Cutoff Sampling

Cutoff sampling is a sampling technique that is most often applied to highly skewed populations, such as business establishments that vary considerably in employee size, gross revenues, production volume, and so on. Data collected on establishment surveys (from businesses or other organizations, including farms) are often heavily skewed. For any variable of interest there would be a few large values, and more and more, smaller and smaller values. Therefore, most of the volume for a given data element (variable) would be covered by a small number of observations relative to the number of establishments in the universe of all such establishments. If a measure of size is used, say, number of employees or a measure of industrial capacity or some other appropriate measure, then the establishments can be ranked by that size measure. A cutoff sample would not depend upon randomization, but instead would generally select the largest establishments, those at or above a cutoff value for the chosen measure of size. This is the way cutoff sampling is generally denned, but the term has other interpretations. Four methods are discussed here.

Cutoff sampling is used in many surveys because of its cost-effectiveness. Accuracy concerns—for example, noncoverage bias from excluding part of the population—are different than in design-based sampling and are mentioned following. Note that cutoff sampling could be used for other than establishment surveys, but these are where it is generally most appropriate.

of the following methods, the first two are probably more universally considered to be cutoff sampling:

• Method 1. Assign a probability of one for sample selection for any establishment with a measure of size at or above (or just above) a cutoff value, and a zero probability of selection for all establishments with a measure of size below (or at or below) that cutoff. No estimation is made for data not collected from establishments not in the sample.
• Method 2. In the second case, the same cutoff method is applied as in the first case, but estimation is made for the data not collected from establishments not in the sample.
• Method 3. A cutoff level is established, as in the first two cases, but some establishments below the cutoff are also included in the sample. This is often referred to as “take all” and “take some” stratification. An example would be a stratified random sample with a “certainty” stratum of which all members would be sampled.
• Method 4. Data may simply be collected starting with the largest establishment and through a size-ordered list of establishments until a certain point is reached by some measure or measures, possibly subjective.

Method 1 is simple and may minimize survey costs, and it may be of suitable accuracy under a couple of alternatives. First, if the main objective of a survey is to obtain information on unit prices, or some other ratio of totals, accuracy may not be a big problem. A unit price is actually the ratio of total cost to total volume of product. If each of these totals is underestimated by truncating part of the population, then the impact on the ratio of these two totals is not as adverse as it is to each of the two totals themselves. Another consideration, even for totals, may be that the data are so highly skewed that considering the smallest numbers to be zeroes may not cause an appreciable downward bias. Considering total survey error, if collecting data from more of the smallest establishments detracts from resources needed for better accuracy in collecting from the largest establishments, this may be undesirable. However, perhaps in most cases, the main impetus for Method 1 is cost-effectiveness.

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