Let N be the population size. Let p denote the proportion of this population with a certain characteristic (ie. has diabetes, divorced, homosexual, etc.) Let's say we are trying to estimate p using a sample of size n. So we collect our sample and calculate p^ to be the proportion of elements in our sample with our characteristic of interest. Then we calculate the standard of deviation of p^ (also known as the standard error) because it gives us an idea of how close our sample proportion is to the real proportion.
Now, my statistics textbook says the standard of deviation is given by SD(p^) = root[(p^(1-p^))/n] when sampling with replacement or when the sample size is significantly smaller than the population size. My question is why isn't there a N variable in our equation for SD(p^)? According to this formula, if we are trying to figure out the proportion of people with diabetes in Berkeley, California with sample size n, we would get the same standard of error as if we are trying to figure out the proportion of people with diabetes in the world with sample size n. (In the former, the N is a lot smaller than in the later). . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
