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I am using SPSS as statistical analysis tool for my data set. I have few queries on kurtosis concept and the one generated by SPSS and excel. Please correct the understandings below and follow up questions:

  1. Kurtosis as a measure of flatness or peakness (hump) around the mean in the distribution. In terms of distribution tails, it tells whether the dataset is heavy-tailed or light-tailed relative to a normal distribution.

  2. A normal distribution has kurtosis exactly 3 (excess kurtosis exactly 0 which is kurt-3) and also called as mesokurtic distribution. A distribution with high kurtosis will have its peak bigger than mesokurtic peak and is called as leptokurtic A distribution with low kurtosis will have its peak smaller than mesokurtic peak and is called as platykurtic.

Questions:

  1. What does it mean by excess kurtosis and what is the significance of using it? I am not getting clear picture between kurtosis vs excess kurtosis except that excess kurtosis is kurtosis-3 so that we take 0 as baseline.

  2. SPSS tool generates "excess kurtosis" values or simple "kurtosis" values? In other words what baseline we generally consider in SPSS for kurtosis measurement and inference? Is it 0 or 3? In SPSS I am getting kurtosis of 1.16. So if I consider 3 as baseline then 1.16 is less than 3 and so my distribution could be platykurtic. But if I consider baseline as 0 (excess kurtosis), then 1.16 is clearly greater than 0 and so my distribution could be leptokurtic.

  3. How it works out in excel again? Does the excel formula internally compute kurtosis as (kurt - 3) or simple kurt? I mean how to infer the result in MS excel too (baseline 3 or 0)?

vinsinraw
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Kurtosis does not measure "peakedness" or "height" of a distribution. It measures (potential) outliers (rare, extreme observations) only. For a clear explanation, please see here: https://en.wikipedia.org/wiki/Talk:Kurtosis#Why_kurtosis_should_not_be_interpreted_as_.22peakedness.22

BigBendRegion
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  • Thank you for the clarification and sharing link of kurtosis. Regarding interpretation of results generated by SPSS and MS Excel, what baseline can be used to arrive at the conclusion about platykurtic and leptokurtic. I am getting a kurtosis value of 1.16 on my data set. So is it platykurtic or leptokurtic distribution? – vinsinraw Oct 05 '17 at 13:35
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    EXCEL provides excess kurtosis by default; hence, values >0 suggest leptokurtic (more outlier-prone than the normal distribution), and values < 0 suggest platykurtic (less outlier-prone than the normal distribution). The value 1.16 is not much different from 0. The margin of error will depend on the sample size. – BigBendRegion Oct 11 '17 at 15:27
  • Thanks again for the kurtosis clarifications on EXCEL. Any thoughts on SPSS front? Can we consider SPSS generated kurtosis values as excess kurtosis? – vinsinraw Oct 11 '17 at 16:02