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ALLSTAT  June 2007

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Subject:

Use of kurtosis and skewness in testing for Normality

From:

Margaret MacDougall <[log in to unmask]>

Reply-To:

Margaret MacDougall <[log in to unmask]>

Date:

Sat, 23 Jun 2007 12:00:32 +0100

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Hello
   
  Earlier this month, I posted a request re literature references on skewness and kurtosis. Thank you very much to all those who replied.
For those interested, I have posted the relevant responses below.
   
  My own experience, perhaps in consistency with 3., below, is that the use of the Biometrika tables is rather a conservative approach by comparison with that of using Q-Q plots. Conservativeness increases enormously when the use of these tables is replaced by the chi-square test described under 4. and hinted at under 2. When asking the question, “Does my data approximate to Normality?” the conclusions are very inconsistent if based on any one of these methods alone.
   
  Best wishes
  Margaret
   
  Dear all
   
  I would be interested to receive details of good literature 
references to rely on when interpreting values of kurtosis and skewness as 
measures of Normality, particularly with respect to defining relevant 
cut-off points. I have found from my own reading that the rules of thumb for 
such cut-off points are not very consistent. Any useful thoughts on 
best practice would be welcome.
   
  A related point is how to transform the data appropriately to correct 
for kurtosis alone.
   
  Many thanks
   
  Best wishes
   
  Margaret
   
  Responses :
  =======================================================
  
1. Take a look at Modstat.  It uses a number of tests on data to help 
identify 
normalacy,
   <A HREF="MODSTAThttp://members.aol.com/rcknodt/pubpage.htm">MODSTAT</A> 
   
  2. Ah, how nice to be able to return to the easygoing 1960s, and
specifically to Vol 1 of Biometrika Tables (1962)!
  For cut-off points for skewness & kurtosis, I'd start with
Tables 34B (skewness) and 34C (kurtosis).  I'm pretty
sure I remember that there's a bivariate test based on b_1
and b_2, as well.
   
  3. A personal view is that though Skewness is meaningful, it measures the 
relative weight given to the two tails, kurtosis is a relatively 
meaningless measure, there has been little agereement down the ages on how to 
interpret it, since it relates to both flatness and to tail shape.It 
also depends on fourth powers so it has a high variability. A much better 
approach is to look at tail shape, see Gilchrist.(2000) Statistical 
Modelling with Quantile Functions. CRC/Chapman and Hall.
   
  4. On the first point, try looking at Durbin & Koopman: Time Series 
Analysis by
State Space Methods, OUP 2001, pp. 33-34. Note also that they give a
combination test for the simultaneous checking of skewness and 
kurtosis.
  I regret that I have no thoughts on the second point.
   
  =======================================================
  
 

 		
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