# Multistage Sampling – Definition, Examples, Advantages

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The multistage sampling technique is an example of a subsampling technique. Subsampling techniques were initially developed for the purpose of sampling plots in agricultural field experiments.

## Multistage Sampling – What is it?

By utilizing sub-sampling within the clusters, one can achieve better and more effective estimates as opposed to counting all the sample units in the chosen clusters. In two-stage sampling, clusters are referred to as primary units and the units within the clusters as secondary units.  The aforementioned method can be used generalized to multistage sampling.

Multistage sampling, as the name suggests, is a sampling approach that involves several phases. The population is viewed in this context as being made up of a number of primary units, each of which is further made up of a number of secondary level units, and so on until we finally reach the target sampling unit in which we are interested.

Thus, subsequent phases of multistage sampling involve hierarchical groupings of units. Existing groups, a geographic divide, or a geographical grouping fulfilling administrative or operational roles are frequently ideal for multistage sampling. People in families, houses in blocks, census enumeration districts or local government areas, children in schools, goods in crates or on shelves of storage systems, consignments, patients in hospitals, on the pages of ledgers, and records in drawers or on shelves of record files are a few examples of ready-made units suitable for multistage sampling. The majority of these types of clusterings that are appropriate for use as sampling units for multistage sampling have a spatial basis, and as a result, the clusters acting as sampling units are made up of nearby elementary units. The main difference between multistage sampling and cluster sampling lies in the complexity of the two sampling methods. Multistage sampling is a much more complicated technique compared to cluster sampling.

### Examples of Multistage Sampling:

#### Example 1:

Suppose we want to test the effect of different teaching methods on the learning outcomes of students.

1. The different schools where the study is being conducted are the sampling units.
2. The different classes in the school are the sampling subunits.
3. When choosing the students from a particular class, we may not choose all students. We may choose a random selection of students from that class.

Here we see that the primary sample units (schools) have been divided into secondary subunits (classes) out of which a subset of students are chosen.

#### Example 2:

1. In surveys to estimate crop production, the village is a convenient sampling unit.
2. Within a village, only some of the fields growing the crop in question are selected, so that the field is a subunit.
3. When a field is selected, only certain parts of it are cut for the determination of yield per acre: thus the subunit itself is sampled.
4. If physical or chemical analyses of the crop are involved, an additional subsampling may be used, since these determinations are often made on a part of the sample cut from a field.

The three steps in this sampling are – village, followed by field, followed by the selection of crops. We now list some of the pros and cons of the multistage sampling process.

The most useful benefit of multistage sampling is that we only need the second stage frame for the units that were chosen in the first stage sample, which results in significant operating cost savings. While it would be difficult and expensive to sample widely dispersed populations using any single-stage sampling approach, multistage sampling is much cheaper. It could be expensive to compile the entire list of individual sampling units needed for every single-stage probability sampling.

For instance, listing the whole human population of a city would require no less than a thorough canvass. In order to choose a sample of the present population, it would also be highly expensive to update such a lengthy list to account for additional births, deaths, and population moves. Additionally, it is likely that any single-stage sample of a city’s population will be dispersed throughout the whole city, subjecting survey fieldworkers to the greatest amount of travel possible for a sample of a given size.

Contrarily, multistage sampling allows for the selection of individuals from very condensed lists. As a preliminary step in the selection process, a sample of homes may be used, limiting the necessary list of people to those who are already residents in the sample homes chosen. It is only necessary to update the lists of homes inside the sample blocks and the lists of people within the sample homes for any subsequent census of the city’s population. The fieldwork can be concentrated while still covering a vast region, making it simple to execute and administratively convenient.

This method is especially useful in surveys of underdeveloped areas or pockets where it is typically impossible to divide the data into reasonably tiny sampling units using an accurate and up-to-date frame.

These operational benefits of simpler listing and collection are typically partially offset by a resulting reduction in sample efficiency. In general, an appropriate single-stage random sampling of the same size is usually more efficient than multistage sampling.

The multistage sampling method is more likely than any other method to produce greater errors. In order to generate similar sample estimates subject to sample errors of the same extent, a multistage sample must typically be significantly bigger than the equivalent simple random sample.

Compared to estimates based on simple random sampling, the variability of the estimates using the multistage method may be higher. The composition of the primary units has an impact on this variability.