Hi everyone,
I am giving a lecture next week on transforming non-normal data to normal. Transforming skewed data to normal is fairly easy to do using the Box-Cox transformation. However, I cannot find a transformation that helps with kurtotic data? I have seen some recommend the modulus transformation. I tested it using a monte carlo simulation and it failed to normalize symmetrical but highly leptokurtic data (approx 0 skew and 10 kurtosis).
Does anyone know of a transformation that normalizes kurtotic data?
thanks,
Cristian
Hello Cristian,
Have you tried before using a normal scores transformation? William Conover's text Nonparametric Statistics goes over transformations from the raw data to Normal z scores in a section on "Tests with ARE greater than One". Google Van der Waerden Scores. In SAS, such normal scores transformations are covered under proc rank.
This is a tough one. The link below gives a transformation from normal to kurtotic and the inverse transformation which is what I would try. The Lambert transform also given there would be my second choice. There is also a reference there which may be helpful. Another possibility is given in the second link. Hope some of this helps. Best wishes, David
http://stats.stackexchange.com/questions/43482/transformation-to-increase-kurtosis-and-skewness-of-normal-r-v
http://stats.stackexchange.com/questions/85687/how-to-transform-leptokurtic-distribution-to-normality
Dear Cristian,
Try to apply the Johnson transformation (the Johnson translation system) for normalizing the data.
In your case I would recommend you to use Su family of the Johnson transformation for normalizing the data (approx 0 skew and 10 kurtosis).
See, for example:
http://onlinelibrary.wiley.com/doi/10.1002/0471667196.ess1309/abstract?systemMessage=Wiley+Online+Library+will+be+unavailable+on+Saturday+17th+December+2016+at+09%3A00+GMT%2F+04%3A00+EST%2F+17%3A00+SGT+for+4hrs+due+to+essential+maintenance.Apologies+for+the+inconvenience
Dear Raid,
I thought about the integral transformation. I think this is also called the normal score transformation. It is a great method in that it can transform any distribution into the normal. Unfortunately, I do not believe it is monotonic and hence, there is no back transformation. I would like to offer my students a method that can later be back transformed so they interpret results in the original scale.
I need to read more on David's suggestion. I came across the second page but not the first.
Thank you both.
Cristian
try this
Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...
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