Measures of variability

Preliminary process capability studies are those based on measurements collected from one operating run to establish that the process is in statistical control and hence no special causes are present. Studies of unpredictable processes and the determination of associated capability indices have little value. Preliminary studies should show acceptable results for special characteristics before production approval can be given. These studies and associated indices only apply to the measurement of variables and not to attributes (see below). 

In addition, the protocol should specify a sufficient number of process runs to prove consistency of the process, and provide an accurate measure of variability among successive runs. The number of batches should depend on the extent of validation and complexity of the process or importance of any process changes. Furthermore, the protocol should address the quality of materials used in the process from starting materials to new and recovered solvents, and evidence of the performance and reliability of equipment and systems. 

A measure of variability of the estimate can be gained from the standard error but it can be seen from Equations 11.4 and 11.5 that the magnitude of the standard error is inversely proportional to n (i.e., the larger the sample size the smaller will be the standard error). Therefore, without... 

The product specification should include a measure of uniformity of content and a dissolution test following the release of the active ingredient until steady state is achieved (or justifying shorter periods of testing). Where possible, the dissolution specification (often expressed as quantity of active ingredient released per unit area of surface per unit time) should be related to the results obtained from batches found to be acceptable in clinical studies. In these tests six units should be tested for dissolution characteristics and the mean value stated with a measure of variability. 

Dissolution test data will be required in all cases (and for all strengths of product) for development and routine control and should be based on the most suitable discriminatory conditions. The method should discriminate between acceptable and unacceptable batches based on in vivo performance. Wherever possible Ph Eur test methods should be used (or alternatives justified). Test media and other conditions (e.g., flow through rate or rate of rotation) should be stated and justified. Aqueous media should be used where possible and sink conditions should be maintained. A small amount of surfactant may be added where necessary to control surface tension or for active ingredients of very low solubility. Buffer solutions should be used to span the physiologically relevant range—the current advice is over pH 1 6.8 or perhaps up to pH 8 if necessary. Ionic strength of media should be reported. The test procedure should employ six dosage forms (individually) with the mean data and a measure of variability reported. 

Depending on the source of the graphite, one obtains distinctly different IR/PA spectra (frequently caused by adsorbed species) and the response of the DTGS detector of an IR spectrometer turns out to be a more accurate measure of variable source intensity (12). A normalization technique (13) requiring measurement of the spectrum at two different mirror velocities and corrected by black body spectra taken at the same two velocities appears to be the best normalization method reported thus far. 

With outliers. For comparison, we use the same data set (without outliers) and the same window size, 25, only we substitute one set of measurements with an outlier of y = [0.1858 4.4735 1.2295 3.88]T. The outlier is assumed to be in the measurement of variable x2. Figures 9 and 10 show the sampling data of variable x2 and the corresponding QQ-plots. In Fig. 10, most of the measurements (24 of 25) approximate a straight line, which indicates that the main data has a Gaussian distribution. Only the 25th measurement is far away from this main structure and is obviously an outlier. 

Two terms refer to the quality and reproducibility of our measurements of variables. The first, accuracy, is an expression of the closeness of a measured or computed value to its actual or true value in nature. The second, precision, reflects the closeness or reproducibility of a series of repeated measurements of the same quantity. 

It is the average of the differences between the individual results and the mean. It is regarded as a measure of variability. In the case of a small number of observations the average deviation is found to be not quite significant statistically. The average or mean distribution may be calculated by adopting the following steps, namely ... 

The identification and measurement of variability during drug development and evaluation. 

A second, simple measure of variability is the inter-quartile range that is the interval between the upper and lower quartiles. The upper quartile of a set of data is that value that is less than 25% of the data and greater than 75% similarly, the lower quartile is the value that is greater than 25% of the data and less than 75%. For the blood glucose data the lower quartile is 3.6 mmol / Land the upper quartile 4.55 mmol/L, giving an interquartile range of 0.95 mmol/L. 

Generating two replicate designs provides a measure of variability within a method due to chance. 

When one analyzes cost data derived from randomized trials, one should report means of costs for the groups under study as well as the difference in the means, measures of variability and precision, such as the standard deviation and quantiles of costs (particularly if the data are skewed), and an indication of whether the costs are likely to be meaningfully different from each other in economic terms. 

For reasons best known to mathematicians, much of the method ology of statistics, and many of the simplified tables and computa tions have been based on the use of the standard deviation as a measure of variability. Who are we to argue Later, however, the use of the range as a simplified measure in certain situations will be developed. 

This table is used for comparing an observed mean with some standard value, using the range as a measure of variability. The criteria for decision are the same as those for Table III. 

The coronene analysis also represented the first definite measurements of variable carbon-carbon bond lengths for any condensed ring aromatic hydrocarbon. Earlier indications of this effect had, however, been found in naphthalene and anthracene by Pauling et al. (1935) from an examination of Robertson s (1933a) publications on these molecules. 

Measures of variability, the range, the mean deviation and variance... 

As we can see, mean or average, median and mode are measure of Location. Having determined the location of our data, we might next ask how the data are spread out about mean. The simplest measure of variability is range or interval. The range is defined as the difference between the largest and smallest values in the sample. 

This measure can be calculated easily but it offers only an approximate measure of variability of data as it is influenced only by the limit values of observed property that can be quite different from other values. For a more precise measure of variability we have to include all property-response values, i.e. from all their deviations from the sample mean, mostly the average. As the mean of the values of deviation from the sample mean is equal to null, we can take as measures of variability the mean deviation. The mean deviation is defined as the mean of the absolute values of deviation from the sample mean ... 

The sample variance is essentially the sum of the squares of the deviation of the data points from the mean value divided by (n-1). A large value of variance indicates that the data are widely spread about the mean. In contrast, if all values for the data points were nearly the same, the sample variance would be very small. The standard deviation sx is defined as the square root of the variance. The standard deviation is expressed by the same units as random variable values. Both standard deviation and the average are expressed by the same units. This characteristic made it possible to mutually compare variability of different distributions by introducing the relative measure of variability, called the coefficient of variation ... 

EPA round robin studies is another quality assessment tool that is effective in revealing deficiencies in laboratory s ability to correctly identify and quantify environmental pollutants. The EPA performs these studies on a regular schedule and evaluates the results for the purpose of establishing interlaboratory precision, which is a measure of variability among the results obtained for the same sample at different laboratories. (Interlaboratory precision or reproducibility is another secondary DQI.)... 

Mean of possible measurements of variable (the population mean, true mean)—ft Individual measurement of variable—a-, ... 

It is also interesting to briefly consider online measurements of variables different from temperature [5], Since pressure is defined as the normal force per unit area exerted by a fluid on a surface, the relevant measurements are usually based on the effects deriving from deformation of a proper device. The most common pressure sensors are piezoresistive sensors or strain gages, which exploit the change in electric resistance of a stressed material, and the capacitive sensors, which exploit the deformation of an element of a capacitor. Both these sensors can guarantee an accuracy better than 0.1 percent of the full scale, even if strain gages are temperature sensitive. 

As a measure of variability or dispersion, the sum of squares considers how far the Xt s deviate from the mean. The mean sum of squares is called the variance (or mean squared deviation), and it is denoted by a2 for a population ... 

Why is the standard deviation a good measure of variable significance Reduce the dataset to 100 significant variables with the highest standard deviations to give a 10 x 100 data matrix. 

External validation of a model means determining whether it performs well in groups of patients other than those on whom it was derived that is, how is it likely to do in real clinical practice. These other groups almost certainly will differ in case mix, referral patterns, treatment protocols, methods of measurement of variables and definition of outcomes. Nevertheless, if a prognostic model includes powerful predictive variables, appropriately modeled, it should vaUdate reasonably well in other groups of patients. For example. Fig. 14.1 shows the vaUdation of the ABCD score on pooled individual patient data from six independent groups of patients with TIA (Johnston et al. 2007) (Ch. 15). 

Kolber, Z. S., Prasil, O., and Palkowski, P. G. (1998). Measurements of variable chlorophyll fluorescence using fast repetition rate techniques Defining methodology and experimental protocols. BBA-Bioenergetics 1367, 88—106. 

Of these three measures of variability, the range is much used for small samples (n not greater than 10) in process control work (the quality control chart, discussed in Chapter VIII) on account of its arithmetical simplicity. It is clear that it does not utilise the whole of the information from the data, for the detail of the intermediate results does not enter into the determination. 

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