Estimates of the skewness and kurtosis can be found 

 with the above method; but it does not give any indication of 

 whether these estimates are significantly different from the 

 expected values, if the sample is taken from a gaussian 

 distribution. Using the previous overlay, a method can be 

 developed so that a sample can be accepted or rejected at 

 any desired level of probability. Basically the method is 

 to have two of the curves on the overlay plotted so that they 

 will represent the maximum deviations allowed in the par- 

 ticular parameter of a sample with (N) points. The method 

 will be developed for kurtosis, but a similar method can be 

 used for skewness. 



The variance of kurtosis is given by 4 



var(o ) = 24/N (4) 



for large TV. This holds for a sample taken from a normal 

 parent population. The standard deviation of kurtosis is 

 (24/710 2; if the kurtosis is distributed normally, then from 

 the ratio of a particular value of kurtosis (g s ') and the 

 standard deviation we can obtain the probability of getting a 

 value of kurtosis as large or larger than g ' . The ratio is 



(24/70 2 



The probability of getting a value of kurtosis as large as or 

 larger than g ' is given by the amount of area under a 

 normal curve outside the -7? and +7? standard deviations. 

 A value of 7? = 1. 96 corresponds to a probability level of 



(5) 



16 



