Sampling frame

Three groups sit inside one another and the frame is the middle one. The population is who the question is about. The frame is the list, register, or map the method actually draws from. The sample is who gets selected out of the frame. Only individuals on the frame have any chance of being selected at all, so every probability statement a survey makes is a statement about the frame.

A town has 9,000 adult residents and the pollster works from a landline directory covering 6,300 of them, or 70 percent. The other 2,700 have selection probability zero. Suppose 55 percent of listed adults support a measure and 30 percent of unlisted adults do. The population value is $\frac{0.55(6300) + 0.30(2700)}{9000} = 0.475$, while a flawless random sample of the frame centers on 0.55. The method is off by 0.075 before anyone picks up a phone, and calling 6,300 people rather than 300 does not move it. A census of the frame is still not a census of the population.

The wrong sentence is "the sampling frame is the group the researcher wants to study." That is the population. The frame is the operational stand-in for it, and naming the gap between the two is the entire reason the term exists. A second slip: a frame can be too big as well as too small. A voter list still holding people who moved away, or a mailing list where some households appear twice, contains units outside the population and gives some units two chances of selection.

An SRS drawn from a frame is a simple random sample of the frame. It inherits the frame's gaps exactly, and the absence of the missing group is undercoverage, which no sample size repairs. The first question worth putting to any survey is who the method could never have reached, and the frame answers it rather than the data.

Potential problems with sampling is topic 1.12 in Unit 1.