Additional Findings: I believe it has to do with how p-values are being calculated. Consider the following R code: binom.exact(51, 235, (1/6), tsmethod = "central") This will give you the same result as SAS with a p-value of 0.05309. However, if you use binom.exact(51, 235, 1/6, tsmethod = "minlike") This will give you the same results as binom.test() and a p-value of 0.04375. As far as I can tell, minlike: sum of probabilities of outcomes with likelihoods less than or equal to observed. central: is 2 times the minimum of the one-sided p-values bounded by 1. I have two follow up questions: 1. Statistically, which is the appropriate way to calculate the p-value and why would an algorithm like binom.test have minlike as a default? 2. How can we get PROC FREQ to use minlike calculation of the p-value? I think it is based on Hirji 2006 probability based method. Reference: https://cran.r-project.org/web/packages/exactci/exactci.pdf (this discusses the tsmethods as described above)
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