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This Demonstration shows the effect of a power data transformation, ... , on data, ... , from simulated samples of size ... or ... from normal, exponential, lognormal, inverse Gaussian, or Weibull distributions for ... . In practice, a suitable power transformation can be selected by examining the effect of the transformation using a box-and-whisker plot. The simplest power transformation which makes the data approximately symmetric is selected. With actual data, often ... corresponding to reciprocal, log, square root, or no transformation. Two skewness statistics—the usual Pearson skewness, ... , and the Bowley skewness, ... —are displayed for comparison with the plot. Another method for choosing ... treats ... as a parameter and makes the assumption that for some value of ... , the data is normally distributed. Under this assumption, the likelihood function ... may be obtained and it may be numerically maximized to obtain the maximum likelihood estimate for ... , ... . A range of plausible values for ... is given by all ... for which ... , where ... . Try experimenting with different sample sizes ... and different distributions. In actual applications, real data (not simulated data) would be used. Using a suitable power transformation often simplifies the statistical analysis.
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