Using the square root to transform variables
The square root transformation, √x, as well as its variations, the Anscombe transformation, √(x+3/8), and the Freeman-Tukey transformation, √x + √(x+1), are variance stabilizing transformations that transform a variable with a Poisson distribution into one with an approximately standard Gaussian distribution. The square root transformation is a form of power transformation where the exponent is 1/2 and is only defined for positive values.
The Poisson distribution is a probability distribution that indicates the number of times an event is likely to occur. In other words, it is a count distribution. It is right-skewed and its variance equals its mean. Examples of variables that could follow a Poisson distribution are the number of financial items of a customer, such as the number of current accounts or credit cards, the number of passengers in a vehicle, and the number of occupants in a household.
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