Basic Analysis and Graphing - SAS

Chapter 2 Performing Univariate Analysis 69
Statistical Details for the Distribution Platform
Statistical Details for Quantiles
This section describes how quantiles are computed.
To compute the pth quantile of N non-missing values in a column, arrange the N values in ascending order
and call these column values y 1 , y 2 ,...,y N . Compute the rank number for the pth quantile as p /100(N +1).
• If the result is an integer, the pth quantile is that rank’s corresponding value.
• If the result is not an integer, the pth quantile is found by interpolation. The pth quantile, denoted q p , is
computed as follows:
where:
– n is the number of non-missing values for a variable
– y 1 , y 2, ..., y n represents the ordered values of the variable
– y n+1 is taken to be y n
– i is the integer part and f is the fractional part of (n+1)p.
– (n + 1)p = i + f
For example, suppose a data table has 15 rows and you want to find the 75th and 90th quantile values of a
continuous column. After the column is arranged in ascending order, the ranks that contain these quantiles
are computed as follows:
--------
75
( 15 + 1) = 12 and --------
90
( 15 + 1) = 14.4
100
100
The value y 12 is the 75th quantile. The 90th quantile is interpolated by computing a weighted average of the
14th and 15th ranked values as y 90 =0.6y 14 +0.4y 15 .
Statistical Details for Summary Statistics
Mean
Std Dev
q p
= ( 1 – f)y i
+ ()y f i + 1
This section contains statistical details for specific statistics in the Summary Statistics report.
The mean is the sum of the non-missing values divided by the number of non-missing values. If you
assigned a Weight or Freq variable, the mean is computed by JMP as follows:
1. Each column value is multiplied by its corresponding weight or frequency.
2. These values are added and divided by the sum of the weights or frequencies.
The standard deviation measures the spread of a distribution around the mean. It is often denoted as s and is
the square root of the sample variance, denoted s 2 .