I'm looking for a method to determine the likelihood that two percentages from independent groups are EQUAL. In this case I'm looking at the likelihood of symptom improvement from patients gathered through two different methods (one traditional double-blind study and one from an online enrollment).
So if in the traditional method 60% of 169 patients reported improvement and in the online study 63% of 110 patients reported improvement. Is there a way to tell whether these two percentages are the same? I know I can use a chi-squared test to determine the likelihood that they are different but can I use 1 minus chi-squared as the likelihood that they are the same?
Is there a more appropriate test I can do?