EXAMPLE 9 The woes of telephone samples

In principle, it would seem that a telephone survey that dials numbers at random could be based on an SRS. Telephone surveys have little need for clustering. Stratifying can still reduce variability, however, and so telephone surveys often take samples in two stages: a stratified sample of telephone number prefixes (area code plus first three digits) followed by individual numbers (last four digits) dialed at random in each prefix.

The real problem with an SRS of telephone numbers is that too few numbers lead to households. Blame technology. Fax machines, modems, and cell phones demand new phone numbers. Between 1988 and 2008, the number of households in the United States grew by 29%, but the number of possible residential phone numbers grew by more than 120%. Some analysts believe that, in the near future, we may have to increase the number of digits for telephone numbers from 10 (including the area code) to 12. This will further exacerbate this problem. Telephone surveys now use “list-assisted samples” that check electronic telephone directories to eliminate prefixes that have no listed numbers before random sampling begins. Fewer calls are wasted, but anyone living where all numbers are unlisted is missed. Prefixes with no listed numbers are, therefore, separately sampled (stratification again), perhaps with a smaller sample size than if included in the list-assisted sample, to fill the gap.

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The proliferation of cell phones has created additional problems for telephone samples. As of December 2013, about 41% of households had cell phones only. Random digit dialing using a machine is not allowed for cell phone numbers. Phone numbers assigned to cell phones are determined by the location of the cell phone company providing the service and need not coincide with the actual residence of the user. This makes it difficult to implement sophisticated methods of sampling such as stratified sampling by geographic location.