Standard deviation variance

In Eq. 13.15, the squared standard deviations (variances) act as weights of the squared residuals. The standard deviations of the measurements are usually not known, and therefore an arbitrary choice is necessary. It should be stressed that this choice may have a large influence of the final best set of parameters. The scheme for appropriate weighting and, if appropriate, transformation of data (for example logarithmic transformation to fulfil the requirement of homoscedastic variance) should be based on reasonable assumptions with respect to the error distribution in the data, for example as obtained during validation of the plasma concentration assay. The choice should be checked afterwards, according to the procedures for the evaluation of goodness-of-fit (Section 13.2.8.5). 

There were two reasons for increasing the sample size a larger than expected standard deviation (variance) for the primary endpoint and a higher drop-out rate (15 per cent compared to 10 per cent). 

Precision is usually expressed as a standard deviation, variance, or percentage relative standard deviation of a series of measurements. The most useful term is the percentage relative standard deviation (RSD%) or coefficient of variation... 

In a series of standard deviations, variances, or ranges the COCHRAN test [ISO 5725] is used for evaluating the largest value. It is primarily used in (planned) method comparisons, cooperative tests, and analysis of variance where the number of the measurements and the levels of the means should be the same. 

Standard deviations, variances and covariances are useful common functions. It is important to recognise that there are both population and sample functions, so that STDEV is the sample standard deviation and STDEVP the equivalent population standard deviation. Note that for standardising matrices it is a normal convention to use the population standard deviation. Similar comments apply to VAR and VARP. 

The second means of collecting multiple spectra involves collection from numerous locations within the vessel at one or more times. Multiple spectra drawn at one time from various locations in a blender may be compared to themselves or to spectra collected at different times, with similarity indicating content uniformity. Parameters for comparison can again include common statistical factors such as standard deviation, relative standard deviation, variance, a host of indices based on standard deviation, or the results from pattern recognition routines. Of course, spectra collected in this manner can also be compared to a library of spectra from previous homogenous blends. 

Three terms are widely used to describe the precision of a set of replicate data standard deviation, variance, and coefficient of variation. These three are functions of how much an individual result x,- differs from the mean, which is called the deviation from the mean... 

Mean Value, Standard Deviation, Variance, and Confidence Intervals. Every experiment is subject to uncertainty. Statistical methods are the best tool for determining these uncertainties, which, in turn, can be used for parameter estimation. 

An overview of statistical methods covers mean values, standard deviation, variance, confidence intervals, Student s t distribution, error propagation, parameter estimation, objective functions, and maximum likelihood. 

Calculate the following descriptive statistics for the data on water hardness (mmoll ) given as follows arithmetic mean, median, standard deviation, variance, standard error, confidence interval at a significance level of 0.01, range, and the interquartile distance - 8.02 7.84 7.98 7.95 8.01 8.07 7.89. 

To weight variances changing at the different observation points x, a weight based on the reciprocal standard deviation (variance) could be applied ... 

In all these ROIs, mean pixel value, maximum and minimum pixel value, standard deviation, variance and deviating pixels are calculated. 

Measurement precision is usually expressed numerically by measures of imprecision, such as standard deviation, variance, or coefficient of variation under the specified conditions of measurement. Measurement precision pertains to the repeatability of a process but sometimes is erroneously used to mean measurement accuracy. The term accuracy refers to the degree of agreement of the measured dimension with its true magnitude or, in other words, it is the ability to hit what is aimed at. The term precision refers to the degree to which an instrument can give the same value when repeated measurements of the same standard are made therefore precision pertains to the repeatability of a process (De Garmo et al. 1964 Taniguchi 1983 Kalpakjian and Schmid 1995). 

Variance is defined as the square of the standard deviation, Variance is often preferred as a measure of precision because variances from m independent sources of random error are additive. The standard deviations themselves are not additive. The use of variance allows us to calculate the... 

The aim of training is to obtain sets of spectral data that can be used to determine decision rules for the classification of each pixel in the whole image data set. The training data for each class must be representative of all data for that class. Each training site consists of many pixels, conventionally it is taken that if there are n number of bands the number of pixels in each band is n+1. The mean, standard deviation, variance, minimum value, maximum value, variance-covariance matrix and correlation matrix for training classes are calculated, which represent the fundamental information on the spectral characteristics of all classes. Since for selection of appropriate bands only this information is not enough, thus feature selection is used. The training sites are presented on true color map bands 1, 2, and 3 for 13 classes (Fig. 16). 

To find out if the total influence of these deviations on the mean content is still within the set amount of 5 %, all deviations have to be accumulated. Weighing deviations may compensate for each other so straightforward totalling limit values will reflect an extremely worst case. Combining deviations that have a different mathematical type is essentially an addition of quadratic standard deviations (variances), but only after limit values have been turned into standard deviations according to their specific statistical distribution. This propagation (or accumulation) of uncertainties is elaborated in Sect. 5 and Annex E.4 of [4] and applied to small-scale preparation in [10]. 

The remainder of the code illustrates some important statistical functions and plots which will be useful in this chapter. The mean, standard deviation, variance and skewness coefficient of the data are calculated and printed on line 9 using the stats() function. These quantities are defined in the standard way by ... 

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