solutions and equipment. Reproducibility, on the other hand, is the precision obtained under any other set of conditions, including that between analysts, or between laboratory sessions for a single analyst. Since reproducibility includes additional sources of variability, the reproducibility of an analysis can be no better than its repeatability. 

To evaluate the effect of indeterminate error on the data in Table 4.1, ten replicate determinations of the mass of a single penny were made, with results shown in Table 4.7. The standard deviation for the data in Table 4.1 is 0.051, and it is 0.0024 for the data in Table 4.7. The significantly better precision when determining the mass of a single penny suggests that the precision of this analysis is not limited by the balance used to measure mass, but is due to a significant variability in the masses of individual pennies. 

Uncertainty expresses the range of possible values that a measurement or result might reasonably be expected to have. Note that this definition of uncertainty is not the same as that for precision. The precision of an analysis, whether reported as a range or a standard deviation, is calculated from experimental data and provides an estimation of indeterminate error affecting measurements. Uncertainty accounts for all errors, both determinate and indeterminate, that might affect our result. Although we always try to correct determinate errors, the correction itself is subject to random effects or indeterminate errors. 

It is unclear, however, how many degrees of freedom are associated with f(a, v) since there are two sets of independent measurements. If the variances sa and sb estimate the same O, then the two standard deviations can be factored out of equation 4.19 and replaced by a pooled standard deviation. Spool, which provides a better estimate for the precision of the analysis. Thus, equation 4.19 becomes... 

The standard deviation about the regression, Sr, suggests that the measured signals are precise to only the first decimal place. For this reason, we report the slope and intercept to only a single decimal place. 

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. 

The goal of a collaborative test is to determine the expected magnitude of ah three sources of error when a method is placed into general practice. When several analysts each analyze the same sample one time, the variation in their collective results (Figure 14.16b) includes contributions from random errors and those systematic errors (biases) unique to the analysts. Without additional information, the standard deviation for the pooled data cannot be used to separate the precision of the analysis from the systematic errors of the analysts. The position of the distribution, however, can be used to detect the presence of a systematic error in the method. 

In the two-sample collaborative test, each analyst performs a single determination on two separate samples. The resulting data are reduced to a set of differences, D, and a set of totals, T, each characterized by a mean value and a standard deviation. Extracting values for random errors affecting precision and systematic differences between analysts is relatively straightforward for this experimental design. 

Control charts were originally developed in the 1920s as a quality assurance tool for the control of manufactured products.Two types of control charts are commonly used in quality assurance a property control chart in which results for single measurements, or the means for several replicate measurements, are plotted sequentially and a precision control chart in which ranges or standard deviations are plotted sequentially. In either case, the control chart consists of a line representing the mean value for the measured property or the precision, and two or more boundary lines whose positions are determined by the precision of the measurement process. The position of the data points about the boundary lines determines whether the system is in statistical control. 

Usually, 10 to 20 measurements are made of the isotope ratio for one substance. Sometimes, one or more of these measurements appears to be sufficiently different from the mean value that the question arises as to whether or not it should be included in the set at all. Several statistical criteria are available for reaching an objective assessment of the reliability of the apparently rogue result (Figure 48.10). Such odd results are often called outliers, and ignoring them gives a more precise mean value (lower standard deviation). It is not advisable to remove such data more than once in any one set of measurements. 

Statistically, a similar Indication of precision could be achieved by utilising the 95% probability level if the results fell on a "Gaussian" curve, viz., the confidence would lie within two standard deviations of the mean. R 2 x SD = 56.3 24.8... 

The average value of the rephcates is reported along with the standard deviation, which reflects the variabihty in the measurement. Large standard deviations relative to the average measurement indicate the need for an action plan to improve measurement precision. This can be accomphshed through more rephcate measurements or the elimination of the source of variation, such as the imprecision of an instmment or poor temperature control during the measurement. 

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. 

To determine of Ce(IV) in acid soluble single crystals, a simple and sensitive method is proposed. The method is based on the reaction of tropeoline 00 oxidation by cerium(IV) in sulfuric acid solution with subsequent measurement of the light absorption decrease of the solution. The influence of the reagent concentration on the analysis precision is studied. The procedure for Ce(IV) determination in ammonium dihydrophosphate doped by cerium is elaborated. The minimal determined concentration of cerium equal to 0.04 p.g/ml is lower than that of analogous methods by a factor of several dozens. The relative standard deviation does not exceed 0.1. 

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