The difference between Kurtosis and standardized kurtosis

[jeremy2828]

Hey guys!

I need your help on explaining me the difference between kurtosis and "standardized kurtosis" which is often abreviated in papers by SKrt... this is a good application example:

http://www.statgraphics.com/basic_statistics.htm

it's very odd I noticed that to get from kurtosis to standardized kurtosis it's the same multiplier for all 6 examples... I also noticed that that to get from skewness to standardized skewness it's the same multiplier/2 ... I believe it must have something to do with n but am unable to find the formula on internet...

Thank you I really appreciate it !

[GretaGarbo]

Sometimes kurtosis is defined so that the normal distribution has kurtosis=3.

Sometimes a value of 3 is withdrawn so that the normal distribution has kurtosis=0.

If you hesitate about the software you use, generate some normally distributed random numbers, estimate the kurtosis and check if it is close to 0 or 3.

Look at wikipedia kurtosis.

How statgraphics has defined it I don’t know.

[jeremy2828]

yes that's why one uses the terms kurtosis and excess kurtosis. Thanks for your answer anyways ! I did some trial and error and managed on my own to figure out how one get's from kurtosis to standardized kurtosis. The base was that under normal hypothesis the distribution of kurtosis is N(0, 24/N) and skewness is N(0, 6/N)

afterwards all you do is centre and reduce the kurtosis to get to standardized kurtosis like this: kurtosis-0 / (sqrt(24/n)) = standardized kurtosis. If standardized kurtosis is above 1.96 in absolute value than this means that at 5% error level we can reject normal hypothesis on the data !