Question

Describe each of the following sampling methods and indicate conditions under which each is appropriate.

(a) Systematic random sampling

(b) Cluster sampling

(c) Stratified random sampling with proportional allocation

Short answer

(a) Systematic random sampling: It uses a specific interval to choose the sample group from within the target population.

(b) Cluster sampling: In it, the population is divided into different groups (clusters) for research purposes.

(c) Stratified random sampling with proportional allocation: In it, the strata is formed based on some shared traits or characteristics

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

Describe each of the following sampling methods and indicate conditions under which each is appropriate.

(a) Systematic random sampling

(b) Cluster sampling

(c) Stratified random sampling with proportional allocation

Part (a) Step 2. Systematic random sampling.

Given below are the steps for getting a systematic random sampling:

1. First, divide the population size by the sample size and then round the result to the nearest whole integer,m.
2. Use a random number table (or such equivalent device) to generate a number, k between among the numbers 1 and m.
3. At last, members of the population with the numbers k. km, k + 2m..... should be chosen for the sample.

Simple random sampling is more difficult to carry out if we compare it with systematic random sampling, but the results are usually equivalent.

The exception is the presence of a cyclical pattern in the list of population members, which is a rather uncommon occurrence.

Part (b) Step 1. Cluster sampling.

Cluster sampling is a process that involves a number of steps which are mentioned below:

1. Separate the people into groups (clusters).
2. Collect a random sample of the resulted clusters.
3. As the sample, use all of the members of the clusters created in step 2.

Cluster sampling, on the other hand, could save time and money. It also does have certain drawbacks.

Each cluster should, in theory, reflect the total population.

In actuality, however, cluster members may be more homogeneous than the population as a whole, which might present complications.

Part (c) Step 1. Systematic random sampling.

Stratified Random Sampling with Proportional Allocation: Stratified random sampling with proportional allocation entails the following steps:

1. Subdivide the population into groups (strata).
2. Take a basic random sample proportional to the size of each stratum, i.e., the sample size for a stratum equals the total sample size multiplied by the stratum size divided by the population size.
3. As a sample, use all of the people you encounter in step 2.

This stratified sampling approach assures that no group is left out, improves the precision of statistical estimations, and it allows for the estimation of individual strata viewpoints.