Abstract: This chapter examines changes in the value of variances from one sample to another. The computed standard deviation, being itself a statistic, is variable in the sense that when it is computed from one sample, it gives one value, and when computed from a different sample, even though taken from the same population, it gives a different value. The same is true for the variance, the square of the standard deviation. The formula for the variance of the variances—using Hald's somewhat nonstandard notation—is given. One of the most important features of the equation is that the variance of the variance increases as the fourth power of σ (the population variance). The variance of variance also depends upon n, the number of data included in the computation of s2 (the sample variance), and on the variance itself. Another notable feature of the variance is the fact that its distribution is asymmetric. There are differences between the particular distribution of variances presented in the test population and the general one, which is valid for most real data. One difference is that the distribution of variances from limited (finite) population is a set of discrete values that is represented by a finite number of discrete bars, while the general case is represented by a continuous distribution containing infinity of possible values.
Publication Year: 2003
Publication Date: 2003-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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