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The STDIZE Procedure |
The one-pass approach used in PROC STDIZE modifies the P^{2} algorithm for histograms proposed by Jain and Chlamtac (1985). The primary difference comes from the movement of markers. The one-pass method allows a marker to move to the right (or left) by more than one position (to the largest possible integer) as long as it does not result in two markers being in the same position. The modification is necessary in order to incorporate the FREQ variable.
You may obtain inaccurate results if you use the one-pass approach to estimate quantiles beyond the quartiles (that is, when you estimate quantiles < P25 or > P75). A large sample size (10,000 or more) is often required if the tail quantiles (quantiles <= P10 or >= P90 ) are requested. Note that, for variables with highly skewed or heavy-tailed distributions, tail quantile estimates may be inaccurate.
The order-statistics approach for estimating quantiles is faster than the one-pass method but requires that the entire data set be stored in memory. The accuracy in estimating the quantiles is comparable for both methods when the requested percentiles are between the lower and upper quartiles. The default is PCTLMTD=ORD_STAT if enough memory is available; otherwise, PCTLMTD=ONEPASS.
Let n be the number of nonmissing values for a variable, and let x_{1}, x_{2}, ... , x_{n} represent the ordered values of the variable. For the tth percentile, let p = t/100. In the following definitions numbered 1, 2, 3, and 5, let
Given the preceding definitions, the tth percentile, y, is defined as follows:
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