More and more people choose not to answer the important studies that form the basis for political decisions. And as the non-response rates becomes higher, it gets increasingly difficult for Statistics Bureau and other government agencies that produce statistics to draw conclusions that can be trusted. The result might be that people start to doubt the content of the surveys.

- We are awash with surveys and cannot sift. Many do not bother to answer anything, and then there is a problem when people do not answer surveys that actually form the basis for decisions on the national level, says Per Gösta Andersson, senior lecturer in statistics.

The starting point for Per Gösta Andersson and Carl-Erik Särndals method, presented in the journal Statistical Journal of the IAOS (International Association for Official Statistics), is that the statisticians work with the responses that they have actually received. To get a better estimate of the population as a whole, they use so-called auxiliary information.

### Important clues from auxiliary information

The idea behind the method is simple. For example, if someone wants to investigate how many people are unemployed in a population, they send out a survey to a random sample of the population (a sample survey), and get a certain rate of non-response. Meanwhile there is a lot of auxiliary information about the population, that can help in this matter. For example, you may know how many older and younger it is, or how incomes vary.

- If you know the values of these so-called auxiliary variables, one can also infer what individuals who have failed to respond - the non-respondents. So we know something about those who have responded, and we know something about those who have not responded, says Per Gösta Andersson.

Hopefully there is a link between the variable that we wish to examine, in the example the unemployment rate in a population, and the auxiliary information that is available. The point is that it is possible to figure out how to adjust for non-response. In this way it is possible to get an estimate of how many people are unemployed in the population as a whole.

- You use a so-called calibration estimation. By using the values of the auxiliary variables, you can get a pretty good estimate, even though you have a certain non-response rate, says Per Gösta Andersson, Stockholm University.

Facts: calibration estimation

Calibration is a kind of weighting. It weighs up the answers of the groups that were underrepresented because of the non-response, and the weights down to those who were over-represented. Per Gösta Andersson and Carl-Erik Särndal develop this method further, and compare whether it is better to do the calibration in one or two steps, since auxiliary information may be available on two levels.

**Text:** Leila Zoubir