Dataplot Vol 2 Vol 1

# SEMI INTERQUARTILE RANGE LOWER SEMI INTERQUARTILE RANGE UPPER SEMI INTERQUARTILE RANGE

Name:
SEMI-INTERQUARTILE RANGE (LET)
Type:
Let Subcommand
Purpose:
Compute either the lower semi-interquartile range or the upper semi-interquartile range for a variable.
Description:
The interquartile range is:

IQ = UPPER QUARTILE - LOWER QUARTILE

That is, it is the difference betweeen the 75th and 25th percentiles of a variable.

The lower semi-interquartile range is:

$$\mbox{SIQR}_L = q_2 - q_1$$

and the upper semi-interquartile range is:

$$\mbox{SIQR}_U = q_3 - q_2$$

with $$q_1$$, $$q_2$$, and $$q_3$$ denoting the lower quartile, median, and upper quartile respectively.

The semi-interquartile range is sometimes used in place of the interquartile range when there is significant skewness in the data. For example, it can be used to provide an alternate definition of the fences in a box plot.

Syntax 1:
LET <par> = LOWER SEMI INTERQUARTILE RANGE <y>
<SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
<par> is a parameter where the computed lower semi-interquartile range is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 2:
LET <par> = UPPER SEMI INTERQUARTILE RANGE <y>
<SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
<par> is a parameter where the computed upper semi-interquartile range is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = LOWER SEMI INTERQUARTILE RANGE Y1
LET A = UPPER SEMI INTERQUARTILE RANGE Y1
LET A = UPPER SEMI INTERQUARTILE RANGE Y1 SUBSER TAG > 2
LET A = INTERQUARTILE RANGE Y1 SUBSET TAG > 2
Note:
Dataplot statistics can be used in a number of commands. For details, enter

Default:
None
Synonyms:
None
Related Commands:
 INTERQUARTILE RANGE = Compute the interquartile range of a variable. BOX PLOT = Generate a box plot.
Reference:
Walker, Dovedo, Chakraborti and Hilton (2019), "An Improved Boxplot for Univariate Data", The American Statistician, Vol. 72, No. 4, pp. 348-353.
Applications:
Robust Data Analysis
Implementation Date:
2019/08
Program:

LET NU = 1
LET Y = CHISQUARE RANDOM NUMBERS FOR I = 1 1 100
LET SIQRL = LOWER SEMI INTERQUARTILE RANGE Y
LET SIQRU = UPPER SEMI INTERQUARTILE RANGE Y
SET WRITE DECIMALS 4
PRINT SIQRL SIQRU

The following output is generated

PARAMETERS AND CONSTANTS--

SIQRL   --         0.4803
SIQRU   --         0.8989


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Date created: 08/29/2019
Last updated: 08/29/2019