Hello.
Mr. Tarrou.
Ok.
We are doing part 2 of our Sampling Technique video.
Because we are going to start collecting data so we don't always need to have it given to
us by our textbooks.
Ok, Sampling Techniques Part 2.
The remedy for biased in sampling is to allow for random impersonal chance to do the sampling.
I do realize I never talked about bias in the previous set of notes even though I wrote
it in there.
Ok, so what is bias?
Bias is like maybe you could have a question, "Hey, given the fact that some expert says
so and so, what is your opinion?"...
Or...
"Wow, we just had a tragic lose.
Some kid was just accidentally shot by his brother when playing with a toy.. or playing
with a gun like it was a toy.
Based on that, what is your opinion on gun control?"....
Or...
"Man the economy sucks right now.
What is your opinion on those in power?
The president or the whatever...
the government."
So bias can come from...
I want to find...
I am a bakery company, and I want to find out just how many people in the population
are still baking at home.
So I am going to start calling people at 2 in the afternoon and ask, "I am doing a survey
for so and so, do you still make cakes and pies at home?"
Well, if you are calling during the day when maybe there is a lot more house moms or house
dads.. stay at home dads or stay at home moms, taking care of the family they might have
the time and inclination to do more backing then say those people that are not at home.
If you only call at say at 2 in the afternoon like I am saying.
So you can have bias coming from the wording of your question.
You can have bias coming from bad sampling technique.
Or in an experiment you can have bias show up if maybe the experimenter knows who got
the treatment and who got the control and just interpreting some bias into those results.
And you can have bias from just bad sampling.
If I want to find out again about the people with in school, or education, if I want to
find out what students opinions here at our school about the teachers.
Well, I am teaching AP Stats, right, so I am not going to just survey my students.
First of all they are honor students.
The kids that I get are not a random selection of the school, and so they might..
hopefully feel that the teachers are maybe better at this school than the overall population
because they don't represent the entire population.
My students wouldn't even represent the honors students at my school because again it is
not a random selection.
They chose to take my class.
Ok.
So that is the discussion about bias, you are systematically getting one type of response
or answer another.
Probably not a perfect definition there or wording.
Some good techniques of sampling.
We just talked about Voluntary Response and Convenience Sampling.
Neither one of those are very good.
What are some good sampling techniques?
The most common that we will use in the textbook Introduction to Statistics is a Simple Random
Sample.
Every individual has the same chance of being chosen and that is key characteristic.
It is not the most important characteristic of an SRS.
It is kind of like asking what is a square?
Well, it has four sides.
Ok, can you be a little bit more specific?
Well all four sides are equal.
A rhombus also has four equal sides.
You need to say it has four equal sides and all the angles are 90 degrees.
Well, what is the deal with the simple random sample.
Yes, every individual does have the same chance of being chosen.
But the key characteristic of and SRS is every set of n individuals have the same chance
of being chosen.
So if I want to do a simple random sample of students here at school, if I want to a
simple random sample of 30 then every possible combination of 30 students even if they are
all freshman could be a possibility.
Every group of n individuals has the same chance of being chosen.
And and SRS is one type of Probability Sampling.
Sampling chosen by chance.
Not all will give every individual the same chance of being chosen.
What do I mean by every individual not necessarily having the same chance of being chosen.
Let me keep talking about the school here.
If I wanted to... um... do a technique are going to learn in just a second...
Actually let me go ahead and skip ahead to that.
[nananana] Ok.
I am back.
Alright, copy these down.
Ok.
So what am I talking about here where every individual does not have the same chance,
or may not, have the same chance of being chosen.
Stratified Random Sample.
Let me get back to that in a second.
Stratified Random Samples are good for selecting from a large population, or when you think
different strata will yield very different results.
What you do with a stratified random sample, is you divide the population into strata the
are are similar in some way that you think is important to the response variable.
That is why I am going to go back to this whole idea an example of an education... or
a school setting.
You take an SRS from each of the strata.
And you then combine that to make one full sample.
So if I again want the opinion of the students at my school about how do they feel about
the teachers.
I could take about, I think there is approximately 2400 students this year.
I could put those names in a hat and pull out a random 100 names.
That would be an SRS.
Every group of 100 students would have the same chance of being chosen.
But, a: Our freshmen class is much much larger than our senior class.
Kind of a sad commentary.
And plus b: As we mature and we get into higher level classes at the higher grades our opinions
may change about the teachers that we have.
So I think maybe grade level would influence how students would respond to that question,
"How do you feel about the teachers at your school?"
So I might do a Stratified Random Sample.
Well the starts are already set up for me for grade levels 9, 10, 11, and 12.
And then the second step would be to take an SRS of each strata.
So maybe I could chose 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors to get an even
weight to all of the classes.
Well if I do that, then the seniors will have a more likely chance of being chosen because
I am taking 50 out of a smaller pool of students than if it were talking about the freshman
class.
That freshman class is larger unfortunately.
People drop out if they don't graduate, or they just move away.
So the senior class being smaller, if I choose 50 out of each grade level for high school
would have... each individual students (senior) would have a higher chance of being chosen.
Now I could also make it proportional.
I could say...
Well the smallest group is the seniors, so I will take maybe a group of 40 out of them.
The juniors are a little bit larger, maybe I will take 50.
And then 60 out of the sophomore class, and 70 out of the freshman class.
Or you know, I can make it proportional so that every individual still has a the same
chance being chosen.
I could if I wanted to.
Now the difference between a Stratified Random Sample and an SRS is with an SRS if I choose
a 100 completely random students they could potentially be all freshmen or all seniors,
or somewhere in between.
Whereas a Stratified Random Sample, even if I make it so that every student has the same
chance of being chosen...
I adjust the size of the strata to fit the size of that grade level...
it would be impossible, if I took an SRS out of each grade level, it would be impossible
for all of the kids to be one or two, or even three grade levels.
If I force a strata to be, four of them, freshman..
sophomore.. junior... and seniors... and I combine the SRS's out of each of those four
strata to make one full sample I would be guaranteed to have a few seniors... a few
juniors... a few sophomore... and a few freshman.
I don't know why went out of sequence there.
Whereas as a Simple Random Sample, when you set a sample size every selection of that
particular n size will have the same chance of being chosen.
That is not the case with a Stratified Random Sample.
A Stratified Random Sample can give good data about each strata, so I could find the opinions
and how they vary between seniors, juniors, sophomores, and freshmen if I broke it back
up into those strata when I analyze this.
And the entire population, if individuals in each strata are less varied the population
as a whole a stratified sample can give better information than an SRS of the same size.
If I put together strata, and I am putting those strata together based on a variable
that I think will be important to the overall response, then you would think that in each
group they would be more alike in some way.
And I can actually get results that are more sensitive.
If there is a difference in opinion or a change in the population it will be may easier to
see with a Stratified Random Sample.
However most of the techniques we will learn in our textbook this year are only good for
data collected with an SRS.
So while we are learning different ways to collect data, we might not be able to work
with all of those different types of data.
That is for more advanced Statistics.
Let me talk for a second about this idea of taking an SRS and the idea that we need to
have randomization in our selection process.
I have been talking about how we could just put numbers in a hat.
You can also randomly generate numbers with your calculator.
But if you randomly generate numbers with your calculator in your summary statement
or in your example of how to do.. or your explanation of how to do the randomization
process, you will not be able to use your repeat numbers.
Not if you are actually selecting real individuals.
You cannot use the same person in your survey twice for example.
You will also learn, I am not going to do it in this video but, how to use your random
digit table in the back of the book.
You are not given a random digit table when you take the AP exams.
So that is, you know, good for a text book and being able to grade your work, and be
able to look in the back of the book to check your work, the randomization process.
But, we will be talking how to use a random digit table as well.
But we will generally be either randomly generating numbers with our calculator.
When we are actually doing a selection process we will have to skip the repeat numbers, or
when you are taking a standardized test like the AP exam the best way of describing your
random selection is just putting numbers or names into a hat and pulling them out.
Unless you put the name back in the hat, and why would you, you would be prevented from
ever selecting the same unit or subject twice.
So we will be talking more about randomization in a later video.
Alright.
[nanananana] And our last sampling technique that I am going to get to in this video is
called Cluster Sampling.
This is often used for practical reasons.
It sounds very very close to Stratified Random Sample.
We divide the population into clusters.
We randomly select some of these clusters.
And then all of the individuals in each chosen cluster is going to be part of the overall
sample.
Now with Clustering, it sounds like you are doing a Stratified Random Sample, but in a
Stratified Random Sample you do take an SRS out of each strata.
With Cluster Sampling, maybe... let's stick with again the opinions of students and the
teachers at their school.
Well what if I want to talk about the entire county.
Well, I could choose a particular class... or...
Let's say I want to talk about the opinions of students taking AP Statistics in the entire
county that I work in.
Well, instead of doing a random selection of students in each individual school, the
clusters could actually be the schools..
and then go ok.. we have got...
I don't know... 20 high schools in the county.
And I am going to randomly choose 3 of those 20 high schools.
Ok, so whoever is in those three high schools taking AP Statistics would then be part of
the survey.
Not taking an SRS of each group of Stat kids in each individual school.
So Stratified Random Sample and Clustering sound similar, but once you set up those clusters
you don't take an SRS of a few individuals out of each cluster, you just grab the whole
cluster and then put those together.
So again...
A bunch of high schools in the county, put them in a bag and shake them up and pull out
maybe 3 or 4 or however many school you feel like using, and within each of those schools
there are a cluster of kids taking statistics.
i could use their opinions to answer some kind question or collect data and impose or
inference those results into the entire county.
Multi-Stage Sampling.
It is probably best if you just look this up and find an example on the internet.
Multi-Stage is when you do Stratified Random Samples but you just do it in multiple stages.
I am out of time though, so I might talk about this a little bit in the next video.
But it is just multiple stages of a Stratified Random Sample.
I am Mr. Tarrou.
That is all of my time.
Let's go to part 3.
WHOOOO!