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The coefficient of variation may not have any meaning for data on an interval scale. [2] For example, most temperature scales (e.g., Celsius, Fahrenheit etc.) are interval scales with arbitrary zeros, so the computed coefficient of variation would be different depending on the scale used.
Note that in this expression, the first factor includes the population coefficient of variation, which is usually unknown. When c v {\displaystyle c_{v}} is smaller than 1/3, then K {\displaystyle K} is approximately chi-square distributed with n − 1 {\displaystyle n-1} degrees of freedom.
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]
In probability theory and statistics, the index of dispersion, [1] dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard ...
In this case efficiency can be defined as the square of the coefficient of variation, i.e., [13] e ≡ ( σ μ ) 2 {\displaystyle e\equiv \left({\frac {\sigma }{\mu }}\right)^{2}} Relative efficiency of two such estimators can thus be interpreted as the relative sample size of one required to achieve the certainty of the other.
Ordinary least squares regression of Okun's law.Since the regression line does not miss any of the points by very much, the R 2 of the regression is relatively high.. In statistics, the coefficient of determination, denoted R 2 or r 2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s).
A contrast is defined as the sum of each group mean multiplied by a coefficient for each group (i.e., a signed number, c j). [10] In equation form, = ¯ + ¯ + + ¯ ¯, where L is the weighted sum of group means, the c j coefficients represent the assigned weights of the means (these must sum to 0 for orthogonal contrasts), and ¯ j represents the group means. [8]
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.