Basic Analysis and Graphing - SAS

Chapter 2 Performing Univariate Analysis 71
Statistical Details for the Distribution Platform
where Φ is the cumulative probability distribution function for the normal distribution.
These normal quantile values are Van Der Waerden approximations to the order statistics that are expected
for the normal distribution.
Statistical Details for the Wilcoxon Signed Rank Test
The Wilcoxon signed-rank test uses average ranks for ties. The p-values are exact for n ≤ 20 where n is the
number of values not equal to the hypothesized value. For n > 20 a Student’s t approximation given by Iman
(1974) is used.
Statistical Details for the Standard Deviation Test
Here is the formula for calculating the Test Statistic:
( n – 1)s 2
--------------------
σ 2
The Test Statistic is distributed as a Chi-square variable with n - 1 degrees of freedom when the population
is normal.
The Min PValue is the p-value of the two-tailed test, and is calculated as follows:
2*min(p1,p2)
where p1 is the lower one-tail p-value and p2 is the upper one-tail p-value.
Statistical Details for Normal Quantiles
The normal quantile values are computed as follows:
Φ – 1 r
-------------
i where:
N + 1
• Φ is the cumulative probability distribution function for the normal distribution
• r i is the rank of the ith observation
• N is the number of non-missing observations
Statistical Details for Saving Standardized Data
The standardized values are computed using the following formula:
X–
X
------------
S X
where:
• X is the original column
• X is the mean of column X
• S X is the standard deviation of column X