A researcher wants to study the relationship of family size to income. He/She classifies population into different income slabs and then takes a random sample from selected slabs. Which one of the following techniques is he/she working with?

Question

Prepp Team · Accepted Answer

Understanding Sampling Techniques in Research

Let's analyze the research method described in the question. The researcher wants to investigate the relationship between family size and income. To do this, they first divide the entire population into specific groups based on their income levels. These income groups are referred to as 'income slabs'. After classifying the population into these distinct income slabs, the researcher proceeds to select a random sample of individuals from within the selected slabs.

This process of dividing the population into subgroups or 'strata' based on a characteristic (in this case, income) and then taking a sample (specifically, a random sample) from each stratum is a defining characteristic of a particular sampling method. Let's look at the options provided and see which one matches this description.

Analyzing the Sampling Options

We are given four potential sampling techniques:

Cluster sampling
Random sampling (often implying Simple Random Sampling)
Stratified random sampling
Systematic sampling

What is Stratified Random Sampling?

Stratified random sampling involves the following steps:

Divide the population into distinct, non-overlapping subgroups called strata. These strata are typically formed based on shared characteristics relevant to the study (like age, gender, income level, education, etc.).
Ensure that each member of the population belongs to only one stratum.
From each stratum, take a random sample of individuals. The sample size from each stratum can be proportional to the stratum's size in the population or based on other criteria.
Combine these samples from all strata to form the final sample for the study.

The researcher in the question divides the population into income slabs, which act as strata. Then, they take a random sample from these selected slabs (implying from each slab chosen). This perfectly aligns with the definition of stratified random sampling.

Why Other Options Don't Fit

Cluster sampling: In cluster sampling, the population is divided into clusters (often geographical areas). Then, a random sample of *clusters* is selected, and *all* or a sample of individuals within the selected clusters are surveyed. The method described in the question divides by income slabs (characteristics), not clusters, and samples from *each* slab, not from selected clusters.
Random sampling (Simple Random Sampling): Simple random sampling involves selecting individuals from the entire population purely by chance, where every individual has an equal probability of being selected. The method in the question is more structured; it involves pre-defined income groups from which samples are drawn, not a single random selection from the whole population list.
Systematic sampling: This technique involves selecting individuals at regular intervals from a list, starting from a random point. For example, selecting every 10th person from a list. This method is not described by the researcher's process of dividing by income slabs and sampling within them.

Based on the methodology described – dividing the population into income slabs (strata) and then taking a random sample from these selected slabs (from each stratum) – the technique being used is clearly stratified random sampling.

Revision Table: Comparing Sampling Methods

Sampling Method	How it Works	Example (Income Study Context)
Stratified Random Sampling	Divide population into strata (subgroups based on characteristics); randomly sample from EACH stratum.	Divide population by income levels (slabs); randomly sample from each income slab.
Cluster Sampling	Divide population into clusters (often geographical); randomly select some clusters; sample ALL or some within SELECTED clusters.	Divide city into blocks (clusters); randomly select blocks; survey all households in selected blocks.
Simple Random Sampling	Select individuals randomly from the entire population; every individual has an equal chance.	Put all names in a hat and draw names randomly.
Systematic Sampling	Select individuals at regular intervals from a list, starting point is random.	Get a list of all households; pick a random start point; select every 50th household.

Additional Information on Stratified Sampling

Stratified random sampling is particularly useful when:

The population is heterogeneous (diverse) with respect to the characteristic being studied. Income levels vary greatly, making stratification by income beneficial.
You want to ensure representation from all important subgroups (strata) in your sample. This is important for studying how factors like family size relate to income across different economic groups.
You want to potentially reduce sampling error compared to simple random sampling, especially if the variable of interest is strongly related to the stratification variable.

By using income slabs as strata, the researcher ensures that their study includes participants from low, middle, and high-income groups, providing a more representative picture of the family size-income relationship across the entire population.