Weighting is a statistical technique to compute a general mean or a percentage out of a non-representative response.
When should weighting be used?
Suppose a survey has been conducted about whether or not to hold a party in honour of the mayor. The city has a million inhabitants who are spread over four city districts. People can indicate whether they are for or against this party. The results are in the table below.
It looks like the majority of the population is for holding the party: 54%.
But is this conclusion correct? From each district a proportional part of the population should have responded, but that appears not to be the case. In the South district, the number of respondents is much lower. It appears that the population in this district is mostly against the festival. Perhaps these people hoped that there would be too little response and the research would not produce valid results. Can you still say that the majority of all residents want the festival?
How to calculate the weights
To obtain the correct percentage, the scores must be weighted. It is therefore assumed that these respondents represent their district. The easiest way to get the right percentage for the entire population is to multiply the score of the district by the number of inhabitants of the district; then add up these scores and divide this number by the total number of inhabitants. In this case this calculation is made:
The conclusion is that 44% of the population wants the party and that is less than the majority. That does not mean that the party should not go on, because there is still a substantial part of the population that finds it important.
When should weighting not be used?
It is recommended not to use weights in statistical tests. The weights influence the variance of the groups. It is no longer possible to make a fair comparison between the groups.