Base SAS 9.1.3 Procedures Guide - Acsu Buffalo

144 Chapter 2. The FREQ Procedure
upper bound for the longest path and a lower bound for the shortest path, following
the approach of Valz and Thompson (1994).
The longest and shortest path distances or bounds for a node are compared to the
value of the test statistic to determine whether all paths through the node contribute
to the p-value, none of the paths through the node contribute to the p-value, or neither
of these situations occur. If all paths through the node contribute, the p-value is incremented
accordingly, and these paths are eliminated from further analysis. If no paths
contribute, these paths are eliminated from the analysis. Otherwise, the algorithm
continues, still processing this node and the associated paths. The algorithm finishes
when all nodes have been accounted for, incrementing the p-value accordingly, or
eliminated.
In applying the network algorithm, PROC FREQ uses full precision to represent all
statistics, row and column scores, and other quantities involved in the computations.
Although it is possible to use rounding to improve the speed and memory requirements
of the algorithm, PROC FREQ does not do this since it can result in reduced
accuracy of the p-values.
For one-way tables, PROC FREQ computes the exact chi-square goodness-of-fit test
by the method of Radlow and Alf (1975). PROC FREQ generates all possible oneway
tables with the observed total sample size and number of categories. For each
possible table, PROC FREQ compares its chi-square value with the value for the observed
table. If the table’s chi-square value is greater than or equal to the observed
chi-square, PROC FREQ increments the exact p-value by the probability of that table,
which is calculated under the null hypothesis using the multinomial frequency
distribution. By default, the null hypothesis states that all categories have equal proportions.
If you specify null hypothesis proportions or frequencies using the TESTP=
or TESTF= option in the TABLES statement, then PROC FREQ calculates the exact
chi-square test based on that null hypothesis.
For binomial proportions in one-way tables, PROC FREQ computes exact confidence
limits using the F distribution method given in Collett (1991) and also described by
Leemis and Trivedi (1996). PROC FREQ computes the exact test for a binomial
proportion (H 0 : p = p 0 ) by summing binomial probabilities over all alternatives. See
the section “Binomial Proportion” on page 118 for details. By default, PROC FREQ
uses p 0 = 0.5 as the null hypothesis proportion. Alternatively, you can specify the
null hypothesis proportion with the P= option in the TABLES statement.
See the section “Odds Ratio and Relative Risks for 2 x 2 Tables” on page 122 for
details on computation of exact confidence limits for the odds ratio for 2 × 2 tables.
See the section “Exact Confidence Limits for the Common Odds Ratio” on page 138
for details on computation of exact confidence limits for the common odds ratio for
stratified 2 × 2 tables.
Definition of p-Values
For several tests in PROC FREQ, the test statistic is nonnegative, and large values of
the test statistic indicate a departure from the null hypothesis. Such tests include the
Pearson chi-square, the likelihood-ratio chi-square, the Mantel-Haenszel chi-square,
Fisher’s exact test for tables larger than 2 × 2 tables, McNemar’s test, and the one-