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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.
An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for example, the variance of a sum of uncorrelated random variables is equal to the sum of their variances. A disadvantage of the variance for practical applications ...
One way to do that is to explain the distribution of weights by dividing the dog population into groups based on those characteristics. A successful grouping will split dogs such that (a) each group has a low variance of dog weights (meaning the group is relatively homogeneous) and (b) the mean of each group is distinct (if two groups have the ...
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 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.
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]
Heritability increases when genetics are contributing more variation or because non-genetic factors are contributing less variation; what matters is the relative contribution. Heritability is specific to a particular population in a particular environment.