Dear Bassam Aldohkaini:

There are many ways to calculate and apply sample weights when subgroups of a sample have been selected using different probabilities of selection. One of the most common ways, used in DHS and UNICEF MICS, is standardized weighting. The sampling fraction is calculated for each subgroup separately and for the entire sample as a whole. Survey subjects in those subgroups in which the probability of selection is higher than the overall probability need to be down weighted for any analysis containing more than one subgroup. Survey subjects in subgroups where the probability of selection is lower need to be weighted up. To calculate the standardized weights, the overall probability of selection is divided by the subgroup-specific probability. This produces statistical weights which makes the weighted sample size identical to the crude sample size. A simple example is shown below:

Subgroup Number in sample Number in population Sampling fraction Standardized sample weight A 100 100,000 0.001 0.00035/0.001 = 0.35 B 100 500,000 0.0002 0.00035/0.0002 = 1.75 C 100 250,000 0.0004 0.00035/0.0004 = 0.875 TOTAL 300 850,000 0.00035  

After calculation, the standardized sample weights should be entered into the main database. Each subject should be assigned a sample weight. Any subject without a sample weight will not be included in a weighted analysis. Most data analysis programs which can correctly analyse data obtained by complex sampling, such as SPSS, SAS, STATA, and R, will have a mechanism by which you can identify the name of the variable containing the sample weight. Remember, using these weights is only necessary if you are doing a combined analysis of more than one subgroup of the sample where subgroups have different probabilities of selection. The standard cluster sampling techniques described in the SMART manual and in other sources produce an equal probability sample; such samples do not need sample weighting.