 # Explain the difference between a stratified sample and a cluster sample

## Explain the difference between a stratified sample and a cluster sample (select all that apply.)

A. In a cluster sample, every sample of size n has an equal chance of being included.

B. In a stratified sample, every sample of size n has an equal chance of being included.

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C. In a stratified sample, the clusters to be included are selected randomly, and all members of each selected cluster are included.

D. In a cluster sample, random samples from each strata are included.

E. In a cluster sample, the clusters to be included are selected randomly, and all members of each selected cluster are included.

F. In a cluster sample, the only samples possible are those including every kth item from the random starting position.

G. In a stratified sample, random samples from each strata are included.

I. In a stratified sample, the only samples possible are those including every kth item from the random starting position.

A. In a cluster sample, every sample of size n has an equal chance of being included.

G. In a stratified sample, random samples from each strata are included.

E. In a cluster sample, the clusters to be included are selected randomly, and all members of each selected cluster are included.

B. In a stratified sample, every sample of size n has an equal chance of being included

## Now let’s take a look at the options given:

F. In a cluster sample, the only samples possible are those including every kth item from the random starting position: The statement is FALSE because, in the cluster sample, all items from the cluster are selected.

A. In a cluster sample, every sample of size n has an equal chance of being included: The statement is very TRUE because if we have a sample and we decide to divide the sample into clusters of size n then every cluster has an equal chance of being selected. Clusters here are selected randomly.

B. In a stratified sample, every sample of size n has an equal chance of being included: The statement is TRUE because samples are taken from elements, not stratas.

C. In a stratified sample, the clusters to be included are selected randomly, and then all members of each selected cluster are included: The statement is FALSE because this is the definition of a cluster sample.

D. In a cluster sample, random samples from each strata are included: The statement is FALSE.because this is the definition of stratified sample.

E. In a cluster sample, the clusters to be included are selected randomly, and all members of each selected cluster are included. The statement is TRUE because this is the definition of cluster sample.

G. In a stratified sample, random samples from each strata are included: The statement is TRUE because in a stratified sample we take a random sample.

I. In a stratified sample, the only samples possible are those including every kth item from the random starting position: The statement is FALSE because different methods can be used to select our sample from each strata.

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## Definition of Stratified Sampling

In statistics and research, stratified sampling is dividing a population into subgroups, called strata, based on one or more variables. The population is then sampled proportionately from within each stratum using a random process.

### Overview

• In this approach, the population is initially separated into subgroups (or strata) that all have a common trait.
• It is employed when we want to ensure that all the subgroups are represented, and reasonably anticipate that the measurement of interest will fluctuate.
• Equal sample sizes from each stratum are taken to create the study sample (Equal Allocation).
• Additionally, it might be useful to use proportionate sampling to select non-equal sample sizes from each stratum.
• It would be appropriate to select the sample numbers from each hospital proportionally in a study of the health outcomes of nursing staff in a county, for instance, if there are three hospitals, each with a different number of nurses (hospital A has 500 nurses, hospital B has 1000, and hospital C has 2000). (e.g.10 from hospital A, 20 from hospital B, and 40 from hospital C).
• As opposed to simple random sampling, which would overrepresent nurses from hospitals A and B, this ensures a more realistic and accurate evaluation of the health outcomes of nurses throughout the county. It is important to consider how the sample was stratified at the analysis stage.
• By decreasing sample bias, stratified sampling increases the accuracy and representativeness of the results; yet, it can be challenging to choose the characteristic(s) to stratify against without knowledge of the proper sampling frame characteristics.

## Definition of Cluster Sampling

Cluster sampling is a subtype of probability sampling in which the population is separated into groups (clusters) first, and then a sample is randomly chosen from each cluster.

### Overview

• A clustered sample, as opposed to an individual sample, uses subsets of the population as the sampling unit.
• The population is broken down into clusters, which are chosen at random to be a part of the study.
• Clusters are typically already identified; for instance, specific towns maybe 42 designated as clusters. All participants in the selected clusters are then included in the research when using single-stage cluster sampling.
• In a two-stage cluster sampling procedure, some people are randomly chosen from each cluster to be included.
• Cluster sampling can be more effective when a study spans a large geographic area than simple random sampling. For example, it is simpler to contact many people in one township than a small number of people in many townships.
• If the selected clusters are not representative of the population, there is an increased chance of bias. As a result, the sampling error rises.

## Differences Between Stratified Sampling and Cluster sampling.

### 1. In terms of their definition

Stratified sampling is a probability sampling in which the population is divided into subgroups (strata), and then a random sample is taken from within each stratum by first randomly choosing a single element, and then choosing additional elements from among those elements that belong to the same stratum.

In cluster sampling, the population is divided into clusters, and then a random sample is taken from each cluster by first randomly choosing a single element within each cluster, and then choosing additional elements from the elements that belong to the same cluster.

### 2. In terms of sampling the individuals

In stratified sampling, the sample is obtained by selecting a sufficient number of individuals. Hence, each group has a roughly equal number of elements, and then randomly selecting elements from the selected individuals. In cluster sampling, the sample is obtained by randomly choosing elements from within each cluster.

### 3 . In terms of homogeneity

In stratified sampling, if the population is divided into subgroups, the elements (individuals or clusters) within each subgroup must be similar before taking a sample. For example, if we want to study the voting behavior of men and women, men and women must have equal rights. In other words, men and women are homogeneous in this regard.

In cluster sampling, homogeneity is not required for each individual or cluster. For example, if we want to study the voting behavior of men, women, whites, and blacks, homogeneity is not required.

### 4. In terms of objectives

In stratified sampling, the objective is to make the sample more representative of the population. This is because a random sample has a greater chance of representing the population because it includes a greater number of individuals than a simple random sample. It is difficult to achieve a representative sample from clusters because it is difficult to verify whether each cluster member appears in the final sample is truly representative of that specific cluster.

### 5. In terms of population elements

In stratified sampling, the population elements are selected according to their characteristics. For example, if we want to study the voting behaviors of women and men in China, we will first select a certain number of counties or townships with relatively large populations so that they can be divided into subgroups (strata), and then randomly sample from within the strata. In cluster sampling, population elements are not selected according to their characteristics.

### 6. In terms of heterogeneity

In stratified sampling, the population elements are heterogeneous before the sample is selected. In cluster sampling, no restriction is placed on the population elements when a sample is being determined.

Based on the above differences, we can see that stratified sampling is more scientific and precise than cluster sampling. In terms of scientific accuracy and precision, stratified sampling is better than cluster sampling.