In statistics, benchmarking is a method of using auxiliary information to adjust the sampling weightss used in an estimation process, in order to yield more accurate estimates of totals.

Suppose we have a population. So we take a sample, get a sampling weight W(k.

described here is that if we sum) will also differ from true population total.

are over all units in the population. For example, we may not know the total earnings of the population or the total cost of the population, but often we know the total employment or total volume of sales. And even if we don't know these exactly, there often are surveys done by other organizations or at earlier times, with very accurate estimates of these auxiliary quantities. One important function of a population census is to provide data that can be used for benchmarking smaller surveys.

] will tend to be more accurate.

Relationship to stratified sampling

Benchmarking is sometimes referred to as 'post-stratification' because of its similarities to stratified sampling. The difference between the two is that in stratified sampling, we decide in advance how many units will be sampled from each stratum (equivalent to benchmarking cells); in benchmarking, we select units from the broader population, and the number chosen from each cell is a matter of chance.

The advantage of stratified sampling is that the sample numbers in each stratum can be controlled for desired accuracy outcomes. Without this control, we may end up with too much sample in one stratum and not enough in another – indeed, it's possible that a sample will contain no, leading to a divide-by-zero problem. In such cases, it is necessary to 'collapse' cells together so that each remaining cell has an adequate sample size.

For this reason, benchmarking is generally used in situations where stratified sampling is impractical. For instance, when selecting people from a telephone directory, we can't tell what age they are so we can't easily stratify the sample by age. However, we can collect this information from the people sampled, allowing us to benchmark against demographic information.

Further reading