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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.
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 estimating the mean of uncorrelated, identically distributed variables we can take advantage of the fact that the variance of the sum is the sum of the variances.In this case efficiency can be defined as the square of the coefficient of variation, i.e., [13]
In descriptive statistics, the range of a set of data is size of the narrowest interval which contains all the data. It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum). [1] It is expressed in the same units as the data. The range provides an indication of statistical ...
Example of samples from two populations with the same mean but different dispersion. The blue population is much more dispersed than the red population. In statistics , dispersion (also called variability , scatter , or spread ) is the extent to which a distribution is stretched or squeezed. [ 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 ...
Let X be a random vector, and Y a random variable that is modeled by a normal distribution with centre =. In this case, the above-derived proportion of explained variation ρ C 2 {\displaystyle \rho _{C}^{2}} equals the squared correlation coefficient R 2 {\displaystyle R^{2}} .
The table shown on the right can be used in a two-sample t-test to estimate the sample sizes of an experimental group and a control group that are of equal size, that is, the total number of individuals in the trial is twice that of the number given, and the desired significance level is 0.05. [4] The parameters used are: