
DIFFERENCE OF QUANTILEName:
Dataplot supports two methods for computing the quantile. The first method is based on the order statistic. The formula is:
where
NI1 = INT(q*(n+1)) NI2 = NI1 + 1 r = q*(n+1)  INT(q*(n+1)) An alternative method is called the HerrellDavis estimate. This method attempts to provide a lower standard error for X_{q} by utilizing all the order statistics rather than a single (or a weighted average of two) order statistic. Note that there are caes where the HerrellDavis has a substantially smaller standard error than the order statistic method. However, there are also cases where the reverse is true. To compute the HerrellDavis estimate, do the following:
For the difference of quantiles, the quantile is computed for each of two samples then their difference is taken.
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the first response variable; <par> is a parameter where the computed difference of the quantiles is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET A = DIFFERENCE OF QUANTILE Y1 Y2 SUBSET X > 1
where <value> is a number in the interval (0,1) that specifies the desired quantile.
Frank Herrell and C. E. Davis (1982), "A New DistributionFree Quantile Estimator," Biometrika, 69(3), 635640.
SKIP 25 READ IRIS.DAT Y1 TO Y4 X . LET XQ = 0.9 . LET A = DIFFERENCE OF QUANTILE Y1 Y2 TABULATE DIFFERENCE OF QUANTILE Y1 Y2 X . XTIC OFFSET 0.2 0.2 X1LABEL GROUP ID Y1LABEL DIFFERENCE OF (0.9) QUANTILE CHAR X LINE BLANK DIFFERENCE OF QUANTILE PLOT Y1 Y2 X CHAR X ALL LINE BLANK ALL BOOTSTRAP DIFFERENCE OF QUANTILE PLOT Y1 Y2 XDataplot generated the following output.  
Privacy
Policy/Security Notice
NIST is an agency of the U.S. Commerce Department.
Date created: 03/27/2003 