Question

Provide an example of when you might want to take a stratified random sample instead of a simple random sample and explain what the advantages of a stratified sample might be

Answer 1

DEF 1:Stratified random sampling refers to a sampling method that has the following properties.

• The population consists of N elements.
• The population is divided into H groups, called strata.
• Each element of the population can be assigned to one, and only one, stratum.
• The number of observations within each stratum N_h is known, and N = N₁ + N₂ + N₃ + ... + N_H-1 + N_H.
• The researcher obtains a probability sample from each stratum

OR

DEf 2: It is a method of sampling from a population which can be partitioned into subpopulations.

In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation (stratum) independently. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling.It should be collectively exhaustive and mutually exclusive: every element in the population must be assigned to one and only one stratum.Then simple random sampling or systematic sampling is applied within each stratum. (The aim is to improve the precision of the sample by reducing sampling error.)

For Example:

Assume that we need to estimate the average number of votes for each candidate in an election. Assume that a country has 3 towns: Town A has 1 million factory workers, Town B has 2 million office workers and Town C has 3 million retirees. We can choose to get a random sample of size 60 over the entire population but there is some chance that the resulting random sample is poorly balanced across these towns and hence is biased, causing a significant error in estimation. Instead if we choose to take a random sample of 10, 20 and 30 from Town A, B and C respectively, then we can produce a smaller error in estimation for the same total sample size. This method is generally used when a population is not a homogeneous group.

Two main stratergies are used here:

1. Proportionate allocation : uses a sampling fraction in each of the strata that is proportional to that of the total population
2. Optimum allocation (or disproportionate allocation) - The sampling fraction of each stratum is proportionate to both the proportion (as above) and the standard deviation of the distribution of the variable.

• Advantages

The reasons to use stratified sampling rather than simple random sampling include.

1. If measurements within strata have lower standard deviation, stratification gives smaller error in estimation.
2. For many applications, measurements become more manageable and/or cheaper when the population is grouped into strata.
3. It is often desirable to have estimates of population parameters for groups within the population.

• Disadvantages

1. Can't be Used in All Studies :This method of research cannot be used in every study. The method's disadvantage is that several conditions must be met for it to be used properly. Researchers must identify every member of a population being studied and classify each of them into one, and only one, subpopulation. As a result, stratified random sampling is disadvantageous when researchers can't confidently classify every member of the population into a subgroup.