Title: Weights
Course: UGQuants (SSPS) > Section: Probability

Explains the concept of statistical weights.

We need to discuss one last thing before you can effectively use your sample-based data set: no matter how well the data collection is conducted, we are always going to have some bias in the data, e.g. through unequal probabilities of selection in the survey sampling design (for practical and financial reasons, surveys often work with cluster and stratified samples, rather than with perfect random samples; they might also choose to oversample a specific group of people) or people refusing to take part in the survey (non-response). To adjust for this bias to the best of our abilities, survey conductors usually provide us with statistical weights.

Weights are usually based on known population parameters, such as gender and age distribution. On the website of the Office for National Statistics, you can, for example, look up the 2011 Census data for England & Wales. Censuses aim to capture information about the whole population and, because they are mandatory, are the best means of obtaining knowledge about population characteristics. According to the Census dataset DC1117EW, 51.3% of the people aged 20 were male. However, perhaps in the specific survey you are using, the interviewers have not been successful in recruiting 20 year old males, so that your unweighted rate of them is only 42%. Weights can adjust for this by providing a specific factor for each single respondent. In this case, the men of that age would receive a factor larger than 1 and the women would receive a factor smaller than one.

You can check what the weights in the European Social Survey do:

- Open the full ESS data set for the UK.
- Run a frequency table for age.
- Then activate the design weight by following this path: Data > Weight cases
- It will open this window, in which you simply enter the design weight variable from the list and press okay.

- At the bottom right corner of your data window, you will now see the message 'weight on'. This is a quick way to check your weight status.

- Now produce the frequency table of age a second time. You should find that unweighted, 51.8% of your sample are aged fifty or below, whereas with the weight on, 56.6% of your respondents are in that age group.

You may have noticed that there are two weight variables in the ESS dataset: the design weight and the population weight. They have one main difference: the design weight's factors adjust merely the proportions in the sample, whereas the population weight's factors blow up the absolute counts to match those of the whole population or at least ensure that when comparing several countries, each country is represented in proportion to its population size.

In the ESS, for example, each European country has a similar sample size, even though, for example, the UK has a population of ca. 60 million people, whereas Belgium has a population of merely 11 million. Therefore, when you apply the population weight in the ESS5 data set for the UK, it suddenly shows a sample of 5119 even though only 2422 people were interviewed. This can be missleading and should thus only be used if you want to compare countries. If you, e.g., combined the datasets for the UK and Belgium and wanted to know what the overall mean age in both countries was, you would require the population weight.

Whenever you use weights, you should first read the survey documentation to find out what exactly the weights adjust for.