Statistics dispersion, measures

In this scheme, digital particles are still wandering localized clusters of informa-tionl but (conventional) variables such as space, time, velocity and so on become statistical quantities. Given that no experimental measurement to date has yet detected any statistical dispersion in the velocity of light, the sites of a hypothetical discrete underlying lattice can be no further apart than about 10 cm. 

Results verification is totally different from results validation. Results validation (point 4.7.5. and 5.9. of NBN-EN-ISO-CEI 17025 standard) shows, each year, or when it is judged necessary, that a given laboratory has the capacity to apply a particular method, repetitively, in respect of obtained data during initial validation. Trueness and statistical dispersion of results are the basis of the definition of the uncertainty of the standard of measurement [16] and, in some cases, the basis for the definition of the limit of detection and quantification. Management of data from validation results, as control card, could permit the detection and control of eventual deviation. Validation of results is the internal quality control procedure which verifies the stability of performance of the methods for which accreditation is sought, in the limited-scope procedural context. 

Optical microscopy on phase contrast mode allows observation of the different morphologies obtained for each PP/interfacial modifier/PA6 blend. By image analysis techniques, it is possible to carry out statistical field measurements not only of the mean number of particles on the dispersed phase but also of their preferential geometry, mean size, and size distribution. 

Platinum catalysts have been the subject of several studies with that perspective. Using Pt on various soUds (silicas, alumina, with various porosities etc.), Praliaud et al. [15] found a very clear correlation between dispersion and catalytic activity, whatever the support and its morphology. The lower the dispersion, and thus the bigger the particle size (in the range 1-20 nm), the more active the catalyst The selectivity (i.e. the reaction pathway itself) was not affected by particle size. It is noteworthy that the excellent correlation with metal dispersion on the solid was not observed for particle size, determined by TEM. This is probably related to the low accuracy of the measurement of size by TEM, which is a local method, whereas dispersion measurement is done by global analysis, thus providing a perfect statistical average. 

The software Microsoft Excel for Windows and the Statistical Package for Social Sciences 12.0 (SPSS) were used to create a database and to conduct statistical analysis. Measures of central tendency and dispersion were used to describe data, with means and standard deviations for quantitative variables. The Student t test for paired samples was used for comparisons between groups. The level of significance was established at p<0.05. 

The standard deviation is an error of a given value expressed in the units of this value. The standard deviation is a statistic which measures the variability or dispersion of the set of data. 

Variance—1) The difference between the expected (budgeted or planned) value and the actual. 2) In statistics, a measure of dispersion of data. 

In view of the relative scarcity of experimental data in relation to the large number of parameters that play a role in dense gas dispersion, statistical measures do not have an absolute meaning in the sense that by changing the validation data set, the statistical measures can change significantly. Therefore, statistical performance measures of different models can only be compared if exactly the same data sets are used for all models. 

The variance is a measure of the statistical dispersion, indicating how the possible values are spread around the expected value. The variance of a random variable Xis, = E X — /u.) with the expected value E X) = f X dP. 

The most basic step in statistical analysis of a data set is to describe it descriptively, that is, to compute properties associated with the data set and to display the data set in an informative manner. A data set consists of a finite number of samples or data points. In this book, a data set will be denoted using either set notation, that is, jti, X2,..., x or vector notation, that is, as if = (x],jC2,..., x ). Set notation is useful for describing and listing the elements of a data set, while vector notation is useful for mathematical manipulation. The size of the data set is equal to n. The most common descriptive statistics include measures of central tendency and dispersion. 

Variance n One of the most used descriptive measures of a probability distribution, population or sample. It is equal to the square of the standard deviation. It is a measure of deviation from the expectation value or mean. It is a measure of statistical dispersion which quantifies the deviations from the expectation value as the mean of the squares of the distance from the mean. The variance of a random variable is defined as the second central moment of the random variable and is often denoted by cr and sometimes by Var(X), defined on a probability space, S, is given by ... 

At first, it is statistical standard of the undefective section. Such standard is created, introducing certain lower threshold and using measured data. Under the classical variant of the shadow USD method it is measured fluctuations of accepted signal on the undefective product and installed in each of 512 direction its threshold in proportion to corresponding dispersions of US signal in all 128 sections. After introducting of threshold signal is transformed in the binary form. Thereby, adaptive threshold is one of the particularities of the offered USCT IT. 

The main sources of error which define the accuracy are counting statistics in tracer concentration measurements, the dispersion of the tracer cloud in the flare gas stream, and the stationarity of the flow during measurements. 

The Offshore and Coastal Dispersion (OCD) model (26) was developed to simulate plume dispersion and transport from offshore point sources to receptors on land or water. The model estimates the overwater dispersion by use of wind fluctuation statistics in the horizontal and the vertical measured at the overwater point of release. Lacking these measurements the model can make overwater estimates of dispersion using the temperature difference between water and air. Changes taking place in the dispersion are considered at the shoreline and at any points where elevated terrain is encountered. 

The standard deviation, Sj, is the most commonly used measure of dispersion. Theoretically, the parent population from which the n observations are drawn must meet the criteria set down for the normal distribution (see Section 1.2.1) in practice, the requirements are not as stringent, because the standard deviation is a relatively robust statistic. The almost universal implementation of the standard deviation algorithm in calculators and program packages certainly increases the danger of its misapplication, but this is counterbalanced by the observation that the consistent use of a somewhat inappropriate statistic can also lead to the right conclusions. 

The error expresses the standard deviation of the actual age. The standard deviation is an index of variance used in statistics to characterize the dispersion of measured values (see Fig. 64). This implies that there is a 68% probability, that is, a likelihood of 2 to 1, that the real age is within the indicated... 

Traditionally, analytical chemists and physicists have treated uncertainties of measurements in slightly different ways. Whereas chemists have oriented towards classical error theory and used their statistics (Kaiser [ 1936] Kaiser and Specker [1956]), physicists commonly use empirical uncertainties (from knowledge and experience) which are consequently added according to the law of error propagation. Both ways are combined in the modern uncertainty concept. Uncertainty of measurement is defined as Parameter, associated with the result of a measurement that characterizes the dispersion of the values that could reasonably be attributed to the measurand (ISO 3534-1 [1993] EURACHEM [1995]). 

Parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand . The uncertainty should combine both statistical and non-statistical contributions to the variation of the measured values which may occur in all steps of the analytical process. 

Dispersion parameter for the distribution of measured values, s2, or analytical results, s2, for a given sample or the population, o2 and o2. Statistically defined as the second moment about the mean. 

Strictly speaking, monodisperse samples would be required for the determination of the Mark-Houwink coefficients. Since, however, the poly-dispersities of the nine individual fractions are only moderate (Mw/Mn 2) and since both Mw and [tj] are measured as weight averages with the same statistical weights, the error introduced by the incorrect treatment of the polydispersity could be neglected. 

One of the prime objectives of the statistical chemistry of these polymers is establishing the dependence of their composition inhomogeneity on a macromolecule length l and on the reaction system parameters. A quantitative measure of this inhomogeneity is the dispersion (Eq. 2) of the composition distribution... 

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