
H15Name:
Let X = x_{1}, x_{2}, ..., x_{p} denote the response values and x* and s* denote the robust estimates of location and scale, respectively. The initial estimate for x* is the median. The initial estimate for s* is
where MAD is the median absolute deviation. To update the values for x* and s*, calculate
\( \begin{array}{lcll} x_{i}^{*} & = & x^{*}  \delta \hspace{10pt} & \mbox{if } x_{i} < x^{*}  \delta \\ & = & x^{*} + \delta \hspace{10pt} & \mbox{if } x_{i} > x^{*} + \delta \\ & = & x_{i} \hspace{10pt} & \mbox{otherwise} \end{array} \) The updated values of x* and s* are
\( s^{*} = \frac{1} {\beta^2} \sqrt{\frac{\sum_{i=1}^{p}{(x_i^{*}  x^{*})^2}} {p  1}} \) This process is iterated until the values of x* and s* converge. For H15, c = 1.5 and \( \beta \) = 0.778. There are several alternative estimates that use different values for c and \( \beta \). Specifically,
Dataplot currently supports the H10, H12, H15, H17, H20 variations of this command. The H15 variant is the most commonly used. In the ISO 57255 and ISO 13528 standards, H15 is referred to as "Algorithm A".
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <stat> is one of H10, H12, H15, H17, H20; <par> is a parameter where the computed location value is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <stat> is one of H10, H12, H15, H17, H20; <par> is a parameter where the computed scale value is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET ASCALE = H15 SCALE Y LET ALOC = H15 LOCATION Y SUBSET Y > 0 LET ALOC = H20 LOCATION Y
ISO 13528 (2005), "Statistical Methods for use in proficiency testing by interlaboratory comparisons," Section C.2 Algorithm S.
SKIP 25 READ GEAR.DAT Y X LET A = H15 LOCATION Y . LABEL CASE ASIS Y1LABEL H15 Location X1LABEL Batch H15 LOCATION PLOT Y X . LET A = H15 LOCATION Y SET WRITE DECIMALS 4 SET LET CROSS TABULATE COLLAPSE LET XGROUP = CROSS TABULATE GROUP ONE X LET YMEAN = CROSS TABULATE H15 LOCATION Y X LET YSD = CROSS TABULATE H15 SCALE Y X PRINT XGROUP YMEAN YSDThe following output is generated.  XGROUP YMEAN YSD  1.0000 0.9978 0.0046 2.0000 0.9995 0.0048 3.0000 0.9957 0.0037 4.0000 0.9981 0.0042 5.0000 0.9919 0.0085 6.0000 0.9989 0.0108 7.0000 1.0009 0.0075 8.0000 1.0003 0.0041 9.0000 0.9983 0.0045 10.0000 0.9950 0.0046  
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Date created: 01/06/2011 