Answer to the Question

Multi-phase sampling is useful when the frame lacks auxiliary information that could be used to stratify the population or to screen out part of the population.

It consists of several subpopulations. In this case, rather than selecting a sample randomly from the entire population, it is convenient to divide such population into subpopulations according to certain criteria. This subpopulation, grouped according to certain criteria is called strata.

When one is selecting stratified sample from the population as there are many sub- population & the group is heterogenous then, Multi phase sampling will be helpful as if the auxiliary that is the secondary information to be used for stratifying the population is not available. Multiphase sampling as mentioned in my post is in which some information is collected from the whole sample and additional information is collected, at the same time or later, from sub samples of the entire sample. So auxiliary information is also collected through multiphase sampling.

Now about the pictures, well the first one is depiction of the whole multiphase sampling process, where in the first stage there in first phase all the samples are involved & then in other phases some of the samples are involved in each phase. The second one shows how from the whole sample selected in the next phase some of the part of sample is selected for data collection.