Research Writing

# Stratified sampling

Stratified sampling is a statistical sampling technique that consists of dividing a population into different subgroups or strata. Stratified sampling advantages and disadvantages

Stratified sampling is a technique or procedure in which the population under study is divided into different subgroups or strata. An essential characteristic of stratification is that each element must belong to a single stratum, so that the strata are exclusive (they do not overlap).

To achieve an adequate stratification, a variable must be defined that effectively allows assigning each element a single group or stratum.

## How does stratified sampling work?

The procedure used to carry out stratified sampling has several stages. We describe the most relevant below:

1. Define the target (total) population
2. Choose the stratification variables and how many strata will exist.
3. Identify each item in the population and assign a unique identifier. Each element of the population must belong to a single stratum.
4. Determine the size of each stratum (explained in the next section)
5. The elements of each stratum are randomly selected until the specific number defined for each stratum is obtained. Stratified sampling advantages and disadvantages

## Types of stratified samples

The type of stratified sampling is defined by the size that we define for each stratum. The types of sampling are as follows:

### 1-Proportional stratified sampling:

In this approach, each stratum sample size is directly proportional to the size of the total population. That means that each sample of strata has the same sampling fraction.

Proportional stratified random sampling formula: nh = (Nh / N) * n

nh = Sample size of stratum h

Nh = Population size in relation to stratum h

N = Size of the entire population

N = Full sample size

If you have 4 strata with 500, 1000, 1500, 2000, etc., and the research organization selects ½ as the sampling fraction. An investigator must select 250, 500, 750, 1000 members from the respective state.

Stratum TO B C D
Population size 500 1000 1500 2000
Sample fraction ½ ½ ½ ½
Final sample 250 500 750 1000

Regardless of the sample size of the population, the sampling fraction will remain uniform across all strata. Stratified sampling advantages and disadvantages

### 2-Disproportionate stratified sampling:

The sampling fraction is the main differentiating factor between proportional and disproportionate stratified sampling. In a disproportionate sampling, each stratum has a different sampling fraction.

The success of this sampling method depends on the precision of the investigator in assigning fractions. If the assigned fractions are not accurate, the results may be biased due to overrepresented or underrepresented strata.

Stratum TO B C D
Population size 500 1000 1500 2000
Sample fraction ½ 1/3 ¼ 1/5
Final sample 250 333 375 400

## Stratified sampling example

Researchers and statisticians use stratified sampling to analyze relationships between two or more strata. As this sampling involves multiple layers or strata, it is crucial to calculate the strata before calculating the sample value. Stratified sampling advantages and disadvantages

Now that you know how to do stratified sampling, here is a classic example:

Let’s say that 100 (Nh) students in a school of 1000 (N) students are asked questions about their favorite subject. It is a fact that first graders will have different preferences than fifth graders. For the survey to yield accurate results, the ideal way is to divide each grade into several strata.

Here is a table of the number of students in each grade:

5 150
6 250
7 300
8 200
9 100

Calculate the sample for each grade using the stratified sampling formula:

Stratified sample (n1) = 100/1000 * 150 = 15
Stratified sample (n2) = 100/1000 * 250 = 25
Stratified sample (n3) = 100/1000 * 300 = 30
Stratified sample (n4) = 100/1000 * 200 = 20
Stratified sample (n5) = 100/1000 * 100 = 10