Probability and Statistics > Sampling > Stratified Random Sample

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## Stratified Random Sampling: Definition

Stratified random sampling is used when your population is divided into strata (characteristics like male and female or education level), and you want to include the stratum when taking your sample. The stratum may be already defined (like census data) or you might make the stratum yourself to fit the purposes of your research. Stratified random sampling is very similar to random sampling. However, these samples are more difficult to create as you must have detailed information about what categories your population falls into.

## How to Perform Stratified Random Sampling

To perform stratified random sampling, take a random sample from within each category or stratum. Let’s say you have a population divided into the following strata:

- Category 1: Low socioeconomic status — 39 percent
- Category 2: Middle class — 38 percent
- Category 3: Upper income — 23 percent

To get the stratified random sample, you would randomly sample the categories so that your eventual sample size has 39 percent of participants taken from category 1, 38 percent from category 2 and 23 percent from category 3. What you end up with is a mini representation of your population. According to University of California at Davis, the following steps should be taken to obtain the stratified sample:

- Name the target population.
- Name the categories (stratum) in the population.
- Figure out what sample size you need.
- List all of the cases within each stratum.
- Make a decision rule to select cases (for example, you might select the items using the largest set of random numbers).
- Assign a random number to each case.
- Sort each case by random number.
- Follow your decision rule (#5 above) to choose your participants.

Stratified random sampling for larger data sets is usually performed using statistical software. For example, click here for the procedures in SAS.

## How to Get a Stratified Random Sample: Example

“Stratified” means “in layers,” so in order to get a stratified random sample you first need to make the layers. What layers you have depends on characteristics of your population. For example, if you are surveying U.S. residents about their plans for retirement, you might want your layers to represent different age groups. The sample size for each strata (layer) is proportional to the size of the layer:

Sample size of the strata = size of entire sample / population size * layer size.

## How to Get a Stratified Random Sample: Steps

**Sample question:** You work for a small company of 1,000 people and want to find out how they are saving for retirement. Use stratified random sampling to obtain your sample.

Step 1: **Decide how you want to stratify (divide up) your population.** For example, people in their twenties might have different saving strategies than people in their fifties.

Step 2: **Make a table representing your strata**. The following table shows age groups and how many people in the population are in that strata:

Age | Total Number of People in Strata |

20-29 | 160 |

30-39 | 220 |

40-49 | 240 |

50-59 | 200 |

60+ | 180 |

Step 3: **Decide on your sample size.** If you don’t know how to find a sample size, see: Sample size (how to find one). For this example, we’ll assume your sample size is 50.

Step 4: **Use the stratified sample formula **(Sample size of the strata = size of entire sample / population size * layer size) to calculate the proportion of people from each group:

Age | Number of People in Strata | Number of People in Sample |

20-29 | 160 | 50/1000 * 160 = 8 |

30-39 | 220 | 50/1000 * 220 = 11 |

40-49 | 240 | 50/1000 * 240 = 12 |

50-59 | 200 | 50/1000 * 200 = 10 |

60+ | 180 | 50/1000 * 180 = 9 |

Note that all of the individual results from the stratum add up to your sample size of 50: 8 + 11 + 12 + 10 + 9 = 50

Step 5: **Perform random sampling** (i.e. simple random sampling) in each stratum to select your survey participants.

*That’s how to get a stratified random sample!*

**Tip:** Each element in your population should only fit into one stratum. In other words, one person cannot be in more than one group.

If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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The example has really helped me understand the whole technique.

very helpful

Thank you it is very helpful. Please can you tell me how to get the relevant categories of age. 20 -29; 30 -39 etc Do we need to use a cluster analysis ?

You could use k-means clustering, yes.

Hi. Can we stratfied sample according to region (north, central, south)? My sample of study is teachers. So can i stratified them based on

1st layer is Region – north central south

Then i choose randomly 1 district for each region.

2nd layer based on urban and rural.

*The geographical area that i want to conduct my study is too large.

You can stratify by pretty much anything, as long as it makes sense to you — only you know your data!

Hi,

I am creating stratified sampling for conversion of a user in a user-journey and Calculated the Arear Under Curve for model verification using ROC. But I want my sampling error to reduce so that I can have better AUC & what parameter are more important for my models computation efficiency.

Can you Help?

Hi, Andale,

I want to have stratified random sampling from healthcare workers in X hospital because the healthcare workers include 33 nurses, 20 midwives, 10lab technicians, 8 pharmacists, 9 doctors, and 20 cleaners. the total number of the study population (healthcare workers) is 100, and the sample size I determined is 50. so Can I directly apply this technique?

Hi, Andale,

Remember my research topic is entitled as “Knowledge, attitude and practice of healthcare workers towards occupational hazards in X hospital.

May you help the sample technique applicability with this?

Hi, Andale,

May I stratify the healthcare workers by groups of same professions for stratification?

Yes.

Yes, you can use this technique.

is there formular used to collect the 50 that was being used to calculate the stratums or the 50 is just a random number

In this case, it’s just a random number I chose for the example.

Hi, Andale

I want to assess the attitudes of societies on the effects of parental divorce on children’s well-being from parents’ perspective at ‘X’ kebele. What types of sampling techniques I must use?

Please! help me soon

It depends on more factors than what you’ve written here. Quantitative or qualitative study? Do you want to use probability or non probability sampling? Are you writing this for school (if so your prof should have guidelines) or for a journal? (in which case you’d want to look at prior similar research). etc. You can find a list of sampling techniques here.

is there a formula through which a sample size of 60 can be obtained from a population of 1200

You could use the formula in Step 4:

Sample size of the strata = size of entire sample / population size * layer size

Hi, our desired sample size is 71. And we want 3 strata. We computed the sample size per strata but it has decimal places. Do we round up or not? If we round up, our sample size become more than 71 but if we don’t, it’s less. Can we just use the same sample size even if the population per strata is not the same?

Please where a total population is about 128000 made up of Mechanics, Welders and painters. How should I determine the sub population since is unknown?

hello there.. anyone who could help, please.. thank you..

Population of household (N)=10,000;

Distribution of household characteristics of heads of families as respondents:

Age: young=35%, middle age = 45%, old =20%

income: Low Bracket = 30%, middle bracket = 55%, high bracket = 15 %

Occupation: Self- employed/practitioner = 20%, Business/ Store Owners – 10%, Employees = 70%

Education: High School = 25%, Vocational = 10%, College = 65%

Required: 1. Determine sampling size based on 95% of level of confidence.

2. Distribute or stratify sample size according to:

a. age and education;

b. income and population.

Thank you vey much in advance for anyone who could be able to answer it..

Hello, Gwen,

You have a lot of questions here. You might have better luck posting one question at a time and letting us know where you get stuck (i.e. try to answer the question).