
DIFFERENCE OF QNName:
An analogous scale estimate can be obtained by replacing pairwise averages with pairwised distances:
This estimate has high efficiency for normal data (86%), but a breakdown point of only 29%. Rousseeuw and Croux proposed the following variation of this statistic:
where d is a constant factor and k = \( \left( \begin{array}{c} h \\ 2 \end{array} \right) \) which is approximately \( \left( \begin{array}{c} n \\ 2 \end{array} \right) \). The value of h is [n/2]+1 (i.e., roughly half the number of obserations). In other words, we take kth order statistic of the \( \left( \begin{array}{c} n \\ 2 \end{array} \right) \) interpoint distances. The value of d is choosen to make Q_{n} a consistent estimator of scale. We use the value 2.2219 since this is the value that makes Q_{n} a consistent estimator for normal data. Enter HELP QN SCALE for a more detailed discussion of the Q_{n} scale estimate. For the difference of Q_{n} scale estimates, the Q_{n} scale estimate is computed for each of the two samples then their difference is taken.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <par> is a parameter where the computed difference of Q_{n} scale estimates is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET A = DIFFERENCE OF QN Y1 SUBSET TAG > 2
Mosteller and Tukey (1977), "Data Analysis and Regression: A Second Course in Statistics," AddisonWesley, pp. 203209.
SKIP 25 READ IRIS.DAT Y1 TO Y4 X . LET A = DIFFERENCE OF QN Y1 Y2 TABULATE DIFFERENCE OF QN Y1 Y2 X . MAJOR XTIC MARK NUMBER 3 MINOR XTIC MARK NUMBER 0 XTIC OFFSET 0.2 0.2 X1LABEL GROUP ID Y1LABEL DIFFERENCE OF QN CHARACTER X LINE BLANK DIFFERENCE OF QN PLOT Y1 Y2 X CHARACTER X ALL LINE BLANK ALL BOOTSTRAP DIFFERENCE OF QN PLOT Y1 Y2 XDataplot generated the following output. ************************************** ** LET A = DIFFERENCE OF QN Y1 Y2 ** ************************************** THE COMPUTED VALUE OF THE CONSTANT A = 0.43340060E+00 ***************************************** ** TABULATE DIFFERENCE OF QN Y1 Y2 X ** ***************************************** * Y1 AND Y2 X * DIFFERENCE OF QN ********************************************** 1.00000 * 0.506639E06 2.00000 * 0.206496 3.00000 * 0.206497
 
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Date created: 05/21/2003 