The Design weight adjusts for unequal probability of selection within the household - this is simply applying the reverse of the probability of selection. The sample selection for the survey is based on households; however, only one person was interviewed per household. This means that people who lived in households where there was more than one eligible adult had a different (lower) probability of being interviewed than those who lived alone. The design weight simply makes an adjustment to compensate for the unequal probability of selection.
The Population size weight adjusts for the size of the population in a country. In most surveys the sample size is not related to population of the country so many of the samples are around the same size. Without applying a population weight the sample from small countries would contribute the same value as the sample from larger countries. The population weight adjusts the relative contributions in proportion to the size of the country. See the following example:
Which weights need to be applied depends on the analysis being conducted. When making comparisons between countries, using distributions and without reference to the combined total, then only the design weights are needed.
When making comparisons with reference to the average for the combined data then both the design weight and the population weights need to be applied.
In any analysis where countries are being grouped together, for example, countries from different geographical regions, or language groups, then design and population weights are required.
