Spread, of data

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. 

Allowing for tire spread of data and tending to be conservative, use 85% of value read from chart ... 

Relative measures of the spread of data are often used, particularly where, for example, the spread of results seems to increase with analyte concentration. The relative standard deviation (RSD) is a measure of the spread of data in comparison to the mean of the data ... 

Given the same underlying spread of data (standard deviation, s), as more data are gathered, we become more confident of the mean value, x, being an accurate representation of the population mean, x. 

Once data have been collected, the values will be distributed around a central point or points. Various terms are used to describe both the measure of central tendency and the spread of data points around it. 

A measure of the spread of data around a central point. Described by the following equation. 

The spread of data is often described by quoting the percentage of the sample or population that will fall within a certain range. For the normal distribution, 1SD either side of the mean will contain 68% of all data points, 1.96SD 95%, 2SD 95.7% and 3SD 99.7%. 

Obviously, correlations of one of these friction factors with an analogous Reynolds number, or with two-phase pressure-drop, throws little light on the other variables concerned, and these quantities will appear as parameters in any proposed relationship. However, Govier and Omer point out that plots of such a form do give a systematic spread of data above the single phase lines and allow easy comparison of trends. 

The first principal component explains the maximum amount of variation possible in the data set in one direction. Stated another way. it is the direction that describes the maximum spread of data points. Furthermore, the percent of the total variation in the data set described b) any principal component can be precisely calculated. 

The answer is a technique called population kinetics. In this, blood samples are taken on a few occasions, carefully timed in relation to the previous drug dose, in as big a population as can be observed. The blood samples may be obtained at widely different time points after dosing and ah are analyzed for drug concentration. The next step is a statistical treatment of the results which makes the assumption that ah the patients belong to one big, if variable, population. A spread of data points is obtained over the dose interval and one gigantic curve of concentration-time relationships created. If the population is big enough, the mathematics iron out any awkward individuals whose data do not tit the overall pattern and from this derived curve the kinetic parameters we have been discussing can be deduced. 

RE) of the questionable calibrator with the standard deviation (SD) of all calibrators (RE/SD) is greater than the absolute t9 value at the corresponding degree of freedom (number of independent calibrators minus 1), the individual calibrator is identified as an outlier (i.e., if RE/SD > 95, the outlier may be discarded, where RE is the difference between the percent accuracy value of an individual standard and the mean of the accuracy values of n independent standards and SD is the closeness of the replicate measurements in a set, i.e., the spread of data around the mean). 

Peter H. Given Whereas Tschamler and Fuks, and Peover studied more or less pure vitrinites, Mazumdar apparently worked with whole coals. Moreover, Indian coals, being from Gondwanaland strata, are most probably of very different petrographic composition compared with European and North American coals (rich in exinites and inert macerals See p. 284). Quite apart from the question whether sulfur dehydrogenation really is free of side reactions, there may well be a spread of data at any level or rank because of petrographic differences. 

Although supplier engineering contracts are usually fulfilled on satisfactory completion of the SAT, the performance of a computer system over a spread of data-handling conditions in the real-time environment of a manufacturing process is difficult to fully test at any one time. Consequently, consideration should be given to extending contractual conditions related to system performance into the system operational period, where the broader system performance issues can be better evaluated and reported. 

For IC5o determinations, the substrate concentration should be close to the Am for the marker reaction. As discussed previously, this choice of substrate concentration allows an estimate of the A) value because IC50 = 2A) for competitive inhibition and IC50 = A, for noncompetitive inhibition. For A) determinations, a common substrate concentration scheme is Am/3, Am, 3Am, 6Am, and 10Am. Assuming that the Km for the reaction has been accurately determined, this range of substrate concentrations will provide an adequate spread of data on an Eadie-Hofstee plot to readily observe the mechanism of direct inhibition. For some substrates, solubility can become limiting at concentrations >2Am. In such cases, it becomes necessary to choose alternate concentrations so that no fewer than five concentrations are used in a A, determination. The choice of substrate... 

The variance in the data, a measure of the spread of a set of data, is related to the precision of the data. For example, the larger the variance, the larger the spread of data and the lower the precision of the data. Variance is usually given the symbol s2 and is defined by the formula ... 

The spread of data about the mean is usually measured with the standard deviation ct, but another common parameter is the range. (In our discussion of Gaussian chromatographic peaks, we have used peak width.) By definition,... 

Does the spread of data points for a particular severity category indicate major differences between species or are the results from different species congruent ... 

For a normal distribution of variance, the spread of data about the mean is described by the probability equation... 

The comparison work also helps to provide a baseline for the monitoring programmes in the event of changing analytical laboratories, or the methods being used for analysis. Results can be assessed against the spread of data from the two laboratories, for the sites compared (as well as against past data sets). 

Just as variance describes the spread of data about its mean value for a single variable, so the distribution of multivariate data can be assessed from the covariance. The procedure employed for the calculation of variance can be extended to multivariate analysis by computing the extent of the mutual variability of the variates about some common mean. The measure of this interaction is the covariance. 

An estimate of the average variance over all k groups represents the "typical" spread of data over the entire study or experiment. This variability is often referred to as random variation or noise. In the ANOVA strategy this number is called the within-group variance (or mean square error), and is calculated as a weighted average of the sample variances ... 

In an ANOVA involving more than two groups, we estimate the underlying variability from more than two samples, and yet we are interested in the extent to which (only) two of the means differ from each other. Therefore, when comparing the means of two samples, the pooled standard deviation from the two-sample case, is replaced by an estimate that captures the variability across all groups in the analysis - the mean square error or the within-samples mean square. Recall from Section 11.4 that this quantity has the same interpretation as the pooled standard deviation, the typical spread of data across all observations. 

This is another measure of the spread of data in a data set. It is in fact almost identical to the standard deviation it is simply the standard deviation squared. 

A plot of Sij[5ij(C) - <5jj(TBP)] versus 217.9° - [ (C) - (SP)] is linear. Consideration of a series of compounds with different ligands attached to the same central atom showed a spread of data about the theoretical Berry reaction coordinate. The method of Auf der Heyde and Nassimbini is more rigorous, as it uses all of the available information, whereas the previous approaches used only selected parameters. All three methods suffer from the fact that the relationship of structural data to only one reaction coordinate can be considered. 

Consider the data in Table 1.6, which shows ten replicate measures of the molar absorptivity of nitrobenzene at 252 nm, its wavelength of maximum absorbance. The value of e= 1056 mol m appears out of line with the other nine values - can it be classed as an outlier Figure 1.5 shows these ten values as points on a line, and the suspect value is widely separated from the others in relation to the spread of the data. This observation leads naturally to test statistics of the form N/D, where the numerator iV is some measure of separation of the assumed outlier and the denominator D is a measure of the spread of data. 

Further, the initial ratio correction only works when the isotope ratio within the samples is homogeneous, in cases of heterogeneous excess argon, a spread of data makes precise age determination impossible (e g., Cumbest et al. 1994 Pickles et al. 1997). 

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