Interpretation of Zelen's Exact Test for homogeneity of odds ratios

[Rodcjones]

I am struggling to understand the meaning of/difference between the two stats provided for Zelen's Exact Test in the output below.

My guess is that the 0.0274 would be used to reject the hypothesis that the crude and adjusted Odds ratios are equal. But the other value 0.0314 gave me pause.

Tests for Homogeneity of Odds Ratios
-------------------------------------
Breslow-Day-Tarone Chi-Square 5.4384
DF 1
Pr > ChiSq 0.0197

Zelen's Exact Test (P) 0.0274
Exact Pr <= P 0.0314

I reviewed the section on Zelen's test on this page but it didn't clarify it for me.

https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.3/statug/statug_freq_details90.htm

I'm hoping someone has experience and can help out. Thanks!

[Watts · Accepted solution]

The value that is labeled "Zelen's Exact Test (P)" is the test statistic, and the value that is labeled "Exact Pr <=P" is the p-value for the test. 

From the documentation (section "Zelen's Exact Test for Equal Odds Ratios"):

"The test statistic [for Zelen's test] is the probability of the observed table conditional on the fixed margins, which is a product of hypergeometric probabilities.

The p-value for Zelen’s test is the sum of all table probabilities that are less than or equal to the observed table probability, where the sum is computed over all tables in the reference set determined by the fixed margins and the observed sum of cell (1,1) frequencies. This test is similar to Fisher’s exact test for two-way tables.

For more information, see Zelen (1971); Hirji (2006); Agresti (1992)."

[SAS_Rob]

The actual p-value for the test is labeled as "Exact Pr <= P "

The 0.0274 is actually the Test statistic which is probability of observing the table you did.  It is not a p-value. 

[Rodcjones]

Thank you @Watts and @SAS_Rob  for the quick and helpful replies!