Variance-stabilizing Transformation
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High Quality Content by WIKIPEDIA articles! In applied statistics, a variance-stabilizing transformation is a data transformation that is specifically chosen either to simplify considerations in graphical exploratory data analysis or to allow the application of simple regression-based or analysis of variance techniques. The aim behind the choice of a variance-stabilizing transformation is to find a simple function to apply to values x in a data set to create new values y = (x) such that the variability of the values y is not related to their mean value. For example, suppose that the values x a...
High Quality Content by WIKIPEDIA articles! In applied statistics, a variance-stabilizing transformation is a data transformation that is specifically chosen either to simplify considerations in graphical exploratory data analysis or to allow the application of simple regression-based or analysis of variance techniques. The aim behind the choice of a variance-stabilizing transformation is to find a simple function to apply to values x in a data set to create new values y = (x) such that the variability of the values y is not related to their mean value. For example, suppose that the values x are realizations from different Poisson distributions: i.e. the distributions each have different mean values . Then, because for the Poisson distribution the variance is identical to the mean, the variance varies with the mean. While variance-stabilizing transformations are well-known for certain parametric families of distributions, such as the Poisson and the binomial distribution, some types of data analysis proceed more empirically: for example by searching among power transformations to find a suitable fixed transformation.
