LUKE WILCOX: Hello, AP stat students.
And welcome to AP Daily--
Practice Sessions.
My name is Luke Wilcox.
I am an AP Statistics teacher at East Kentwood High
School in Kentwood, Michigan.
And in this session, I'm going to take you
through two free response questions related
to collecting data.
Now, I highly recommend that you download these questions first
and try them on your own before watching the video.
So click the link on the video here or down
below in the description, download these questions,
give them a try on your own, and then come back here
to check your work.
So let's jump right into the first free response question.
Number one, a dermatologist will conduct an experiment
to investigate the effectiveness of a new drug to treat acne.
The dermatologist has recruited 36 pairs of identical twins.
Each person in the experiment has acne
and each person in the experiment
will receive either the new drug or a placebo.
After each person in the experiment
uses either of the new drug or the placebo for two weeks,
the dermatologists will evaluate the improvement
in acne severity for each person on a scale from 0,
no improvement, to 100, complete cure.
part a says, identify the treatments, experimental units,
and response variable of the experiment.
So three things we need to identify here let's start
with the treatments.
Now, the treatment is the condition
that is being imposed on the subjects in the experiment.
And if we read through the description here,
we see that they'll each get the new drug or a placebo.
So those are the two treatments for this experiment.
Now, for the experimental units, we're
looking for who or what is being randomly assigned
to these treatments in the experiment.
And you'll see that we have 36 pairs of identical twins.
But we have to be careful, it is not
the pairs of twins that are being randomly assigned
to the treatments.
It is the individual subjects, and there are 72 of them.
So it would be incorrect to say 36 pairs here.
The correct answer is that each person, each of the 72 subjects
are being randomly assigned to the treatments.
And then finally, the response variable
is the thing at the end that we're measuring.
What at the end of the experiment are we measuring?
And we can see here that we care about the improvement
in acne severity.
So that would be considered the response variable.
Now, each twin in the experiment has
a severity of acne similar to that of the other twin.
However, the severity of acne differs
from one twin pair to another.
Part b, for the dermatologists experiment,
describe a statistical advantage of using a matched pairs
design where twins are paired rather than using
a completely randomized design.
For this one I want to think about the completely randomized
design first.
In that scenario, we have 72 subjects that we would randomly
assign into two groups--
the new drug and the placebo.
Now, let's suppose that the new drug
looks like it's working extremely well, that acne
is improving with the group that gets the new drug compared
to the group that gets the placebo.
Now, we don't know whether the difference between those two
groups is in fact, because the drug is
working better or because of some other variable.
Specifically, the variable of initial acne
could be an issue here.
If all of the people that end up in the new drug group
all had really bad acne to begin with,
well, then maybe the reason we're
seeing an improvement is because of the initial acne severity
and not because the drug was working.
Now, let me try and summarize that here.
I'm going to say the improvement scores
will vary due to many factors, including initial acne
severity, what treatment has received,
and other variables such as diet and genetics.
Now, that's the problem with a completely randomized design.
So what's the advantage now of using a matched pairs design?
Well, because the pair of twins are
similar in their initial acne severity,
pairing allows for the variation in improvement scores
due to the treatment received to be
distinguished from the variation due to the initial acne
severity unlike in a completely randomized design.
So overall, what's the advantage of matched pairs?
Well, using the matched pairs design
will make it easier to find convincing evidence
that the new drug is better if it is in fact better.
Part c, for the dermatologist's experiment,
describe how the treatments can be randomly assigned
to people using a matched pairs design in which twins
are paired.
So this question is all about how
do we do random assignment for a matched pairs design.
And there are several different ways to do it.
But I'm going to present one of them to you.
So what we're going to do is we're
going to take one pair of twins, and label one of them
is Twin A and the other one as Twin B. Now, I'm
going to use a coin toss.
And when I toss the coin, if it lands on heads,
Twin A will get the placebo and Twin B will get the new drug.
If instead it lands on tails, we flip that.
Twin A gets the new drug and Twin B gets the placebo.
Then once we've done that for that one pair of twins,
we need to repeat that same exact process
for each pair of twins until we've
done this for all 36 pairs of identical twins.
Now, a coin toss is not the only way
that you could describe the random assignment?
So let me talk about two other ways.
You could use a random number generator here.
So suppose you generate a random number
one or two where one would mean that Twin A gets
the placebo and Twin B gets the new drug, and two,
means that Twin A gets the new drug and Twin B
gets the placebo.
The other one I have listed here is you could use notecards.
Let's suppose you had two notecards.
One of them said new drug, one of them said placebo,
and you just shuffled them up.
And for each pair of twins you just randomly handed them
each one, and that was the treatment that they received.
Now, the important thing in your writing
up your solution on this one is you
want to describe the random assignment
process for one pair of twins but then
you also need to indicate that that same process needs
to be used for all pairs of twins, all 36
pairs of identical twins.
Let's move to free response question number two,
which says, Alzheimer's disease results
in a loss of cognitive ability beyond what
is expected with typical aging.
A local newspaper published an Article
with the following headline.
Study Finds Strong Association Between Smoking
and Alzheimer's.
The Article reported that a study
tracked the medical histories of 21,123 men and women
for 23 years.
The Article stated that for those
who smoked at least two packs of cigarettes a day,
the risk of developing Alzheimer's disease
was 2.57 times the risk for those who did not smoke.
Part a, identify the explanatory and response variables
in the study.
So let's start with the explanatory variable, which
is the variable that can explain the other variable
or the variable that can be used to predict the other variable.
And if you look at the way that this is worded here,
we know that this has to be something about smoking.
Now, students often want to just give
that one word answer, smoking.
But what the problem here is that this doesn't exactly
describe the variable, the explanatory variable.
It's not quite enough.
Instead, I'd like to say something
like the degree of cigarette smoking
where we can measure the degree of cigarette smoking
by how many packs of cigarettes they smoke a day.
Now, the response variable is the thing
that we're measuring in the end or the thing
that we would want to predict from the explanatory variable.
And we know from the question that this has something to do
with Alzheimer's.
Now, once again, that one word answer
is not going to be enough.
In fact, the variable that we're measuring here is a categorical
variable with a choice of either yes or no,
either yes you have Alzheimer's or no you don't.
So I'm going to specify the variable as being
the Alzheimer's status.
That's a categorical variable, which could
have the values of yes or no.
Part b, is the study described in the article
an observational study or an experiment?
Explain.
Now, an observational study is when the researcher just
simply observes what's happening and records values
based on what they see.
On the other hand, in an experiment,
the researcher is intentionally imposing
some treatment on the subjects.
In this context, the researcher would
have to be telling some people they
need to smoke cigarettes and some people they need
to stop smoking cigarettes.
Now, clearly, that's not what happened in this study.
And so we definitely have an observational study
here because the researchers did not assign smoking levels
to subjects.
Instead, the degree of cigarette smoking for each person
was passively observed and recorded, not
manipulated by the researchers.
Part c, exercise status, regular weekly exercise
versus no regular weekly exercise,
was mentioned in the article as a possible confounding
variable.
Explain how exercise status could be a confounding
variable in this study.
In order to be able to explain this,
we have to first understand what is a confounding variable.
So a confounding variable is in an experiment
is a variable that is related to the explanatory variable
and influences the response variable.
So it has some sort of a connection
to both the explanatory variable as well as
the response variable.
Now, we already identified with those would be in part A.
And part A we decided that the explanatory variable is
the degree of smoking, and the response variable
is the Alzheimer status.
And clearly according to the Article,
there is an association between these two variables.
What we don't know is if smoking is actually
the thing that's causing the Alzheimer's risk to go up.
And the reason we don't know that
is because there's this other possible confounding variable,
which is exercise status.
Now, what should our solution look like for this question?
Well, according to the definition
of confounding variable, we have to connect it
to both the explanatory variable as well as the response
variable.
So let me start by trying to connect exercise status
with the degree of smoking.
I think it would be reasonable to say that people who exercise
might be more concerned about their health
and therefore less likely to smoke.
So there's our connection with the explanatory variable.
But then we also want to talk about how that confounding
variable influences the response variable.
So I'm going to say here that it's possible that people who
exercise more regularly are, in fact,
reducing their risk of Alzheimer's.
Maybe it's the exercise that's actually reducing the risk
of Alzheimer's.
So if we take both of those statements together,
then we can say that the degree of smoking
and Alzheimer's status would be associated,
even if there was no cause and effect relationship between
smoking and developing Alzheimer's.
So I hope that this video was helpful for you.
I also hope that you will join me for session four
where we will go over two free response questions
both of which are multi-focus.
Hope to see you soon.