Assigning Sampling weights in case of Multi stage sampling

A multi-stage stratified cluster design greatly enhances the feasibility of data collection, it results in differential probabilities of selection; consequently, each sampling unit or in the assessment does not necessarily represent the same number of students in the population, as would be the case if a simple random sampling approach were employed.

To account for differential probabilities of selection due to the nature of the design and
to ensure accurate survey estimates, Sampling weights are needed to correct for imperfections in the sample that might lead to bias and other departures between the sample and the reference population. Such imperfections include the selection of units with unequal probabilities, non-coverage of the population, and non-response.

In other words, the purposes of weighting are:
• To compensate for unequal probabilities of selection.
• To compensate for (unit) non-response/ and or non-coverage.
• To adjust the weighted sample distribution for key variables of interest and to make it conform to a known population distribution.

So, usually three types of weights are assigned:

• Sampling weight to account for unequal probability of selection
• Weights for non response
• Post stratification weights

Though in majority of the cases only sampling weights and weights for non-coverage/non-response is used.

Calculation of sampling weights

Calculation of sampling weights usually starts with the construction of the base weight for each sampled unit, to correct for their unequal probabilities of selection. In general, the base weight of a sampled unit is the reciprocal of its probability of selection into the sample.

For multi-stage designs, the base weights must reflect the probabilities of selection at
each stage and the overall base weight the household is obtained as before, by taking the reciprocal of its overall probability of selection.

The adjustment of sample weights for non-response/non-coverage

It is rarely that all desired information is obtained from all sampled units in surveys. For instance, some households may provide no data at all while other households may provide only partial data. Further not all sampling units in samples may be covered.