Tuesday, April 17, 2007

Multi Stage Sampling

It is the process of taking any portion of a population or universe as representative of that population or universe.

One of the type of sampling is "Multi-Stage Sampling". Let's see some detail information about this type of sampling.

Multi-Stage Sampling:


  • In multi-stage sampling the material is regarded as made up of a number of first-stage units each of which is made up of second-stage units, and so on.

  • At the first stage of sampling, a number of first-stage units are selected; from each of the selected first-stage units, a number of second-stage units are then selected and so on.

An example of multi-stage sampling is where, firstly, electoral sub-divisions (clusters) are sampled from a city or state. Secondly, blocks of houses are selected from within the electoral sub-divisions and, thirdly, individual houses are selected from within the selected blocks of houses.


  • Multi-stage sampling does not require a complete list of members in the target population, which greatly reduces sample preparation cost.

  • Multistage sampling can involve more than one method or combined method of sampling, such as simple random, cluster or stratified sampling.

  • Multistage sampling uses a hierarchy of sampling units or clusters


  • Multi-stage sampling is like cluster sampling, but involves selecting a sample within each chosen cluster, rather than including all units in the cluster.

  • Thus, multi-stage sampling involves selecting a sample in at least two stages.

  • In the first stage, large groups or clusters are selected. These clusters are designed to contain more population units than are required for the final sample.

  • In the second stage, population units are chosen from selected clusters to derive a final sample. If more than two stages are used, the process of choosing population units within clusters continues until the final sample is achieved.

For Example:

A country may be considered as divided into a number of districts; each district into a number of villages; each village into. a number of farms. In multi-stage sampling a number of districts is selected in the first-stage within each such selected district a number of villages is selected in the second-stage, and from each selected village a number of farms is selected at the third-stage for enquiry. In the case of a crop-cutting investigation, the work may be carried further by the selection of fields from each selected farm and by plots within a field.


  • Multi-stage sampling are convenience, economic and efficient.

  • The technique is used frequently when a complete list of all members of the population does not exist.
  • It can dramatically reduce the cost of field operations.
  • Usually more accurate than cluster for same total size.
  • The main disadvantage of multi-stage sampling is the same as for cluster sampling.
  • Lower accuracy due to higher sampling error.
  • Less accurate than SRS (Simple Random Samplig) of same size ·
  • Further analysis is difficult.


You are employed by a market research organisation and have been asked to undertake a study across the whole of the British Isles to determine attitudes towards the National Lottery.
What are the possible sampling frames for this study? You have been asked to interview 4,000 people in total. Consider what would happen if you undertook a simple random survey....... Of these 4,000 you might,

for example, you have to interview 2 people in Shetland, 3 in the Outer Hebrides, a dozen scattered across the Borders, and so on. As this is uneconomic, both in terms of time and money, it would be considered more efficient to undertake a Multi-stage Cluster Sample. Think of some ways in which you could divide the country up into progressively smaller sections to undertake this type of sample.









Presentated by:-

Vandana Jain (4)

Nikita Munot (12)


Hemangi said...

Nikita and Vandana,
Hello both of you! I just read through your post and am sorry for the delay in commenting.

You have presented this type in a very organized way and have also provided many extra resources. I just hope you have taken care of the reliability and validity issues while taking these resources.

The activity that you have provided is also good and interesting but how about an example with names and places we can relate to?

yqwea said...

Was very clarifying. I't trying to figure out how to do a survey of a population which is disperse in small rural villages clearly separated by geographical features. There are 173 villages, settled in well established areas far apart one for each other, and are very heterogeneous in regards to their number of members (few with a thousand of families, others with no more than 10, and all the numbers between).

Seems like a multi-stage sampling is the most suitable, since there is impossible to get a list of members or households, but the list of villages is widely available and accurate.

But I still have lots of doubts about how to apply it in real life.

Firstly, once you have established what will be selected in each stage (in my case, 1st Counties, 2nd Villages in each county, 3rd households, 4th person). How can you know how many should be selected each time? I mean, you cannot apply simple random standard considerations to calculate "sample size" to know how many counties (out of 15), villages (out of 173, but NOT homogeneously distributed in each county), household (unknown number, but for sure, very heterogenous), and person (unknown number but should not be very heterogenous, I presume) , etc.

Secondly, is very likely that each first-stage cluster will have a different number of elements, and then, clusters with less elements will have a proportional higher chance to be selected than elements in large cluster. I could solve this weightening, but I do not know the exact number of persons in each cluster. (I have an approximate value, from a source which seems a but out-of-date).

Thank you!