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A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse. Most measures of dispersion have the same units as the quantity being measured. In other words, if the measurements are in metres or seconds, so is the measure of dispersion.
In statistics, explained variation measures the proportion to which a mathematical model accounts for the variation of a given data set. Often, variation is quantified as variance ; then, the more specific term explained variance can be used.
Measurements are usually subject to variation and measurement uncertainty; thus they are repeated and full experiments are replicated to help identify the sources of variation, to better estimate the true effects of treatments, to further strengthen the experiment's reliability and validity, and to add to the existing knowledge of the topic. [20]
Following Gelman and Hill, the assumptions of the ANOVA, and more generally the general linear model, are, in decreasing order of importance: [5] the data points are relevant with respect to the scientific question under investigation; the mean of the response variable is influenced additively (if not interaction term) and linearly by the factors;
A number have been summarized and devised by Wilcox (Wilcox 1967), (Wilcox 1973), who requires the following standardization properties to be satisfied: Variation varies between 0 and 1. Variation is 0 if and only if all cases belong to a single category. Variation is 1 if and only if cases are evenly divided across all categories. [1]
Standard deviation is a widely used measure of the spread or dispersion of a dataset. It quantifies the average amount of variation or deviation of individual data points from the mean of the dataset. It uses squared deviations, and has desirable properties. Standard deviation is sensitive to extreme values, making it not robust. [7]
The coefficient of variation fulfills the requirements for a measure of economic inequality. [ 20 ] [ 21 ] [ 22 ] If x (with entries x i ) is a list of the values of an economic indicator (e.g. wealth), with x i being the wealth of agent i , then the following requirements are met:
Irregular variation within a historical experience base; and; Lack of significance in individual high or low values. The outcomes of a perfectly balanced roulette wheel are a good example of common-cause variation. Common-cause variation is the noise within the system. Walter A. Shewhart originally used the term chance cause. [1]