Compare two prevalences: magnitude of difference

Theory

The statistical method for comparing two prevalences, estimated from independent samples, is the chi-square test. However, two prevalence estimates can be compared by calculating the confidence interval of the difference as follows:

Where:

Diff	The difference between prevalence 1 and prevalence 2.
z	The value obtained from the standard normal distribution. To each value of confidence there is a corresponding value of z. The levels of confidence more frequently used in biological studies are 90%, 95% and 99%. The values of z corresponding to them are 1.645, 1.96, and 2.58 respectively.
P	The mean of both expected prevalences: (p1 + p1) / 2.
p1 and p2	The expected prevalence in sample 1 and 2.
n1 and n2	The number of animals in sample 1 and sample 2.

Interpretation: if prevalence 1 and 2 are the same, the difference between them will be = 0 and the confidence interval of the difference will include 0. If the difference between them is small the confidence interval of the difference will include also number 0 (the minimum limit will be negative and the upper limit positive). When the confidence interval of the difference excludes 0, it could be said that prevalence 1 and 2 are significantly different at the stated level of confidence.