The first test looks okay. From the table and the syntax, I would say it is testing Ho: p >= .3 Ha: p < .3 where p = Prob (x came from Group1). The "p-value", shown in the right-hand column, is Prob (Group1 =< 6). 1.1 NPAR TESTS. Binomial Test +-+------#--------+--+--------------+----------+---------------------+ | | #Category| N|Observed Prop.|Test Prop.|Exact Sig. (1-tailed)| +-+------#--------+--+--------------+----------+---------------------+ |x|Group1# 1.00| 6| .286| .300| .551| | |Group2# 2.00|15| .714| | | | |Total # |21| 1.00| | | +-+------#--------+--+--------------+----------+---------------------+ To be consistent with the previous table, in which we test Ho: p >= 0.4 Ha: p < 0.4 the one-tailed p-value below should be Pr (Group1 =< 7) = 0.902. But the value shown in table 2.1 is Pr (Group1 >= 6) = 0.229. That would be correct, if the "success" probability of 0.4 referred to group 2, but it seems to refer to group 1, as in the first table. If instead we were testing Ho: p =< .4, and p was associated with Group 1, then the p-value would be 0.098. 2.1 NPAR TESTS. Binomial Test +-+------#--------+--+--------------+----------+---------------------+ | | #Category| N|Observed Prop.|Test Prop.|Exact Sig. (1-tailed)| +-+------#--------+--+--------------+----------+---------------------+ |x|Group1# 1.00| 7| .538| .400| .229| | |Group2# 2.00| 6| .462| | | | |Total # |13| 1.00| | | +-+------#--------+--+--------------+----------+---------------------+