Is it correct that IPW weights (Wi=Ni/ni) are better compared with the EPW weights (wi=Pi/pi)?

The IPW (inverse probability weight) weights are based on inversing the probability of respondents being included into the sample and the EPW (equal proportion weight) weights are based on making the sample proportions similar to the population proportions regarding groups of respondents by age, gender, ethnicity etcetera. When applied to the data both sets of weights produce similar results in terms of weighted proportions, weighted means and other basic statistics. However, the two sorts of weights tell a different story. The IPW weights are mostly more easy to understand and if you have some experience also more intuitive. The IPW weights tell you how many persons in a particular group in the population a single respondent from that group represents. This number is always the same; therefore if you compare different towns with each other, or different areas within the towns, or look at larger regions, you always use the same weights. The EPW weights give the importance of a weighted respondent compared with un-weighted respondents; sometimes a respondent becomes less important after weighing, other times more important. If the weight is larger than one the respondents are more important after weighing, if the weight is smaller than one they are less important. An important disadvantage of the EPW weights is that these change if you change the level of analysis. Therefore for an analysis on the regional level you need other weights than for an analysis on the city level and for areas within the city you need yet other weights. Also if you want to do the analysis for men or women separately instead of for both groups together, or for different age groups, every time you need a new set of weights. Finally, SPSS Complex Samples, EpiInfo Complex Samples, Survey in "R" and other complex samples programs mostly presume that you use the IPW weights.

If you use the SISA weight application the IPW weights are adapted to follow the trimmed EPW weights. A disadvantage of this is that the IPW weights are no longer invariant concerning the level of analysis; you can therefore not apply them in different subgroups without making some kind of correction. However, the bias introduced by this invariance will generally be small.

In one of our local councils we have a larger sample in two districts: do you treat these two districts as independent samples, and split the local council concerned as if it were two local councils? And then compare the population of the oversampled district with the population of the rest of the council (minus the districts)?

Yes, it is best to treat the local council in this case as two local councils. Perhaps that you can weigh for all districts of the council, particularly if you expect a different response by district that might be worth it. However, this depends a bit on your sample size. You must have sufficient numbers of cases to fill the weighing table cells.

And if in the above case you want to say something about the whole local council, can you take the two populations together and do the analyses using the same weights which you have made earlier, or do you have to make new weights?

If you used the IPW weights you do not have to make new weights. In case of the EPW weights, however, you have to make new weights by district for the whole council.

We collected data with both a mail survey and by means of an internet survey. Can you add these data sets?

How you collected the data does not matter much, as long as both are random selections from the population, or one selection were people either answer the mail survey or the internet survey. After you have added the data of the two surveys you compare the profile of your sample with the profile of the population and then calculate the weights. What you must consider is the possibility that respondents had a double chance to enter the sample, when they could have been selected both for the mail survey and for the internet survey, while other respondents did not have this double chance. Although it is in possible to take account of this in developing the weights it is better to prevent this from happening.

Is the value of the design effect important? Generally this value is between 1 and 3. Sometimes however we see a higher value. Are there guidelines as between what values the design effect should be? Are the results of the analysis reliable if the design factor is large?