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# Stratified Random Samples

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Author: Sophia Tutorial
##### Description:

This lesson will explain stratified random sampling.

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Tutorial

This tutorial is going to be talking about Stratified Random Sampling. It's a random sampling procedure that subdivides the population into groups. This lesson will focus on:

1. Stratified Random Sample
2. Strata

## 1. STRATIFIED RANDOM SAMPLE

Stratified random sampling is a method where the population is subdivided into groups called strata. The strata are homogeneous with a characteristic that may affect the overall sample.

• Stratified Random Sample
• A random sampling method where individuals are separated into homogenous groups, then simple random samples are taken within each group.

A high school has just adopted a new, healthy lunch provider, and they would like to solicit student opinion on the healthy lunch options. The school has 100 freshmen, 110 sophomores, 120 juniors, and 90 seniors.

How could the school could select a simple random sample of 42 students? Think of ways that 42 students could be chosen, each having an equal chance of being selected.

There are two ways this could be done and both ways require assigning each student a unique number 1 to 420 (total number of students). Once this is done, you could:

1. Use a random number generator to select 42 numbers, ignoring repeats. The students who corresponded to those numbers will be surveyed about the school's new, healthy options.
2. Put the 420 student names in a hat and draw out 42.

Thinking back to the same scenario of a new, healthy lunch provider for 100 freshman, 110 sophomores, 120 juniors, and 90 seniors.

Is there way that the study might improve and guarantee an accurate cross-section of students between the grades? After all, freshman might feel differently about the healthy options than seniors, so it will be important to have a individuals from each grade weigh in on the lunch options.

Hopefully you came up with something like this: since 42 is 10% of the school's population, your survey should be 10% of each grade. Make sense?

Ten percent of the freshmen class is 10, so you would want to randomly select 10 individuals from the fresh class to participate. You would want to select 11 sophomores to participate since that is 10% of the class, along with 12 juniors and 9 seniors. From here, you would want to use a similar simple random sample method like putting names in a hat or assigning everyone a unique number and randomly selecting numbers.

## 2. STRATA

Strata are groups with homogeneous characteristic(s). They are separated by the characteristic that we think might affect the overall sample. This is to avoid having too many of the sample to be having this one characteristic that may affect the sample.

Once the groups are in place, a simple random sample is carried out within each stratum. And you can have as many strata as you please, but they must be roughly homogeneous.

• Stratum/Strata
• The homogenous groups in a stratified random sample. All individuals in each stratum have something in common, and we would like to see how that affects the outcome of the sample.

IN CONTEXT

Pretend you’ve subdivided billiard balls into low, middle, and high numbers, which is a common way to present strata.

What you can do to take a stratified random sample of these 15 is to put all the low-valued balls in a hat, put all the middle-valued balls in a hat, put all the large-valued balls in a hat, and randomly select, say, two from each hat. And then you can have a stratified random sample of six. You're guaranteed to have exactly two low, exactly two middle, and exactly two high.

The bottom line behind a stratified sample is to say that if you don't break your population down into strata, you risk misrepresenting the population. So you pull from each group that exhibits that defining characteristic to make sure everyone is represented.

In a stratified random sample, the population is broken down into homogeneous groups called "strata." The reason for this is to separate an otherwise homogeneous group that exhibits a characteristics that may misrepresent the population.

The idea is to force them into groups and then take a simple random sample within each of the strata.

Good luck!

Source: This work is adapted from Sophia author Jonathan Osters.

Terms to Know
Stratified Random Sample

A random sampling method where individuals are separated into homogenous groups, then simple random samples are taken within each group.

Stratum/Strata

The homogenous groups in a stratified random sample. All individuals in each stratum have something in common, and we would like to see how that affects the outcome of the sample.