# Thread: Significant difference between proportions

1. ## Significant difference between proportions

Let's say I had a population of 1000 people and I wanted to know if there was a significant difference between the number of people with Disease A and the number of people with Disease B. Let's say 5 people had Disease A and 10 people had Disease B (total of 15 people with a disease).

Would the z score be:

(5/1000 - 10/1000)/(sq rt (15/1000)(985/1000)(1/1000+1/1000))

OR

(5/1000 - 10/1000)/(sq rt (15/2000)(985/1000)(1/1000+1/1000))

OR

(5/1000 - 10/1000)/(sq rt (15/2000)(985/1000)(1/1000))

or something else entirely?

2. ## Re: Significant difference between proportions

None of the above. The first formula assumes that the sample proportions for A and B are independent, but they are not. The other two formulas are just wrong... The problem can be solved by running a likelihood ratio test for the equality of two probabilities in a multinomial distribution.