WEIGHT Statement

The STDIZE Procedure

WEIGHT Statement

WGT | WEIGHT variable ;

The WEIGHT statement specifies a numeric variable in the input data set with values that are used to weight each observation. Only one variable can be specified.

The WEIGHT variable values can be nonintegers. An observation is used in the analysis only if the value of the WEIGHT variable is greater than zero. The WEIGHT variable applies only when you specify the option METHOD=MEAN, METHOD=SUM, METHOD=EUCLEN, METHOD=USTD, METHOD=STD, METHOD=AGK, or METHOD=L.

PROC STDIZE uses the value of the WEIGHT variable w_i, as follows.

The sample mean and (uncorrected) sample variances are computed as

$\overline{x}_{w} = \sum_{i}w_{i}x_{i} / \sum_{i}w_{i}$

${us_{w}}^2 = \sum_{i}{w_{i}{x_{i}}^2} / d$

${s_{w}}^2 = \sum_{i}{w_{i}{(x_{i}-\overline{x}_{w})}^2} / d$

where w_i is the weight value of the ith observation, x_i is the value of the ith observation, and d is the divisor controlled by the VARDEF= option (see the VARDEF= option for details).

PROC STDIZE uses the value of the WEIGHT variable to calculate the following statistics:

MEAN

the weighted mean, $\overline{x}_{w}$

SUM

the weighted sum, $\sum_{i}{w_{i}{x_{i}}}$

USTD

the weighted uncorrected standard deviation, $\sqrt{us_w^2}$

STD

the weighted standard deviation, $\sqrt{s_w^2}$

EUCLEN

the weighted Euclidean length, computed as the square root of the weighted uncorrected sum of squares:

$\sqrt{\sum_{i}w_{i}{x_{i}}^2}$

AGK

the AGK estimate. This estimate is documented further in the ACECLUS procedure as the METHOD=COUNT option. See the discussion of the WEIGHT statement in Chapter 16, "The ACECLUS Procedure," for information on how the WEIGHT variable is applied to the AGK estimate.

L

the L_p estimate. This estimate is documented further in the FASTCLUS procedure as the LEAST= option. See the discussion of the WEIGHT statement in Chapter 27, "The FASTCLUS Procedure," for information on how the WEIGHT variable is used to compute weighted cluster means. Note that the number of clusters is always 1.

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