# Statistical test to compare success rate in different groups

We had different samples of blood with bacterias. With a new method we tried to quickly identify the bacterias in these samples and then we calculated success rate of our method (we know the correct type based on another method - which we consider to be 100% correct). We found out that success rate might be different for different kind of bacteria - we are more succesfull in identifying some kind of bacterias than others. What is the correct statistical method for:

a, compare success rates between two groups?

b, compare success rates between more than 2 groups?

Example of data:

a)

• Aerobic bacteria: succesfully detected in 42 from 50 samples
• Anaerobic bacteria: succesfully detected in 17 from 19 samples

b)

• Group of bacteria 1: successfully detected in 14 from 16 samples
• Group of bacteria 2: successfully detected in 5 from 7 samples
• Group of bacteria 3: successfully detected in 20 from 25 samples
• Group of bacteria 4: successfully detected in 20 from 21 samples

Thank you for any help in advance.

• What do you mean by "compare?" Are you referring the difference between the success rates with respect to each other or with respect to some other null hypothesis? – tchainzzz Mar 29 at 20:26
• statistical difference between success rates with respect to each other, so H0 is that there is no difference in success rates between these groups – damian Mar 30 at 13:54