The NPAR1WAY Procedure
EXACT Statement
EXACT statistic-options </ computation-options> ;
The EXACT statement requests exact tests and confidence limits for selected statistics. The statistic-options identify which statistics to compute, and the computation-options specify options for computing exact statistics. For more information, see the section Exact Tests.
Note: PROC NPAR1WAY computes exact tests by using fast and efficient algorithms that are superior to direct enumeration. Exact tests are appropriate when a data set is small, sparse, skewed, or heavily tied. For some large problems, computation of exact tests might require a large amount of time and memory. Consider using asymptotic tests for such problems. Alternatively, when asymptotic methods might not be sufficient for such large problems, consider using Monte Carlo estimation of exact p-values. You can request Monte Carlo estimation by specifying the MC computation-option in the EXACT statement. For more information, see the section Computational Resources.
Statistic Options
The statistic-options specify which exact tests to compute. Table 3 lists the available statistic-options and the exact statistics that are computed. Descriptions of the statistic-options follow Table 3 in alphabetical order.
PROC NPAR1WAY provides exact p-values for the following nonparametric location and scale tests: Wilcoxon, median, Van der Waerden (normal), Savage, Siegel-Tukey, Ansari-Bradley, Klotz, Mood, and Conover. The procedure also provides exact p-values for tests that use the raw input data as scores. These exact tests are available when the data are classified into two levels (two-sample tests) and when the data are classified into more than two levels (multisample tests). The two-sample exact tests are based on simple linear rank statistics, and the multisample exact tests are based on one-way ANOVA statistics.
For two-sample data, PROC NPAR1WAY also provides the exact Kolmogorov-Smirnov test, the exact ratio mean deviations (RMD) test, and exact Hodges-Lehmann confidence limits for the location shift.
If you list no statistic-options in the EXACT statement, PROC NPAR1WAY computes all available exact p-values for those tests that you request in the PROC NPAR1WAY statement.
Table 3: EXACT Statement Statistic Options
| Statistic Option | Exact Test |
|---|---|
| AB | Ansari-Bradley test |
| CONOVER | Conover test |
| HL | Hodges-Lehmann confidence limits |
| KLOTZ | Klotz test |
| KS | EDF | Two-sample Kolmogorov-Smirnov test |
| MEDIAN | Median test |
| MOOD | Mood test |
| RMD | Ratio mean deviations (RMD) test |
| SAVAGE | Savage test |
| SCORES=DATA | Test with input data as scores |
| ST | Siegel-Tukey test |
| VW | NORMAL | Van der Waerden (normal scores) test |
| WILCOXON | Wilcoxon test for two-sample data or |
| Kruskal-Wallis test for multisample data |
You can specify the following statistic-options:
Computation Options
Computation-options specify options for computing exact statistics. You can specify the following computation-options:
-
ALPHA=
-
specifies the level of the confidence limits for Monte Carlo p-value estimates. The value of
must be between 0 and 1; a confidence level of produces 
% confidence limits. By default, ALPHA=0.01, which produces 99% confidence limits for the exact p-values. This option invokes the MC option.
- MAXTIME=value
specifies the maximum clock 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, the computation terminates. The maximum time value must be a positive number. This option is available for exact p-value computation and for Monte Carlo estimation of exact p-values. For more information, see the section Computational Resources.
- MC
-
requests Monte Carlo estimation of exact p-values instead of direct exact p-value computation. Monte Carlo estimation can be useful for large problems where exact computations require a substantial amount of time and memory but asymptotic approximations might not be sufficient. For more information, see the section Monte Carlo Estimation.
This option is available for all EXACT statistic-options except the HL option, which produces exact Hodges-Lehmann confidence limits. The ALPHA=, N=, and SEED= options invoke the MC option.
- MIDP
-
requests exact mid p-values for the exact tests. The exact mid p-value is defined as the exact p-value minus half the exact point probability. For two-sample data, PROC NPAR1WAY provides exact mid p-values for the one-sided tests of the linear rank statistics. For multisample data, PROC NPAR1WAY provides exact mid p-values for the one-way ANOVA tests. For more information, see the section Definition of p-Values.
The MIDP option is available for all EXACT statement statistic-options except the HL option, which produces exact Hodges-Lehmann confidence limits. You cannot specify both the MIDP option and the MC option.
- N=n
-
specifies the number of samples for Monte Carlo estimation. The value of n must be a positive integer. Larger values of n produce more precise estimates of exact p-values. Because larger values of n generate more samples, the computation time increases. By default, N=10,000.
This option invokes the MC option.
- PFORMAT=format-name | EXACT
-
specifies the display format for exact p-values. PROC NPAR1WAY applies this format to one- and two-sided exact p-values, exact point probabilities, and exact mid p-values. By default, PROC NPAR1WAY displays exact p-values in the PVALUE6.4 format.
You can provide a format-name or you can specify PFORMAT=EXACT to control the format of exact p-values. The value of format-name can be any standard SAS numeric format or a user-defined format. The format length must not exceed 24. For information about formats, see the FORMAT procedure in the Base SAS Procedures Guide and the FORMAT statement and SAS format in SAS Formats and Informats: Reference.
If you specify PFORMAT=EXACT, PROC NPAR1WAY uses the 6.4 format to display exact p-values that are greater than or equal to 0.001; the procedure uses the E10.3 format to display values that are between 0.000 and 0.001.
- POINT
-
requests exact point probabilities for the exact tests. The exact point probability is the exact probability that the test statistic equals the observed value. For two-sample data, PROC NPAR1WAY provides exact point probabilities for the one-sided tests of the linear rank statistics. For multisample data, PROC NPAR1WAY provides exact point probabilities for the one-way ANOVA tests. For more information, see the section Definition of p-Values.
The POINT option is available for all EXACT statement statistic-options except the HL option, which produces exact Hodges-Lehmann confidence limits. You cannot specify both the POINT option and 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 an integer. If you do not specify the SEED= option or if the SEED= value is negative or 0, PROC NPAR1WAY uses the time of day from the computer’s clock to obtain the initial seed.
This option invokes the MC option.