This chapter addresses the frequently asked question “How large a sample do I need to obtain a confidence interval?” To determine sample size requirements, one generally starts with a statement of the needed precision (e.g., in terms of interval width) and then uses the procedures for constructing statistical intervals described in the previous chapters “in reverse.”
This and the following two chapters are concerned with data quantity (sample size). We need, however, to reiterate that the issue of data quantity is often secondary to that of the quality of the data. In particular, in making a statistical estimate or constructing a statistical interval, one assumes that the available data were obtained by using a random sample from a defined population or process of interest. As stated previously, when this is not the case, all bets are off. Just increasing the sample size—without broadening the scope of the investigation—does not compensate for lack of randomness; all it does is allow one to obtain a possibly biased estimate with greater precision. Putting it another way, increasing the sample size per se usually improves the precision of an estimate, but not necessarily its accuracy.
Section 8.1 describes basic requirements for sample size determination. Subsequent sections of this chapter deal with sample size determination methods to estimate a: