# Test if two binomial distribution are significantly different from each other

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.

• Your calculations are erroneous: you appear to have typed an extra zero in the standard error. Your approach is incorrect, as well, for several reasons: a Z-test is inapplicable and the method of computing the SE is not appropriate. Search our site for http://stats.stackexchange.com/search?q=two+sample+binomial+test, for instance. – whuber May 16 '16 at 20:40