Basic Analysis and Graphing - SAS

70 Performing Univariate Analysis Chapter 2
Statistical Details for the Distribution Platform
s = s 2 where
N
s 2 w i
( y i
– y w ) 2
= ----------------------------
N – 1
i = 1
y w = weighed mean
Std Err Mean
Skewness
Kurtosis
The standard error means is computed by dividing the sample standard deviation, s, by the square root of N.
In the launch window, if you specified a column for Weight or Freq, then the denominator is the square root
of the sum of the weights or frequencies.
Skewness is based on the third moment about the mean and is computed as follows:
3
--
2 3 N
x
w i
z ------------------------------------
i wherez i
– x
( N – 1) ( N – 2)
i
= -----------
s
and w i is a weight term (= 1 for equally weighted items)
Kurtosis is based on the fourth moment about the mean and is computed as follows:
n
nn ( + 1)
( -------------------------------------------------- n – 1) ( n – 2) ( n – 3)
w 2 x – x 4 i 3( n – 1) 2
i -----------
– ---------------------------------
s ( n – 2) ( n – 3)
i = 1
where w i is a weight term (= 1 for equally weighted items). Using this formula, the Normal
distribution has a kurtosis of 0.
Statistical Details for the Normal Quantile Plot
The empirical cumulative probability for each value is computed as follows:
r
------------- i
N + 1
where r i is the rank of the ith observation, and N is the number of non-missing (and nonexcluded)
observations.
The normal quantile values are computed as follows:
Φ – 1 r
-------------
i
N + 1