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Home Univariate Data Distributions zTransform  
See also: Scaling of Data, TScores  
zTransformSometimes one has the problem to make two samples comparable, i.e. to compare measured values of a sample with respect to their (relative) position in the distribution. An often used aid is the ztransform which converts the values of a sample into zscores:
with z_{i} ... ztransformed sample observations The ztransform is also called standardization or autoscaling. zScores become comparable by measuring the observations in multiples of the standard deviation of that sample. The mean of a ztransformed sample is always zero. If the original distribution is a normal one, the ztransformed data belong to a standard normal distribution (μ=0, s=1). The following example demonstrates the effect of the standardization of the data. Assume we have two normal distributions, one with mean of 10.0 and a standard deviation of 30.0 (top left), the other with a mean of 200 and a standard deviation of 20.0 (top right). The standardization of both data sets results in comparable distributions since both ztransformed distributions have a mean of 0.0 and a standard deviation of 1.0 (bottom row).


Home Univariate Data Distributions zTransform 