Sampling: Population vs. Sample, Random Sampling, Stratified Sampling

Summary

The video script delves into the concept of sampling as a method for researchers to gather data from a population. It explains the difference between a population and a sample, emphasizing the impracticality of surveying every individual within a large population, such as all Americans. The script introduces two primary forms of sampling: non-probability and probability sampling. It focuses on probability sampling, which includes random sampling and stratified sampling, as a more reliable method for ensuring that every member of the population has an equal chance of being included in the study. The video also discusses the importance of a representative sample for drawing accurate inferences about the population. It concludes by illustrating how these sampling methods could be applied to a hypothetical study on the support for marijuana legalization among Americans, suggesting the use of stratified sampling to account for the country's diversity.

Takeaways

• 🌟 **Population vs Sample**: The population is the entire set of subjects you wish to study, while a sample is a part or subset of that population.
• 🔍 **Representative Sample**: A good sample should be representative of the population in terms of various characteristics like age, gender, and income to allow for accurate inferences.
• ⚖️ **Sampling Methods**: There are two main forms of sampling: non-probability sampling (based on convenience or volunteer basis) and probability sampling (where every member has an equal chance to be included).
• 🎰 **Random Sampling**: Involves random selection from the population, ensuring every member has an equal chance to be included in the sample.
• 📦 **Stratified Sampling**: Divides the population into strata (subgroups) based on certain characteristics, then randomly selects from each stratum to ensure representation of each subgroup.
• 📈 **External Validity**: A representative sample leads to high external validity, meaning the findings can be generalized to the larger population.
• 🤔 **Sample Size Importance**: The size of the sample matters, depending on the size and variability of the population being studied.
• 📊 **Zip Codes for Random Sampling**: As an example, using zip codes can simplify random sampling by reducing a large population to a more manageable number of units.
• 🧩 **Stratified Sampling for Variability**: Especially useful for large and varied populations, ensuring that each subgroup is represented in the sample.
• ❌ **Sampling Bias**: A non-representative sample can lead to sampling bias, resulting in low external validity and potential errors in study conclusions.
• ✅ **Generalization to Population**: The goal of sampling is to make inferences about the population based on the sample, which is more feasible and cost-effective than studying the entire population.
• 📝 **Practical Application**: The concepts of sampling can be applied to real-world research questions, such as determining the percentage of Americans supporting the legalization of marijuana.

Q & A

What is the primary challenge in asking every American about their support for the legalization of marijuana?

The primary challenge is that it would be too time-consuming and expensive. The United States has over 330 million people, making it nearly impossible to reach every individual.

What is the difference between a population and a sample?

A population represents the entire set of something that you wish to study, which could be people, objects, or a specific subgroup. A sample is a part or a subset of the population, representing a smaller percentage of the total.

Why is sampling used in research?

Sampling is used because it is often impractical or impossible to study an entire population. By taking a representative sample, researchers can make inferences about the population based on the sample's characteristics.

What are the two main forms of sampling?

The two main forms of sampling are non-probability sampling and probability sampling. Non-probability sampling is often based on convenience or volunteer participation, while probability sampling involves random selection, giving every member of the population an equal chance to be included.

How does random sampling ensure that every member of the population has an equal chance to be included in the study?

Random sampling uses a process akin to picking names out of a hat, where individuals are selected randomly from the population. This can be done using a computer or an Excel sheet that randomizes the selection process.

What is the importance of a sample being representative of the population?

A representative sample ensures that all characteristics and features of the population, such as different ages, genders, incomes, and backgrounds, are reflected in the sample. This allows for better inferences and conclusions to be drawn about the population from the sample.

What is the concept of external validity in research?

External validity refers to the ability to generalize the findings of a study to the real world or the general population. A study with high external validity can confidently apply its results to the population at large.

What is sampling bias and how can it affect a study?

Sampling bias occurs when the sample is not representative of the population. This can lead to low external validity, meaning the results cannot be generalized to the population, potentially leading to errors in the study.

How does the size of the population and its variation influence the sample size needed for a study?

The size of the population and the amount of variation within it affect the sample size needed. Larger and more varied populations typically require a larger sample size to ensure that the sample is representative and that the study has high external validity.

How can zip codes be used in random sampling to study a large population like the United States?

Zip codes can be used to randomly select areas for study instead of individuals. By randomizing a list of zip codes, researchers can contact people within those selected areas, making the process more manageable and representative.

What is stratified sampling and when is it preferred over random sampling?

Stratified sampling involves dividing the population into subgroups, or strata, based on specific characteristics and then randomly selecting from each stratum. It is preferred over random sampling when the population has a lot of variability to ensure that every subgroup is represented in the sample.

How can stratified sampling be applied to determine the percentage of Americans who support the legalization of marijuana?

Stratified sampling can be applied by dividing the population into strata based on factors like gender, race, income, and educational background. Then, a random selection is made from each stratum to ensure that the sample is representative of the diverse population, allowing for more accurate inferences about the population's views on marijuana legalization.

Outlines

00:00

🔍 Understanding Population and Sample Basics

The first paragraph introduces the challenge of determining the percentage of Americans who support the legalization of marijuana. It explains the impracticality of surveying every American and introduces the concept of sampling as a solution. The difference between a population, which is the entire set of subjects being studied, and a sample, which is a subset of the population, is clarified. The importance of having a representative sample is emphasized to make accurate inferences about the population.

05:01

🎯 Probability Sampling: Random and Stratified

This paragraph delves into the types of probability sampling, which includes random sampling and stratified sampling. Random sampling is based on random selection, ensuring every member of the population has an equal chance to be included in the study. Stratified sampling, on the other hand, involves dividing the population into subgroups or 'strata' based on specific characteristics before conducting random selection from each stratum. The goal is to account for individual differences and make better inferences from the sample to the population.

10:01

📈 Applying Random Sampling to Surveys

The third paragraph discusses the practical application of random sampling, suggesting the use of zip codes to randomly select respondents across the United States. This method is more manageable than surveying 200 million people directly and ensures that every part of the country has an equal chance of being represented in the study. The paragraph also touches on the importance of sample size in relation to the size of the population and the amount of variation within it.

15:01

📊 Stratified Sampling for Varied Populations

The final paragraph focuses on stratified sampling as a method particularly useful for populations with significant variability. It illustrates how to divide the population into strata based on factors like gender, race, income, and educational background to ensure that each subgroup is represented in the sample. This approach is recommended for answering the question about marijuana legalization support, as it would account for the diverse demographics in America.

Keywords

💡Population

In the context of the video, 'population' refers to the entire set of individuals or items that a researcher wishes to study. It could be all people living in a city, a specific subgroup like men or women, or even objects like cars on the road. The population is represented by the letter 'N'. It is crucial for defining the scope of a study and is the basis for drawing conclusions through sampling.

💡Sample

A 'sample' is a subset of the population that is used to represent the whole for the purpose of a study. It is denoted by a lowercase 'n' and is chosen to be more manageable in size than the entire population. The sample allows researchers to make inferences about the population based on the characteristics of the sample, which is vital when studying a large and diverse group like the American population.

💡Sampling

Sampling is the process of selecting a portion of the population to study instead of the entire group. It is essential when the population is too large or diverse to study in its entirety, such as when trying to gauge the opinion of all Americans on a topic. The video discusses two main types of sampling: non-probability and probability sampling, with a focus on the latter for its ability to provide more accurate and representative results.

💡Random Sampling

Random sampling is a method of probability sampling where every member of the population has an equal chance of being included in the sample. It is akin to picking names out of a hat, ensuring fairness and representativeness. The video illustrates how random selection is fundamental to achieving a sample that can be generalized back to the population, thus maintaining high external validity.

💡Stratified Sampling

Stratified sampling is another probability sampling method used when the population has significant variability. It involves dividing the population into subgroups, or strata, based on specific characteristics like gender, race, or income. Then, a random sample is taken from each stratum to ensure that each subgroup is represented in the overall sample. This method is highlighted in the video as particularly useful for studying diverse populations like that of the United States.

💡Non-probability Sampling

Non-probability sampling is a method where samples are selected based on convenience or other non-random criteria. This approach, which includes convenience sampling and volunteer sampling, is less likely to produce a representative sample of the population. The video points out that while non-probability sampling might be easier or quicker, it can lead to biased results and lower external validity.

💡Representation

In the context of sampling, 'representation' means that the sample accurately reflects the characteristics of the population it is drawn from. A representative sample includes proportional parts of the population's various subgroups, such as different ages, genders, and income levels. The video emphasizes that a representative sample is crucial for making valid inferences about the population.

💡External Validity

External validity refers to the ability to generalize the findings of a study to the real world or to the broader population. A study with high external validity can confidently apply its results to the population from which the sample was drawn. The video discusses how random and stratified sampling can contribute to high external validity by ensuring that the sample is representative of the population.

💡Sampling Bias

Sampling bias occurs when the sample is not representative of the population, leading to inaccurate or skewed results. The video warns about the dangers of sampling bias, which can occur if certain subgroups are underrepresented in the sample, and stresses the importance of using random or stratified sampling to avoid it.

💡Zip Codes

In the video, zip codes are suggested as a practical way to conduct random sampling when dealing with a large population like the United States. By randomizing a selection of zip codes, researchers can study a more manageable number of areas while still ensuring a geographically diverse sample that represents the entire country.

💡Generalization

Generalization in research is the process of applying the findings from a sample back to the larger population. The video emphasizes that the ability to generalize is dependent on the quality and representativeness of the sample. High-quality samples obtained through methods like random or stratified sampling allow for more reliable generalizations.

Highlights

The challenge of surveying every American on the legalization of marijuana is addressed by using sampling methods.

Population is defined as the entire set of something that you wish to study, which can vary in size and composition.

A sample is a part or subset of the population, denoted by a lowercase 'n'.

Sampling is suggested as a practical alternative to surveying the entire population due to feasibility issues.

Different types of sampling include non-probability and probability sampling, each with its own methodology and use cases.

Random sampling involves random selection, giving every member of the population an equal chance to be included in the study.

Stratified sampling divides the population into subgroups or strata before random selection to ensure representation of each group.

The importance of sample representativeness for accurate inferences about the population is emphasized.

Sampling bias occurs when the sample is not representative of the population, leading to low external validity.

The size of the sample depends on the size of the population and the amount of variation within it.

Using zip codes can be an efficient way to conduct random sampling for a large population like the United States.

Stratified sampling is particularly useful for populations with a lot of variability to ensure every subgroup is represented.

The video provides an example of how to apply stratified sampling to the question of American support for marijuana legalization.

The concept of external validity is introduced as the ability to generalize findings to the real world or the general population.

The video discusses the practicality of conducting research on a large scale, such as a country, using sampling techniques.

The role of technology in facilitating random selection and ensuring equal chances for participation in a study is highlighted.

The video emphasizes the importance of ethical considerations, such as obtaining consent, especially when dealing with sensitive topics.

An interactive example problem is provided in the comments section for viewers to test their understanding of sampling concepts.

Transcripts

i want you to take on the role of a

researcher and you've been put in charge

of answering the question

what percentage of americans support the

legalization of marijuana

but you quickly run into a problem how

could you possibly ask

every american this question it would be

too time consuming it'd be too expensive

just imagine trying to track down over

330 million people it's near

impossible so what do you do a colleague

suggests

to engage in sampling but what is

sampling

how does it work what are the different

types of sampling

well that's what we'll talk about today

so stick around

so let's start by breaking down two

fundamental concepts

what is the difference between a

population and a sample

now let's start with population the

population represents the entire

set of something that you wish to study

and the reason we use the word something

is because the population could be many

different things

your population for example might be all

the people who live in a specific city

it could also be a specific subgroup

your population could be all men

or all women or all newborn babies

and your population can also be specific

things or objects

maybe your population is all the cars on

the road and you want to know

you know how many of them are electric

so the population is the entirety

of something now another way to look at

a population

is the fact that can vary in size

you can have a giant population right it

could be the entire size of a country

example united states right that's

gigantic

to as small as a nursing home right

maybe you want to

do a research study on aging and you

visit a nursing home that's your

population

to a small as a classroom right maybe a

classroom of

50 preschoolers so the population can

vary in many different ways

subgroups things but also vary in

size also note that the population

is represented by the letter n the

capital letter n

so you ever see capital letters equals

and a number you know they're referring

to the

population so then it becomes what is

our sample

the sample is a part of the

population or it is a subset

of a population okay so like a smaller

percentage

of the population instead of the capital

letter n

you might denote a sample with a

lowercase n

okay so we have capital for a population

and a sample would be a lowercase n

now you might be thinking why have a

sample in the first place

right if i'm handing out a survey why

not just give it to everybody in my

population

well if it's a classroom that's pretty

manageable but if i'm trying to hand out

a survey to

330 million people it's difficult to

almost

near impossible so because of that we

take a small

percentage of that population and that

becomes our sample

or the specific number of people in our

sample become the sample size

and if you have a really good sample in

other words if the sample is

representative

of the population in terms of age and

educational background and income

and we'll dive into representation in a

moment you can draw

inferences about the population right so

i can draw inferences meaning draw

conclusions

for instance if i have a really good

sample

i don't necessarily need to ask

everybody right i only need

a small percentage so let's come back to

our question

what percentage of americans support the

legalization of marijuana what would be

our population

now i bet a lot of you are thinking well

it's all americans

but are we sure can you ask babies that

question

can you ask toddlers that question so

when you think about it that way our

population is actually not the entire

united states

we're going to see our population as

everybody over the age of 18

because they can give consent and they

can actually answer our questions

so for our purposes remember uppercase n

we're going to say our population

is everybody over the age of 18. and

that is roughly

200 million americans i feel like doing

awesome powers 200 million americans

and our lower case end right our sample

we're going to say is about 2 000 people

okay and i'm kind of just making that up

but

you might be thinking you can have 2 000

people and

generalize your results to an entire

country well you can if it's a good

sample

and what good means we will cover in the

next few moments

okay so now that we have our population

for sample what's next i want us to

understand there are various ways

you can do sampling so let me give an

example

sampling as i've written up here comes

in two forms we have one called

non-probability sampling

probability and we also have

probability sampling non-probability

our top one is often based on the idea

of convenience

right who's around me right who are the

people close to me to make this easier

you're close to me

all right you could be my study this is

why we call this convenience sampling

or maybe it's volunteer i want to be in

your study okay well that's easy

but what we really want to focus on is

probability sampling

because this is based on chance and the

reason this is important

is every member of a population has an

equal chance

to be in your study and that way we can

account for individual differences among

groups

age gender race and everybody is

accounted for

you can make better inferences from the

sample to the population

so for this video we're going to focus

on two types of probability sampling

they are called random sampling and

stratified sampling all right so what's

the difference let's start with the

first one

so random sampling begins with a

population and for a population let's

just imagine

there are one two three four

five six seven people in our population

well how do we get those people in our

sample what we do is a process called

and this is extremely important random

selection okay random selection is the

root

of probability sampling and essentially

it's like picking names out of hat

right you're in my study or not on my

study you're in my study or not in my

study right there's picking out of hats

it ensures that everybody in my

population has an equal chance

to be in my sample now typically it's

not putting names in the hat

typically you'll put names in a computer

or an excel sheet

and you just randomize them and it just

randomly picks people

right so i put these names in a computer

and it randomly picks them

and my sample becomes participant three

participant

five and participant six right totally

random

okay so there's our population and that

becomes our sample

remember that random sampling is based

on random selection

now let's focus on the sample the key to

a good sample

is that it is representative of the

population

so what does that mean it means that all

the characteristics and

features of the population right

different ages different genders

uh different incomes different

backgrounds are represented

in the sample so for example if 50

of my population are women what

percentage of my sample should also be

women

50 that makes it representative so we

can essentially have two types of

samples

we can have a representative sample

representative

sample and the reason this is important

as we talked about before is you're able

to generalize those results right make

go back

to the population essentially we are

labeling this

as high

external external validity

okay external validity refers the idea

of being able to

generalize your findings to the real

world all right to the general

population

so if you have a good representative

sample which is done through random

selection

you'll have high external validity but

what if you don't have a good sample

right what if your sample isn't

representative of the population

right let's say 50 of your population is

women but your sample only has 10

percent women

well that's going to be a biased sample

okay

or we can label it as sampling bias

okay a bi-sample or sampling bias

and because of this instead of having

high external validity which is key to a

good study

this is going to result in low external

validity

okay in other words we are not validity

going to be able to generalize

our results to the population and this

is going to be allowed to lead to a lot

of errors

in our study so there's random sampling

now one question i always get from my

students is does it matter how many

people are in your sample

yeah it does i mean there's really two

big things to think about

how big is your population and how much

variation is in it right

if you're studying a classroom you might

not need a big sample

but if you're studying an entire country

then yeah you need a little bigger of a

sample size

and also it's due to the amount of

variation

in that population right if you're a

psychological researcher you're studying

rats

well there's not much differences

between rats i mean a rat is a wrath

they're all the same

i know i'm going to get hate mail about

people who own rats but people are very

different

right we have different ages weights

heights religions backgrounds

everything is so different so because of

those differences

you'll need a larger sample size so how

can we use random sampling

in our question what percentage of

americans support the legalization of

marijuana

well you could technically get everybody

a number write 200 million people

a number and you put them in a generator

some sort of excel sheet computer and

you press a button and it randomizes

them you could do that but that would be

pretty hard

but what's a little easier is what if we

did zip codes

right what if we identify all the zip

codes

in america and by the way i looked this

up there

are over 40 000 zip codes so instead of

200 million we got 40 000 zip codes

you put them in a computer you press

randomize and it spits out let's say

3 000 zip codes okay and from those zip

codes

you're able to gather information about

the people who live within that zip code

and you're able to send out you know

mail to them and email them and call

them or do door to door are you able to

contact them

and that way you're not doing everybody

but you're essentially

you know going to different parts right

each one of these green dots represents

a zip code

so we're not going door to door in every

single town in america

we're doing it so we can space it out

everybody gets uh

equal chance in america to be in our

study and it's easier it's less time

consuming

we'll make phone calls we'll send out

telegrams we'll do we'll do mail

all those kind of things no forget

hawaii don't forget alaska right

so that way everybody has it has an

equal chance represented so

that is a nice way to do it you can use

zip codes all right so what's our last

example of probability sampling that is

called stratified sampling

now why would we use stratified over

random

as i just said before the greater the

population right the bigger the

population the more variation

this is a better method let's break it

down

so the reason we call this stratified

sampling is because

the word strata means layer

right you might have heard the word

stratified like the stratosphere right

one of the layers of the atmosphere okay

so we have

many layers that we're kind of dissect

okay

so here's our population and imagine

that each one of these colors

represents gender race and income okay

so we'll say

you know uh gender is going to be this

color

and race is going to be this color

and income is this color okay

when you have a population that has a

lot of differences in it okay like a

country

how do you ensure that every group is

representative

because historically a lot of subgroups

are not representative

right people low-income or specific

minority groups it's a

it's really hard to get a hold of those

people you know through mail and

telephone and things like that

so we need a way to make sure that every

group every group of population

is represented and the way to do that is

stratified sampling

and here's how it works each one of

these circles

represents what we call a strata

so here's a strata and here's a strata

and here's a strata so these represents

strata a subgroup okay a subgroup of a

population

okay and the first thing we do instead

of doing random selection from here

we first divide people equally so we're

gonna put all of the

you know all females all women into

our strata okay so we first put him here

and then we will

put everybody who let's say is you know

african-american

in this strata

here we go and then we will put

everybody let's say in the middle class

right people who are middle class

into this strata

okay so we first take everybody in a

population

and we divide them into specific strata

so we'll have an arrow here

arrow here and arrow here okay

all right so now that we've divided

everybody into their specific strata

what do we do we do what we did in our

random sampling which is

then we do a random selection from each

strata okay so here's our

random selection like you know picking

names out of a hat

so we might put you know all you know

women and everybody's african-american

everybody in middle class income

into a database and it randomizes them

so it's an equal chance to be in our

sample

so randomly you know this person has to

be chosen and this person is chosen

and then this person is chosen and then

those three

become part of our sample there's first

person

and second person and our third

person right so this way

using stratified we ensure especially in

a population with a lot of variability

that every specific subgroup is

accounted for

all right so that way we can make better

inferences

about the population and each subgroup

as well and how might this apply to our

question

what percentage of americans support the

legalization of marijuana

well you'd probably do a stratified

sampling because of the size

of america in countries in general right

so you could take

you know we have gender race and income

you could also do

educational background you could do i

don't know age right you can do a lot of

different things to make sure that

everybody is accounted for

and that's a nice way to answer that

question alright guys thanks for

watching i really hope you learned

something

please look down in the comments section

i put an example problem

where you've identified the sample and

population test your knowledge

thanks for watching i'll see you next

time don't forget to like the video

subscribe

take care