I'm not sure I understand the question. If the data are known to be representative of the population, I'm not sure why you'd have weights at all (or, rather, all weights would be equal).

Can you elaborate?

Hi!

I am sorry for not being putting the question clearly. In a study we used propbability propotional to size sampling and we have samples from different clusters (PSU's- for urban areas it was enumeration blocks and for rural it was villages). The sampling was two stage selection of clusters and then within clusters Households (HH) and in every selected HH we interviewed one eligible person. Now, sicne it was based on PPS so we have to assign weights. In this case while analyzing the data we will apply weights. Now, what kind of difference in terms of value of estimates these weight can make. I just had some basic analysis and observed that overall there is hardly any difference. Similarly in another study which is on commerical sex workers, we had used weights while analyzing the data and it was observed that there is not much difference in weigthed and un-weighted estiamtes. When we use multivariate analysis how much difference does the weights makes.

Ah, thanks for the clarification.

The answer is, as so often, "it depends." To the extent there are more extremely over- or under-represented subpopulations (whether observed or unobserved) that differ from the population on the variables and relations of interest, it will make more of a difference. For example, if a study that by design oversamples higher-risk subpopulations, it can be very important.

What you did is essentially a sensitivity analysis, if I read it right. If you find that the results are not substantially (by whatever criterion you're comfortable with) sensitive to weighting versus not, I would report that and then figure you can move on with unweighted to save the computational hassles. But that sensitivity analysis is vital before moving forward.

Thanks Patrick! I am planning to work on it and if possible wil try to develop one research paper dicussing the difference and importance of weighting and unweighted estimates.

Sounds great!