Computation of the Statistics

The STDIZE Procedure

Computation of the Statistics

Formulas for statistics of METHOD=MEAN, METHOD=MEDIAN, METHOD=SUM, METHOD=USTD, METHOD=STD, METHOD=RANGE, and METHOD=IQR are given in the chapter on elementary statistics procedures in the SAS Procedures Guide.

Note that the computations of median and upper and lower quartiles depend on the PCTLMTD= option.

The other statistics listed in Table 59.2, except for METHOD=IN, are described as follows:

EUCLEN: Euclidean length.
$\sqrt{\sum_{i=1}^n{x_i}^2}$ where x_i is the ith observation and n is the total number of observations in the sample.
L(p): Minkowski metric. This metric is documented as the LEAST=p option in the PROC FASTCLUS statement of the FASTCLUS procedure (see Chapter 27, "The FASTCLUS Procedure").

If you specify METHOD=L(p) in the PROC STDIZE statement, your results are similar to those obtained from PROC FASTCLUS if you specify the LEAST=p option with MAXCLUS=1 (and use the default values of the MAXITER= option). The difference between the two types of calculations concerns the maximum number of iterations. In PROC STDIZE, it is a criteria for convergence on all variables; In PROC FASTCLUS, it is a criteria for convergence on a single variable.

The location and scale measures for L(p) are output to the OUTSEED= data set in PROC FASTCLUS.
MIDRANGE: ( maximum + minimum) / 2
ABW(c): Tukey's biweight. Refer to Goodall (1983, pp. 376 -378, p. 385) for the biweight 1-step M-estimate. Also refer to Iglewicz (1983, pp. 416 -418) for the biweight A-estimate.
AHUBER(c): Hubers. Refer to Goodall (1983, pp. 371 -374) for the Huber 1-step M-estimate. Also refer to Iglewicz (1983, pp. 416 -418) for the Huber A-estimate of scale.
AWAVE(c): Andrews' Wave. Refer to Goodall (1983, p. 376) for the Wave 1-step M-estimate. Also refer to Iglewicz (1983, pp. 416 -418) for the Wave A-estimate of scale.
AGK(p): the noniterative univariate form of the estimator described by Art, Gnanadesikan, and Kettenring (1982)

The AGK estimate is documented in the section on the METHOD= option in the PROC ACECLUS statement of the ACECLUS procedure (also see the "Background" section in Chapter 16, "The ACECLUS Procedure"). Specifying METHOD=AGK(p) in the PROC STDIZE statement is the same as specifying METHOD=COUNT and P=p in the PROC ACECLUS statement.
SPACING(p): the absolute difference between two data values. The minimum spacing for a proportion p is the minimum absolute difference between two data values that contain a proportion p of the data between them. The mid minimum-spacing is the mean of these two data values.

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