# 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:

- Define the target (total) population
- Choose the stratification variables and how many strata will exist.
- Identify each item in the population and assign a unique identifier. Each element of the population must belong to a single stratum.
- Determine the size of each stratum (explained in the next section)
- 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:

Grade | Number of students |
---|---|

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 |

## Advantages and disadvantages of stratified sampling

**Among the main advantages are:**

- It is possible to make estimates not only for the population in general but also for each stratum in particular.
- Better use is made of the knowledge that the researcher has about the population under study.
- It allows the use of different estimation techniques including the relationship between different strata.
**Stratified sampling advantages and disadvantages**

**Among the main disadvantages are:**

- More information is required than studying the general population, either to stratify or to determine the weight of each stratum in the population.
- It is more expensive both in time and in work.
- Stratification selection can be complex if stratification variables are not well determined or a large number of strata is defined.