If I’m testing a campaign, what size should my sample be? How many people should I contact to get a reasonable idea of the underlying response? It’s important to know this before rolling out larger volumes.

This calculator allows you to choose an expected response rate within bounds, and a confidence interval. Given those, it will tell you what volume you should contact to have confidence in the response rate. For instance, if you want 95% confidence that a response rate of 5% reflects a true response rate of between 4% and 6%, then you’d need to contact 1825 people.

Note that as the response rate changes, there are two effects. The drop in response rate reduces the volume that’s required, because the error bounds become proportionately larger. Adjusting the above example for a response rate of 2.5%+/- 1%, the required volume would be only 936. But if you reduce the bounds in proportion, to 2.5% +/- 0.5% (so that the range  of 2%-3% remains in proportion) the volume goes up to 3746. Be careful to make sure that you choose this right, sometimes the absolute figure is more important than the level of precision.