Stratified Sampling

Summary

This script explains the concept of stratified sampling, a technique that involves dividing a population into distinct groups, or strata, based on shared characteristics. The video demonstrates how to apply simple random sampling (SRS) within each stratum to select a sample size of 12 individuals, ensuring equal representation from different groups. The process emphasizes the importance of avoiding repetition and maintaining randomness to achieve a balanced and representative sample.

Takeaways

• 📚 The script discusses stratified sampling, a technique that builds upon simple random sampling (SRS).
• 🔄 Stratified sampling is not abbreviated as SS, but simply referred to by its name.
• 👥 The population is divided into groups based on a specific characteristic, creating strata.
• 🎨 The example given uses color to group individuals, emphasizing it's a characteristic for grouping, not a discriminatory act.
• 🔢 The goal is to have an equal or nearly equal number of individuals from each group in the sample.
• 🔄 After stratifying the population, SRS is used within each stratum to select individuals for the sample.
• 📝 The script illustrates the process of numbering individuals within each stratum to facilitate SRS.
• 🚫 It's important to avoid selecting the same individual more than once within a stratum.
• 🔢 The script provides a step-by-step example of selecting four individuals from each of three strata to achieve a sample size of twelve.
• 📉 The process involves random selection within each stratum, ensuring that the sample is representative of the entire population.
• 📈 Stratified sampling helps to ensure that the sample is more representative of the population's diversity compared to simple random sampling.

Q & A

What is stratified sampling?

Stratified sampling is a technique where the population is divided into subgroups, or strata, based on a specific characteristic, and then simple random sampling (SRS) is applied to each stratum to obtain a representative sample from each group.

Why is stratified sampling used instead of simple random sampling alone?

Stratified sampling is used to ensure that all subgroups within a population are represented in the sample, which can lead to a more accurate and representative sample, especially when there are distinct and important differences between the subgroups.

How does the script define a 'stratum'?

In the script, a 'stratum' is defined as a subgroup of the population that has been grouped together based on a specific characteristic, such as color or appearance in the example provided.

What is the purpose of grouping individuals by a characteristic in stratified sampling?

Grouping individuals by a characteristic in stratified sampling ensures that the sample obtained from each group is representative of that specific characteristic, which helps in getting a more accurate overall sample.

How does the script ensure that no individual is sampled more than once?

The script ensures that no individual is sampled more than once by skipping over numbers that have already been selected during the simple random sampling process for each stratum.

What is the sample size the script aims to achieve using stratified sampling?

The script aims to achieve a sample size of 12 using stratified sampling, with an equal number of individuals (four) being sampled from each of the three strata.

Why does the script use a different set of numbers for SRS in each stratum?

The script uses a different set of numbers for SRS in each stratum to ensure that the random selection process is independent for each group, which helps in maintaining the randomness and representativeness of the sample.

What happens if the same number comes up more than once during the SRS process in a stratum?

If the same number comes up more than once during the SRS process in a stratum, that number is skipped to avoid sampling the same individual twice.

How does the script ensure equal representation from each stratum in the sample?

The script ensures equal representation from each stratum by sampling an equal number of individuals from each stratum using SRS, thus maintaining the proportionate representation in the sample.

What is the advantage of stratified sampling over simple random sampling?

The advantage of stratified sampling over simple random sampling is that it can reduce sampling error by ensuring that all subgroups are represented in the sample, which can lead to more accurate estimates and a better understanding of the population.

Can stratified sampling be used when the population characteristics are unknown?

Stratified sampling requires knowledge of the population characteristics to group individuals into strata. If the characteristics are unknown, it would not be possible to use stratified sampling effectively.

Outlines

00:00

🔍 Introduction to Stratified Sampling

The script introduces stratified sampling as a technique to divide a population into distinct groups, or strata, based on a specific characteristic before sampling. It builds upon the concept of simple random sampling (SRS) by applying it to each stratum separately to ensure representation from each group. The process begins with grouping individuals by color in this case, creating strata for blue, black, and red individuals. The goal is to select an equal number of individuals from each stratum to form a sample size of 12, reflecting the diversity of the entire population.

05:01

📝 Executing Stratified Sampling with SRS

This paragraph details the execution of stratified sampling using simple random sampling within each stratum. The process involves numbering individuals within each group and then randomly selecting members to interview, ensuring no repetition within a stratum. The script demonstrates the selection process by choosing four individuals from each of the three strata: blue, black, and red. It emphasizes the importance of avoiding the same number selection for each group to maintain randomness. By the end of the paragraph, a sample size of 12 is achieved, illustrating how stratified sampling can maintain the proportionate representation of different groups within the population.

Keywords

💡Stratified Sampling

Stratified sampling is a statistical method where a population is divided into subgroups, or strata, that share similar characteristics. The goal is to ensure that the sample is representative of the entire population by including members from each subgroup. In the video, this technique is used to create a sample of 12 individuals from a larger group of dog walkers or voters, divided by color to represent different strata.

💡SRS (Simple Random Sampling)

Simple random sampling (SRS) is a method where every member of the population has an equal chance of being selected for the sample. In the context of the video, SRS is used within each stratum to select individuals randomly, ensuring that the sample from each group is unbiased and representative of that specific stratum.

💡Population

The term 'population' in statistics refers to the entire group that is the subject of a study. In the video, the population consists of dog walkers or voters, and the aim is to understand this group better by sampling a subset of it.

💡Sample Size

Sample size is the number of individuals or observations included in a sample. The video script specifies a sample size of 12, which is the number of individuals the speaker intends to select from the population using stratified sampling.

💡Strata

In stratified sampling, 'strata' refers to the subgroups within the population that share similar characteristics. In the video, the strata are defined by color, with each color representing a different group of individuals.

💡Characteristic

A characteristic is a distinguishing feature or quality that can be used to categorize individuals within a population. In the video, the characteristic used for stratification is the color of the individuals, which is a visual attribute.

💡Grouping

Grouping in the context of the video refers to the process of organizing individuals into strata based on shared characteristics. The speaker groups the population by color to prepare for stratified sampling.

💡Representativeness

Representativeness in sampling means that the sample accurately reflects the characteristics of the entire population. Stratified sampling aims to enhance the representativeness of the sample by ensuring that each stratum is proportionally represented.

💡Bias

Bias in sampling refers to systematic errors that can distort the results of a study. The video script discusses avoiding bias by using SRS within each stratum to select individuals randomly, thus minimizing the chance of skewed results.

💡Interview

In the context of the video, 'interview' refers to the process of selecting and engaging with individuals from the sample for the purpose of data collection. The speaker plans to interview the individuals selected through stratified sampling.

💡Random Generation

Random generation is the process of selecting numbers or items without any pattern or order, which is crucial for SRS. In the video, the speaker uses random generation to pick numbers for selecting individuals from each stratum.

Highlights

Introduction to stratified sampling as a technique following the discussion on simple random sampling (SRS).

Explanation of stratified sampling, emphasizing the need for equal representation from each group.

Decision to use the same population as in the previous example for consistency.

Setting a sample size of 12 for the stratified sampling exercise.

Grouping individuals by a specific characteristic, such as color, to form strata.

Clarification that grouping is not meant to discriminate but to categorize for sampling purposes.

Demonstration of the process of dividing the population into distinct strata.

Use of SRS within each stratum to select individuals for the sample.

Numbering individuals within each stratum to facilitate SRS.

Selection of four individuals from each of the three strata to meet the desired sample size.

Illustration of the SRS process, including the selection of numbers and corresponding individuals.

Emphasis on avoiding the repetition of selecting the same individual within a stratum.

Continuation of the SRS process across different strata to build the sample.

Finalization of the sample selection with a total of 12 individuals.

Summary of the stratified sampling process and its reliance on SRS within each stratum.

Highlighting the importance of stratified sampling for ensuring representation from different groups.

Transcripts

continue to talk about sampling

techniques this time we're going to talk

about stratified sampling and last time

we talked about SRS or simple random

sampling we're going to use that in our

stratified sampling now this is not

called SS it's just stratified sampling

I've got the same population as last

time let's say these are my dog walkers

or my voters whatever they may be and I

still want a sample size of mmm this

time let's say I want a sample size of

12 okay so what I end up doing in

stratified sampling is I want an equal

or close to an equal amount of people

from each group of people so the first

thing I need to do is group these people

so I'm going to put all of my blue guys

over here and I'm going to put all of my

red ladies over here this will take a

couple minutes to do but what I'm doing

is I am putting them into groups and I'm

grouping them by some kind of

characteristic in this case I'm grouping

them by color and the way that they look

I hope that doesn't sound like I'm

discriminating against anybody or

profiling or anything that's not what

I'm looking to do here I'm just grouping

them by a characteristic and the

characteristic that I decided to go with

is the way that they look almost

finished here

let's take all of these and move them

down a little bit this guy up here with

his group and there we go now each one

of these groups is called a strata so

this would be my blue guy strata this

would be my black guy strata this would

be my red girl strata each one is a

strata they are grouped by some kind of

characteristic so I have stratified them

or put them into strata now comes the

time when I use SRS simple random

sampling I want to get four people from

the blue strata four people from the

black strata and four people from the

red strata so that I can create my

sample size of 12 well if I use SRS when

I then do is number each one one two

three four five six seven eight nine and

ten from my blue and I number these guys

here one two three four five six seven

eight nine and ten and then I also

number the girls here one two three four

five six seven eight nine I skip over

one one two three four five oh my number

too many here let me start that over

nothing wrong with making mistakes six

seven eight nine and then here's number

ten I would then use SRS for each group

I don't want to use the same numbers for

each group so I want to use SRS for the

blue group and I would choose let's say

the numbers that came up for the first

group or the numbers two so I'm going to

interview this guy seven I'm going to

interview this guy five so I'm going

interview this guy and Ted interview

this guy and I'm not finished with my

sample because I want to staple size of

twelve so I've got four from this strata

then I go over to the black strata or

the black the the group of black

characters so here we go I would use SRS

again and the numbers that come up are

seven some airView him and four and I

interview him 10 I'm going to interview

him and then seven comes up again do I

interview seven again no I just skip

over that number it's be pointless to

interview number seven a second time so

I continue to randomly generate numbers

or draw numbers out of a hat for SRS and

the next number that comes up is one so

I'm going to interview this guy well

I've only got one two three four five

six seven eight people for my sample

size now I go to my red group or my red

strata and I use SRS to get four more

people or randomly choose four more

people from this group and in this group

I get number three so I interview her

number nine I interview her number ten I

interview her now where three comes up

again so I skip it and then number six

comes up so I interview her and I have

now got my one two three four five six

seven eight nine ten eleven twelve

people for my interview and I have a

sample size of twelve simple random

sampling is used for each group each

group is called a strata and that is

stratified sampling