EXACT Statement

The NPAR1WAY Procedure

EXACT Statement

EXACT statistic-options < / computation-options > ;

The EXACT statement requests exact tests for the specified statistics. Optionally, PROC NPAR1WAY computes Monte Carlo estimates of the exact p-values. The statistic-options specify the statistics for which to provide exact tests, and the computation-options specify options for the computation of exact statistics.

Warning: For some large problems, exact computations may require a large amount of time and memory. See the section "Computational Resources" for more information.

Statistic-Options

The statistic-options specify the statistics for which to provide exact tests.

Exact p-values are available for all nonparametric tests of location and scale differences produced by PROC NPAR1WAY. These include tests based on the following scores: Wilcoxon, median, Van der Waerden, Savage, Siegel-Tukey, Ansari-Bradley, Klotz, and Mood scores. Additionally, exact p-values are available for tests using the raw data as scores. The procedure computes exact p-values when the data are classified into two levels (two-sample tests) and when the data are classified into more than two levels (multisample tests). Two-sample tests are based on simple linear rank statistics. multisample tests are based on one-way ANOVA statistics. See the section "Exact Tests" for details.

Table 42.3 lists the available statistic-options and the exact tests computed. The option names are identical to the corresponding options in the PROC NPAR1WAY statement and the OUTPUT statement.

If you list no statistic-options in the EXACT statement, then PROC NPAR1WAY computes exact p-values for all the tests of location and scale differences requested in the PROC NPAR1WAY statement.

Table 42.3: EXACT Statement Statistic-Options

Option	Exact Tests Computed
AB	Ansari-Bradley Test
KLOTZ	Klotz Test
MEDIAN	Median Test
MOOD	Mood Test
SAVAGE	Savage Test
SCORES=DATA	Test Using Raw Data as Scores
ST	Siegel-Tukey Test
WILCOXON	Wilcoxon Test for Two-Sample Data
	Kruskal-Wallis Test for Multisample Data
VW	Van der Waerden Test

Computation-Options

The computation-options specify options for computation of exact statistics. You can specify the following computation-options in the EXACT statement.

ALPHA= $\alpha$

specifies the confidence level for the confidence bounds for the Monte Carlo p-value estimates. The value of the ALPHA= option must be between 0.0001 and 0.9999; the default is 0.01. A confidence level of $\alpha$ results in $100(1 - \alpha)$ % confidence bounds. The default of ALPHA=0.01 results in 99 percent confidence bounds. If $\alpha$ is between 0 and 1 but is outside the range of 0.0001 to 0.9999, PROC NPAR1WAY uses the closest range endpoint. For example, if you specify ALPHA=0.000001, PROC NPAR1WAY uses 0.0001 to determine confidence bounds. The ALPHA= option invokes the MC option.

MAXTIME=value

specifies the maximum time (in seconds) that PROC NPAR1WAY can use to compute an exact p-value. If the procedure does not complete the computation within the specified time, it terminates the computation. The value of the MAXTIME= option must be a positive number.

See the section "Computational Resources" for more information.

MC

requests Monte Carlo estimation of exact p-values, instead of direct exact p-value computation. The ALPHA=, N=, or SEED= option also invokes the MC option.

The MC option is available for all the EXACT statement statistic-options. Monte Carlo estimation can be useful for large problems that require a great amount of time and memory for exact computations but for which asymptotic approximations may not be sufficient. See the section "Monte Carlo Estimation" for more information.

N=n

specifies the number of samples for Monte Carlo estimation. The value of the N= option must be a positive integer, and the default is 10000 samples. Larger values of n produce more precise estimates of exact p-values. Because larger values of n generate more samples, the computation time increases. The N= option invokes the MC option.

SEED=number

specifies the initial seed for random number generation for Monte Carlo estimation. The value of the SEED= option must be a positive integer. If you do not specify the SEED= option, PROC NPAR1WAY uses the time of day from the computer's clock to obtain the initial seed. The SEED= option invokes the MC option.

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