I obtained two groups of data from my experiment and calculated the binomial distribution for each group, trying to see if they are significantly different from each other. However, the z sore I got was way smaller than -4, which was a little bit odd to me. Here is how I did my calculation:
The control group: # of trails n1=34; # of successes k1=2, success rate p1=2/34=5.9% The experimental group: # of trails n2=25; # of successes k2=2, success rate p2=2/25=8.0%
average p=6.8% standard error=0.0044 test statistic z=(5.9%-8%)/standard error=-4.77 It's a two-tailed test. I couldn't find a p-value corresponding to the z score I got (-4.77) on the table. Does that mean my p-value was just really small or I made mistakes here? Thank you.