The correction factor-Chapter 20

In fact, many times when we do sample surveys, we do not resurvey someone who has already been surveyed. We are not sampling WITH replacement, but WITHOUT.

This only makes a difference for `small' popuation sizes (N) compared to the sample size (n), the SE is in fact smaller by the correction factor:

$$SE_{without}=SE_{with} \sqrt{\frac{N-n}{N-1}}$$

The table on page 368 of the book shows that when $n=2,500$, the correction factor is close to 1 for N larger than 100,000.