Indicators of dispersion

Equality holds for a single sphere or a collection of identical spheres inequality holds if they are distributed in size or composition. This inequality was used by Hunt and Huffman (1973), for example, as an indicator of dispersion in suspensions of spherical particles. It was pointed out by Fry and Kattawar (1981) that the inequalities they derived are useful consistency checks on measurements of all 16 scattering matrix elements. 

The true value of a particular measurement is 131.9 jxg/l. Four chemists (A, B, C and D) each repeat the same procedure five times. The individual values obtained are displayed in the table below. Comment upon these results in terms of accuracy and precision (use an indicator of dispersion or standard deviation,. sj. 

To indicate the first of these, we quote an indicator of central tendency and for the second an indicator of dispersion . 

Indicators of central tendency how large are the numbers Indicators of dispersion how variable are the numbers ... 

The two machines are very similar in terms of average drug content for the tablets, both producing tablets with a mean very close to 250 mg. However, the two products clearly differ. With the Alpha machine, there is a considerable proportion of tablets with a content differing by more than 10 mg from the nominal dose (i.e. below 240 mg or above 260 mg), whereas with the Bravo machine, such outliers are much rarer. An indicator of dispersion is required in order to convey this difference in variability. 

The inter-quartile range as an indicator of dispersion The inter-quartile range is defined as the difference between the upper and lower quartiles (Q3 — Ql). So, for steroid 1 ... 

Just as the median is a robust indicator of central tendency, the interquartile range is a robust indicator of dispersion. Take the longest half-life seen with steroid 1 (15.8 h) and consider what would have happened if that individual had produced a half-life of 100 h (or any other extreme value). The answer is that it would make absolutely no difference to the inter-quartile range. The value of 15.8 h is already something of an outlier, but it had no undue effect on the inter-quartile range. 

The standard deviation is an indicator of dispersion. It tells us about the variability among the figures within our data. The coefficient of variation describes relative variability by expressing the SD as a ratio to the mean. 

The three quartile values indicate the figures that appear 25, 50 and 75 per cent of the way up the list of data when it has been ranked. The second quartile is synonymous with the median and can act as an indicator of central tendency. The interquartile range (difference between first and third quartile) is an indicator of dispersion. The median and interquartile range are robust statistics, which means that they are more resistant to the effects of occasional extreme values than the mean and SD. The robustness of the median can be abused to hide the existence of aberrant data. 

Maynard J. B. (1981) Carbon isotopes as indicators of dispersal patterns in Devonian-Mississippian shales of the Appalachian Basin. Geology 9, 262-265. 

Statistical indices are fundamental numerical quantities measuring some statistical property of one or more variables. They are applied in any statistical analysis of data and hence in most of Q S AR methods as well as in some algorithms for the calculation of molecular descriptors. The most important univariate statistical indices are indices of central tendency and indices of dispersion, the former measuring the center of a distribution, the latter the dispersion of data in a distribution. Among the bivariate statistical indices, the correlation measures play a fundamental role in all the sciences. Other important statistical indices are the diversity indices, which are related to the injbrmationcontentofavariahle,the —> regressiowparameters, used for regression model analysis, and the —> classification parameters, used for classification model analysis. 

Indices of dispersion (or variation) provide a single value of a variable, which describes the spread of a set of observations or the spread of a distribution around its center. 

Whereas the indices of dispersion measure the variability of samples around a center, concentration indices measure the mutual variability of samples [Bonckaert and Egghe, 1991]. Concentration indices are used, for example, in cell-based methods for the similarity/diversity analysis of chemical libraries. 

Some other predictions such as the amount of dissipated energy of the system, residence time distributions, and indications of dispersive mixing can be obtained from similar calculation procedures to those previously addressed. 

By definition, the standard deviatirai is the root-mean-square deviation about the mean value. It does not provide an indicator of the statistical error about the mean of multiple measurements. If the distribution is unimodal and not too skewed, then the standard deviation will give a reasonable indication of dispersity.. 

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