Stratified sampling method - proportional stratified sample and disproportional stratified sample

The stratified sampling method is used when the population is heterogeneous rather than homogeneous.

A heterogeneous population is composed of unlike elements such as male/female, rural/urban, literate/illiterate, high income/low income groups, etc.

In such cases, use of simple random sampling may not always provide a representative sample of the
population.

In stratified sampling, we divide the population into relatively homogeneous groups called strata. Then we select a sample using simple random sampling from each stratum.

There are two approaches to decide the sample size from each stratum, namely, proportional stratified sample and disproportional stratified sample. With either approach, the stratified sampling guarantees that every unit in the population has a chance of being selected. 

We will now discuss these two approaches of selecting samples.

Imagine you're a researcher studying political opinions, and you want to ensure your findings represent the whole population. But the population itself is diverse - there might be young voters, retirees, and working professionals. A simple random sample might miss a group entirely!

This is where stratified sampling comes in. You divide the population (voters) into subgroups (strata) based on relevant characteristics (age groups). Then, you draw a random sample from each subgroup.

Choosing sample sizes from these subgroups is where proportional and disproportional stratified sampling differ:

• Proportional Stratified Sample: Here, the sample size within each subgroup reflects its proportion in the entire population. Imagine voters are 60% young, 30% retirees, and 10% working professionals. In a sample of 100, you'd take 60 from young voters, 30 from retirees, and 10 from professionals. This ensures all groups are represented proportionally.

  • Example: A school administrator wants to survey students about a new lunch program. The school has 60% freshmen, 20% sophomores, 15% juniors, and 5% seniors. If the administrator wants a total sample of 200 students, they would take a proportional stratified sample: 120 freshmen, 40 sophomores, 30 juniors, and 10 seniors.

• Disproportional Stratified Sample: This approach focuses on specific subgroups you want to study more intensely. Maybe you're particularly interested in the opinions of young voters (60% of the population). You could take a larger sample, say 70, from them, while taking a smaller sample, like 20 each, from retirees and professionals. This way, you get more data on the group of interest (young voters) for better analysis.

  • Example: Researchers want to understand the movie preferences of different age groups. They know teenagers are a smaller population segment (15%) but have a strong influence on movie trends. So, they take a disproportional stratified sample: 40 teenagers, 30 young adults (25% of population), 20 middle-aged adults (40% of population), and 10 seniors (20% of population). This allows a more focused study on teenagers' preferences.