Quantitative Reasoning
Preview Assignment 15.A
Preview Assignment 15.A
Preparing for the next class
In the next class, you will learn more about experimental studies. Remember that, in
experimental studies, researchers manipulate an explanatory variable to observe
changes in a response variable.
Learn more about variables at http://www.oswego.edu/~srp/stats/variable_types.htm.
If you find some variable types with which you are unfamiliar, add them to your personal
statistics dictionary.
1) Read the passage about quantitative and categorical variables.
Part A: Which of the following is not an example of a quantitative variable?
a)
b)
c)
d)
Height
Political affiliation
Temperature
Body Mass Index
Part B: Which of the following is not an example of a categorical variable?
a)
b)
c)
d)
Hair color
Gender
Field of study
Grade point average
2) Researchers are designing an experiment to learn whether eating dark chocolate
can help people have healthy hearts. They plan to give various doses of dark
chocolate to patients for a long-term study. After a specified amount of time, they will
compare heart health among the patients.
Part A: What is the explanatory variable in this study?
a) The patients
b) The chocolate dose
c) The heart health of patients
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Preview Assignment 15.A
Part B: What is the response variable?
a) The patients
b) The chocolate dose
c) The heart health of patients
Part C: What is the manipulated treatment in this study?
a) The patients
b) The various doses of chocolate
c) The various levels of heart health
Monitoring your readiness
3) To effectively plan and use your time wisely, it helps to think about what you know
and do not know. For each of the following, rate how confident you are that you can
successfully do that skill. Use the following descriptions to rate yourself:
5—I am extremely confident I can do this task.
4—I am somewhat confident I can do this task.
3—I am not sure how confident I am.
2—I am not very confident I can do this task.
1—I am definitely not confident I can do this task.
Skills needed for Lesson 15, Part A
Skill or Concept: I can . . .
Question used for
understanding
Distinguish between
quantitative and categorical
variables.
1
Distinguish between
explanatory and response
variables.
2
Identify treatment levels.
2
Rating
from 1 to 5
Now use the ratings to get ready for your next lesson. If your rating is a 3 or below,
you should get help with the material before class. Remember, your instructor is
going to assume that you are confident with the material and will not take class time to
answer questions about it.
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Student Pages 15.A, The video game diet
Lesson 15, Part A
The Video Game Diet
Consider the following research study.
Research question: Dr. Elizabeth Jackson, a professor at the University of Michigan
Health System, surveyed 1,003 middle-schoolers about their snacking habits and their
predominant after-school activity (outdoor activities, video games, or watching TV).1
Conclusion: Kids who spend most of their time outdoors eat the fewest calories from
unhealthy snacks.
(Interestingly, kids who played the most video
games ate fewer calories from unhealthy snacks
than those who tended to watch more TV.)
1) In a statistical study, a variable is an
observation that changes from individual to
individual.
Part A: What are the two variables in this
study?
Credit: ThinkStock
Objectives for the lesson
You will understand that:
o In experimental studies, researchers manipulate an explanatory variable to
observe the effects on a response variable.
o To manipulate the explanatory variable, researchers divide subjects into similar
groups and apply a different treatment to each group.
o If the groups are truly similar, then differences observed in the response variable
might be attributed to the explanatory variable.
You will be able to:
o Determine when a study design allows a conclusion to be made about cause and
effect.
o Design an experimental study.
Part B: Identify the explanatory and response variables in the University of Michigan
study and classify them as categorical or quantitative.
Explanatory variable:
Response variable:
1
Singh, M. (2014, March 28). Why playing Minecraft might be more healthful for kids than TV. Retrieved
November 23, 2014, from http://www.npr.org/blogs/health/2014/03/28/295692162/why-playing-minecraftmight-be-healthier-for-kids-than-tv.
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Student Pages 15.A, The video game diet
Part C: Can researchers in the study conclude that the amount of after-school
activity was the cause for the number of calories that kids consumed from
unhealthy snacks? Can you offer a possible alternate explanation?
In an observational study, researchers simply observe the variables of interest. In an
experimental study, researchers actively manipulate the explanatory variable.
Part D: Was this an observational or experimental study? Justify your answer.
Part E: In what type of study can we make conclusions about cause and effect?
2) Let’s redesign the study about middle-schoolers’ after-school activities into an
experimental study to see if a cause-and-effect conclusion can be made.
Part A: The explanatory variable is after-school activity. In an experimental study,
should the kids (participants) pick an activity according to their preference,
or should researchers control this?
Part B: What does it mean in this context to say that “researchers manipulate the
explanatory variable in an experiment?”
Part C: In an experimental study, the values of the explanatory variable are called
treatments. What are the treatments in this study?
Part D: Suppose you decide to apply the treatments to different groups by dividing
children randomly among three groups. Would there be any reason to think
that one group would be very different from another?
Part E: In an experiment, random assignment into groups tends to create groups
that are similar. The only real difference from group to group is the
explanatory variable that researchers are manipulating. If the children
assigned to the video game group consumed fewer calories than the
children assigned to the TV group, could there be another explanation other
than the activity?
Part F: If the children in the video game group consumed fewer calories than the
children in the TV group, what conclusion could be made about the activity?
In experiments, if we apply the various treatments to groups that are similar in
composition, then we can conclude that they are responsible for any differences
observed in the response variable.
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Suggested Instructor Notes 15.A, The video game diet
Lesson 15, Part A
The Video Game Diet
Overview and student objectives
Overview
Lesson Length: 25 minutes
In this lesson, we begin to look closely at experimental
studies. Some of the ideas in the lesson were discussed
briefly in earlier lessons. We review those concepts and
continue to develop them here. The lesson focuses on
explanatory and response variables, and the idea that in
experiments, researchers manipulate an explanatory variable
to observe changes in a response variable.
Prior Lesson: Lesson 14,
Part C, “Conclusions in
Observational Studies”
Objectives
Next Lesson: Lesson 15,
Part B, “All Things in
Moderation” (25 minutes)
Constructive Perseverance
Level: 1
Theme: Health Literacy
Students will understand that:
Goals: Reasoning,
Evaluation
•
In experimental studies, researchers manipulate an
explanatory variable to observe the effects on a
response variable.
•
To manipulate the explanatory variable, researchers
Outcomes: N1, C1, C2
divide subjects into similar groups and apply a different
treatment to each group.
•
If the groups are truly similar, then differences observed in the response variable
might be attributed to the explanatory variable.
Quantitative Reasoning
Outcomes: S1, S2, S3,
Related Foundations
Students will be able to:
•
Determine when a study design allows us to make a conclusion to be made
about cause and effect.
•
Design an experimental study.
Suggested resources and preparation
Materials and technology
•
Computer, projector, document camera
•
Preview Assignment 15.A
•
Student Pages for Lesson 15, Part A
•
Practice Assignment 15.A
Prerequisite assumptions
Students should be able to utilize the basic vocabulary related to the design of statistical
studies.
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Suggested Instructor Notes 15.A, The video game diet
Making connections
This lesson:
•
Connects back to Lessons 3 and 13 activities about samples, populations, and
numerical summaries.
•
Connects forward to more lessons on statistical studies (Lessons 19–21).
Background context
In Preview Assignment 15.A, students were given instructions to learn more about
variables at http://www.oswego.edu/~srp/stats/variable_types.htm.
Suggested instructional plan
Frame the lesson
(6 minutes)
ThinkPair-Share
•
Ask students to read the introduction to the research study and
answer question 1, Part A.
•
Take responses from students and then ask the class to refine the
responses. For example, students may say “activity” and “snacks.”
Ask:
o “What about the activities? Is the variable the amount of time
spent performing an activity?” [Answer: No, it is the type of
activity.]
o “What about snacks? Is it the number of snacks? The type of
snack?” [Answer: No, it is the amount of calories consumed.]
•
These refinements will help with determining whether the variables
are categorical or quantitative, and with writing a clear conclusion.
•
Also, writing clear variable descriptors can help students to choose
an appropriate graphical display when asked to do so.
•
Transition to the lesson activities by briefly discussing the
Objectives for the lesson.
Lesson activities
(15 minutes)
Group
Work then
Whole
Class
Discussion
•
Ask students to complete question 1. Hold a whole class discussion
to ensure that everyone is clear on the vocabulary associated with
the example.
•
Students often confuse the explanatory and response variables.
Remind them that the explanatory variable is the one that may (but
may not!) influence changes in the other variable.
o “Do we think the activity might explain the calories, or that the
calories explain the activity?”
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Suggested Instructor Notes 15.A, The video game diet
o “Do calories respond to activity, or does activity respond to
calories?”
•
Group
Work
This study is observational in nature, and as students have learned,
observational studies do not allow cause and effect conclusions. It
may be that kids who watch more TV are more complacent
physically and more inclined to eat snacks.
o “Is it possible that kids who watch a lot of TV have traits in
common with kids who snack a lot? What might those traits be?”
Question 2
•
If students have trouble with the idea of manipulating a variable,
remind them that manipulating variables means that the researcher
controls the amount or type of variable that is applied to the
participant. In such an experiment, we would not just observe who
watches a lot of TV; we would actually control the amount each
participant watches.
•
Students should apply the idea of manipulating a variable to this
context. In this case, students are told what their activity will be. If we
let students pick, then the study is not an experiment.
o “Who should control the explanatory variable—the students or the
researchers?”
•
We are attempting to help students understand how the abstract
terms such as variable and value apply in this context. It may be
difficult at first, so remind them that treatments are the manipulations
of the explanatory variable. The explanatory variable is activity, so
how is this being manipulated?
o “If the explanatory variable is an activity, then what are the
possible values (or outcomes) of this variable?”
•
Because the groups are presumably similar, there is only one thing
that varies from group to group—the value of the explanatory
variable. Since it is the only variable, it is the only thing to explain any
responses observed. The main idea is that we are limiting variation
between the groups except for the variable that we are manipulating.
If the groups are different in only one regard, then that difference is
responsible for changes observed.
•
Researchers use various measures to ensure that the groups are
similar or to what degree they are not.
o “Pretend the groups are exactly the same except in their activity
after school. If this is the only difference, then is there any other
explanation for the changes in calories consumed?”
•
Since it is appropriate to make a causal conclusion, students can say
that the values of the explanatory variable are the causes for
differences in the groups. Just as you discouraged the use of that
word in conclusions of observational studies, encourage students to
use the word causes in their conclusions of experimental studies.
Guiding
Questions
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Suggested Instructor Notes 15.A, The video game diet
Wrap-up/transition
(4 minutes)
Wrap-up
•
Review the main ideas of the lesson and remind students to
complete their personal statistics dictionary.
o In experimental studies, researchers are concerned about
explanatory variables and response variables.
o To make a cause-and-effect conclusion, researchers must divide
their subjects into groups that are similar.
o Researchers manipulate the explanatory variable by assigning a
quantity of the variable to each of the similar groups.
o If changes are observed in the response variable, then we can
assume that the values of the explanatory variable are the cause.
•
Have students refer back to the Objectives for the lesson and
check the ones they recognize from the activity. Alternatively, they
may check objectives throughout the lesson.
•
“For the remainder of Lesson 15, we will continue to build on the
concepts of experimental studies.”
Transition
Suggested assessment, assignments, and reflections
•
Give Practice Assignment 15.A.
•
Give the Preview Assignments, if any, for the lesson activities that you plan to
complete in the next class meeting.
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Suggested Instructor Notes 15.A, The video game diet
Lesson 15, Part A
The Video Game Diet – ANSWERS
Consider the following research study.
Research question: Dr. Elizabeth Jackson, a professor at the University of Michigan
Health System, surveyed 1,003 middle-schoolers about their snacking habits and their
predominant after-school activity (outdoor activities, video games, or watching TV).1
Conclusion: Kids who spend most of their time outdoors eat the fewest calories from
unhealthy snacks.
(Interestingly, kids who played the most video
games ate fewer calories from unhealthy snacks
than those who tended to watch more TV.)
1) In a statistical study, a variable is an
observation that changes from individual to
individual.
Part A: What are the two variables in this
study?
Credit: ThinkStock
Answer: The type of after-school activity and the amount of calories from unhealthy
snacks.
Objectives for the lesson
You will understand that:
o In experimental studies, researchers manipulate an explanatory variable to
observe the effects on a response variable.
o To manipulate the explanatory variable, researchers divide subjects into similar
groups and apply a different treatment to each group.
o If the groups are truly similar, then differences observed in the response variable
might be attributed to the explanatory variable.
You will be able to:
o Determine when a study design allows a conclusion to be made about cause and
effect.
o Design an experimental study.
1
Singh, M. (2014, March 28). Why playing Minecraft might be more healthful for kids than TV. Retrieved
November 23, 2014, from http://www.npr.org/blogs/health/2014/03/28/295692162/why-playing-minecraftmight-be-healthier-for-kids-than-tv.
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Suggested Instructor Notes 15.A, The video game diet
Part B: Identify the explanatory and response variables in the University of Michigan
study and classify them as categorical or quantitative.
Explanatory variable:
Answer: Type of after school-activity; categorical.
Response variable:
Answer: Amount of calories consumed from unhealthy snacks; quantitative.
Part C: Can researchers in the study conclude that the amount of after-school
activity was the cause for the number of calories that kids consumed from
unhealthy snacks? Can you offer a possible alternate explanation?
Answer: No. It may be that children who chose to watch a lot of TV had things in
common with kids who ate more calories in snacks. Maybe there was less parental
intervention that caused both of these variables to increase together.
In an observational study, researchers simply observe the variables of interest. In an
experimental study, researchers actively manipulate the explanatory variable.
Part D: Was this an observational or experimental study? Justify your answer.
Answer: This was an observational study. No attempt was made to manipulate the
after school activity.
Part E: In what type of study can we make conclusions about cause and effect?
Answer: Only in (well-designed) experimental studies.
2) Let’s redesign the study about middle-schoolers’ after-school activities into an
experimental study to see if a cause-and-effect conclusion can be made.
Part A: The explanatory variable is after-school activity. In an experimental study,
should the kids (participants) pick an activity according to their preference,
or should researchers control this?
Answer: The researchers should control the explanatory variable.
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Suggested Instructor Notes 15.A, The video game diet
Part B: What does it mean in this context to say that “researchers manipulate the
explanatory variable in an experiment?”
Answer: It means that the researchers will determine each student’s activity.
Part C: In an experimental study, the values of the explanatory variable are called
treatments. What are the treatments in this study?
Answer: Outdoor activities, playing video games, and watching TV.
Part D: Suppose you decide to apply the treatments to different groups by dividing
children randomly among three groups. Would there be any reason to think
that one group would be very different from another?
Answer: If the groups are created randomly, there is no reason that they would be
very different.
Part E: In an experiment, random assignment into groups tends to create groups
that are similar. The only real difference from group to group is the
explanatory variable that researchers are manipulating. If the children
assigned to the video game group consumed fewer calories than the
children assigned to the TV group, could there be another explanation other
than the activity?
Answer: There is no other explanation, other than chance variation in the random
assignment into groups.
Part F: If the children in the video game group consumed fewer calories than the
children in the TV group, what conclusion could be made about the activity?
Answer: We can conclude that the activity was the cause of the differences in
calories from unhealthy snacks.
In experiments, if we apply the various treatments to groups that are similar in
composition, then we can conclude that they are responsible for any differences
observed in the response variable.
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Suggested Instructor Notes 15.A, The video game diet
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Practice Assignment 15.A
Practice Assignment 15.A
In a previous practice assignment, you learned about a study in which volunteers (who
were all around 30 years of age) from the Chicago area wore a light sensor to measure
their exposure to sunshine.1 It was found that those who experienced more daylight had
lower body mass indexes (BMIs). The study was observational. It was not an
experiment, so conclusions about cause and effect could not be made.
1) Let’s redesign the observational study into an experimental study.
Part A: What is the explanatory variable for the new study?
a) Body mass index
b) Sunshine exposure
c) Age
Part B: What is the response variable in the new study?
a) Body mass index
b) Sunshine exposure
c) Age
Part C: In experiments, we divide people into groups and apply treatments to each
group. How should we create these groups in the new study?
a) By grouping people according to their BMI.
b) By grouping people by how much time they spend in the daylight.
c) By randomly assigning people to groups.
Part D: As we apply treatments to the groups, we manipulate the explanatory
variable. How should this be done in the new study?
a) By assigning to each group a specific number of hours each day that
they are to spend in the daylight.
b) By giving each member a light sensor and observing how much time
each group spends in daylight each day.
c) By assigning the groups with higher average BMI more time in the
daylight so that we can see if they lose weight.
1
Aubrey, A. (2014, April 3). Good day sunshine: Could morning light help keep us lean? Retrieved
November 19, 2014, http://www.npr.org/blogs/health/2014/04/03/298358419/good-day-sunshine-couldmorning-light-help-keep-us-lean.
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Practice Assignment 15.A
Part E: After a period of time, suppose that there is no difference in average BMI
from group to group. What would be the best conclusion?
a) There is evidence of an association between amount of sun exposure
and BMI.
b) There is evidence that increased sun exposure contributes to lower BMI.
c) There is no evidence that increased sun exposure contributes to lower
BMI.
Part F: After a period of time, suppose that groups who received the most sunlight
had the lowest average BMI. What would be the best conclusion?
a) There is evidence of an association between amount of sun exposure
and BMI.
b) There is evidence that increased sun exposure contributes to lower BMI.
c) There is no evidence that increased sun exposure contributes to lower
BMI.
2) Research the Carolina Abecedarian Project website: abc.fpg.unc.edu.
Use the left menu bar to read “About the Project,” “Major Findings,” and “Policy
Implications.”
Part A: The project was an ___________ study.
a) Experimental
b) Observational
Part B: How were the children organized into groups?
a)
b)
c)
d)
By socioeconomic class: lower, middle, and upper-class groups.
By race/ethnicity.
By gender: males in one group, females in another.
By random assignment.
Part C: If the randomization process created the groups to be similar enough, we
can infer that the treatment is the cause. Under this assumption, make an
inference about the treatment’s effect relating to college-going behaviors.
a) There is evidence that the intervention contributes to a higher likelihood
of attending college.
b) There is evidence that attending college contributes to a higher
likelihood of being in the intervention group.
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Practice Assignment 15.A
Part D: The sample used in the Carolina Abecedarian Project is not representative
of the entire population of American infants. Still, there may be a sampling
frame—a subset of the population that the sample does represent. Because
the participants in the study were born in the mid-1970s and were from lowincome families, the sampling frame or subset represented by the study is
low-income children in the mid-1970s. (Although not mentioned on this
website, they were also mostly African American).
Experiments focus on making inferences about treatments, but treatments
are applied to populations. Would it be reasonable to infer that all children
who attend quality preschool would receive benefits similar to those
observed in the study?
a) Yes
b) No
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Practice Assignment 15.A
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Preview Assignment 15.B
Preview Assignment 15.B
Preparing for the next class
The next class will focus specifically on experimental studies. You will need to
distinguish an observational study from an experimental study.
1) Consider the following studies.
Study I: A researcher randomly divided 200 high school students into two groups.
The first group was told to not exercise. The second group was told to exercise at
least 5 hours each week. At the end of two months, the heart rates of each
participant in each group were measured at rest. It was found that the group that
exercised 5 hours a week had a significantly lower average heart rate.
Study II: A researcher gathered 200 high school students randomly and asked them
how long they exercised each week and then measured their heart rates at rest. It
was found that students who exercised at least 5 hours a week had a significantly
lower average heart rate.
Part A: Which study was experimental? Why?
a) Study I
b) Study II
Part B: List the explanatory and response variables in the studies.
a) Explanatory: heart rate. Response: exercise time.
b) Explanatory: exercise time. Response: heart rate.
c) Explanatory: student. Response: amount of exercise.
Part C: State whether the variables in the studies are quantitative or categorical/
qualitative.
a)
b)
c)
d)
Explanatory: categorical. Response: quantitative.
Explanatory: categorical. Response: categorical.
Explanatory: quantitative. Response: quantitative.
Explanatory: quantitative. Response: categorical.
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Preview Assignment 15.B
Part D: Identify a flaw in Study I above.
a) The participants should not have been randomly assigned to groups.
b) The participants should not have been told how much to exercise.
c) The participants’ heart rates should have been measured both before
and after the study.
2) In statistics, sometimes a “confounding variable” appears in a statistical model.
Search for information and examples of confounding variables. Write a definition in
your own words and give two brief examples. Be sure to give your source.
Monitoring your readiness
3) To effectively plan and use your time wisely, it helps to think about what you know
and do not know. For each of the following, rate how confident you are that you can
successfully do that skill. Use the following descriptions to rate yourself:
5—I am extremely confident I can do this task.
4—I am somewhat confident I can do this task.
3—I am not sure how confident I am.
2—I am not very confident I can do this task.
1—I am definitely not confident I can do this task.
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Preview Assignment 15.B
Skills needed for Lesson 15, Part B
Skill or Concept: I can . . .
Question used for
understanding
Distinguish observational from
experimental studies.
1, Part A
Determine explanatory and
response variables.
1, Part B
Distinguish quantitative and
categorical variables.
1, Part C
Identify a flaw in an
experimental study design.
1, Part D
Define a confounding variable.
Rating
from 1 to 5
2
Now use the ratings to get ready for your next lesson. If your rating is a 3 or below,
you should get help with the material before class. Remember, your instructor is
going to assume that you are confident with the material and will not take class time to
answer questions about it.
Ways to get help:
•
see your instructor before class for help
•
ask your instructor for on-campus resources
•
set up a study group with classmates so you can help each other
•
work with a tutor
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Preview Assignment 15.B
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Statistical Reasoning
Student Pages 15.B, All things in moderation
Lesson 15, Part B
All Things in Moderation
Chocolate has been a favorite food of humans for over 3,000 years, originating from
Central America and Mexico, where it was enjoyed as a drink. It was thought to have
certain medicinal properties and was even considered valuable enough to be used as
money.1
Lately, studies have emerged that also promote the
health benefits of chocolate.
1) Have you heard of any health benefits from
eating chocolate? If so, what were they?
Credit: ThinkStock
Objectives for the lesson
You will understand that:
o Conclusions about cause and effect cannot be made in observational studies
because of confounding variables.
o Conclusions about cause and effect can be made in experimental studies where
confounding is controlled.
o Experimental groups created through random assignment can usually control
variability among confounding variables.
You will begin to be able to:
o Analyze a statistical study and identify possible confounding variables.
o Decide when confounding variables restrict conclusions about cause and effect.
o Design an experiment that allows conclusions about cause and effect.
In this lesson, we consider how conclusions in statistical studies can be uncertain when
researchers do not know why a particular outcome has happened.
2) A research study in Sweden asked the research question: “Does chocolate reduce
the risk of stroke?”2
1
Benson, A. (2008, March 1.) A brief history of chocolate. Retrieved November 24, 2014, from
http://www.smithsonianmag.com/arts-culture/a-brief-history-of-chocolate-21860917/?no-ist.
2
Larsson, S. C., Virtamo, J., & Wolk, A. (2012). Chocolate consumption and risk of stroke: A prospective
cohort of men and meta-analysis. Neurology, 79(12), 1223-–1229.
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Student Pages 15.B, All things in moderation
A sample of 37,000 Swedish men were divided into four groups based on their
normal chocolate consumption, ranging from those who ate no chocolate to the
group who ate the most (63 grams per week). It is important that the study included
so many people because it makes the results more reliable. Participants were
followed for 10 years.
The study concluded that men who ate more chocolate had a lower risk of
experiencing a stroke.
Part A: Did this study prove that eating chocolate causes a lower risk of stroke?
Explain your response.
Part B: Offer an alternate explanation for this lowered risk among chocolate eaters.
3) In Preview Assignment 15.B, you read about confounding variables, or factors that
give alternate explanations for an effect. When there are confounding variables,
researchers cannot make inferences about cause and effect.
Another article3 pointed out some important facts in the study described above. The
men who ate the most chocolate tended to be younger, were more educated, and
were less likely to smoke or high blood pressure. They also reported eating more
vegetables and drinking more wine. All of these factors have positive health benefits.
Part A: Explain how this information sheds light on the study that says that eating
chocolate lowers the risk for stroke? Does it make us more or less certain
about the effects of eating chocolate?
Part B: Chocolate eaters tended to be more highly educated. What other
confounding variables arise from this fact that may also cause a lowered
risk of stroke? (What other things do people who are better educated tend to
have in common?)
Cause and effect conclusions cannot be made in observational studies because of
confounding variables. Experiments allow such conclusions by holding confounding
variables constant among several groups. To do this, researchers make sure that
groups are similar in terms of education, age, eating habits, and so on. When groups
are similar, confounding variables are controlled (not varying), and it becomes easier to
argue that a treatment (like chocolate) is the cause of an observed effect (like fewer
people having a stroke).
3
Goodman, B. (2013, January 7). Don’t fudge the facts on chocolate studies. Retrieved November 24,
2014, from http://healthjournalism.org/blog/2013/01/dont-fudge-the-facts-on-chocolate-studies.
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Student Pages 15.B, All things in moderation
To control for the confounding variables, researchers divide participants into similar
groups. Some groups are treatment groups—they receive a real treatment. Other
groups are control groups—they receive a placebo (a fake treatment) or nothing at all.
Control groups are used as a basis for comparison to the treatment groups.
4) We want to design a new study to infer whether eating chocolate drinking causes
lowered risk of stroke. To do this, we compare a large group of chocolate eaters with
another large group of non-chocolate eaters.
Part A: Which is the control group? Which is the treatment group?
Part B: Would it make sense to allow the study participants to choose which group
they are in? Explain the possible consequences of such an approach.
Part C: As researchers, it is our job to create control and treatment groups so that
confounding variables, such as education or income, do not interfere with
the outcome. What should be our goal as we decide how to assign subjects
to groups?
In controlled statistical experiments, researchers try to minimize the effects of
confounding variables by creating treatment and control groups that are as similar as
possible. Groups are similar when confounding variables are held constant (on average)
from group to group.
5) You have gathered a group of volunteers who are all in their early 20s. They come
from various socioeconomic backgrounds, and none eat chocolate, but they are all
willing to try it for the sake of the experiment. You want to divide them into two
groups (control and treatment), and you will monitor their health for four decades.
Part A: Devise a method for dividing the volunteers into groups that will minimize
confounding in the long-term results. Be specific.
Part B: What are the explanatory and response variables in this study? Are they
quantitative or categorical?
Part C: With your method of dividing the volunteers into groups, suppose that the
decades-long study concludes with a significantly lower rate of stroke
among those who ate chocolate. Write a sentence that infers a conclusion
for the study.
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Student Pages 15.B, All things in moderation
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Suggested Instructor Notes 15.B, All things in moderation
Lesson 15, Part B
All Things in Moderation
Overview and student objectives
Overview
Lesson Length: 25 minutes
In this lesson, students learn about confounding variables
that can keep us from making causal inferences in statistical
studies. They consider statistical studies that have
documented associations between chocolate consumption
and positive health benefits. Many studies conducted on this
subject are observational and in such cases we are tempted
to infer cause when cause has not been established.
Students learn about controlled studies which attempt to hold
confounding variables constant so that they can make causal
conclusions.
In later lessons, students will consider the placebo effect as
another confounding variable in statistical studies and how to
control this with placebos and blinding.
Prior Lesson: Lesson 15,
Part A, “The Video Game
Diet”
Next Lesson: Lesson 15,
Part C, “The Power of the
Pill” (25 minutes)
Constructive Perseverance
Level: 1
Theme: Health Literacy
Goal: Evaluation
Quantitative Reasoning
Outcomes: S1, S2
Related Foundation
Outcomes: C1, C2
Objectives
Students will understand that:
•
Conclusions about cause and effect cannot be made in observational studies
because of confounding variables.
•
Conclusions about cause and effect can be made in experimental studies where
confounding is controlled.
•
Experimental groups created through random assignment can usually control
variability among confounding variables.
Students will begin to be able to:
•
Analyze a statistical study and identify possible confounding variables.
•
Decide when confounding variables restrict conclusions about cause and effect.
•
Design an experiment that allows conclusions about cause and effect.
Suggested resources and preparation
Materials and technology
•
Computer, projector, document camera
•
Preview Assignment 15.B
•
Student Pages for Lesson 15, Part B
•
Practice Assignment 15.B
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Suggested Instructor Notes 15.B, All things in moderation
Prerequisite assumptions
Students should be able to:
•
Distinguish observational studies from experimental studies.
•
Identify explanatory and response variables.
•
Determine when variables are quantitative or categorical.
•
Define confounding.
Making connections
This lesson:
•
Connects back to Lessons 3 and 13 activities about samples, populations, and
numerical summaries.
•
Connects forward to more on statistical studies (Lessons 19–21).
Background context
In Preview Assignment 15.B, students were asked to research information about
confounding variables.
Suggested instructional plan
Frame the lesson
(2 minutes)
ThinkPairShare
•
Ask students to read the introductory information and respond to
question 1. Take student responses.
•
Transition to the lesson activities by briefly discussing the Objectives
for the lesson.
Lesson activities
(18 minutes)
Group
Work
Guiding
Questions
Question 2
•
Give students time to discuss this question and think about the
problems associated with assigning a cause. This is the first time
confounding has been directly addressed, and we want them to
discover it on their own if they can.
o “If two things happen together, does one always cause the other?”
[Answer: No.]
o “Can you think of other things that chocolate eaters might have in
common?” [Answers may vary. Sample answer: They may have
other dietary commonalities.]
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Question 3
•
Students are given their first concrete evidence of confounding
variables (e.g., education) in this situation. Education can lead to
many things, including a long list of other possible confounding
variables.
•
Encourage students to think of other variables that are associated
with being educated and also might contribute to better health.
•
The term confounding implies a sense of confusion in reasoning.
The more confounding variables there are, the less certainty we have
in drawing conclusions about cause.
Question 4
•
Here students begin to think through the process of designing their
own study. This question leads them to think about the ideas of
treatment and control groups.
•
Allow students to work together and struggle on these questions. As a
group they need to come to the point where they understand that if
people choose their own groups, the groups may end up being quite
different, introducing confounding variables.
o “If people choose their own groups, who will be likely to choose
the chocolate eating group?” [Answer: Chocolate eaters.]
Guiding
Questions
o “If chocolate eaters all go to the chocolate eating group, will they
have things in common that could confound the study? What
might they have in common?” [Answers will vary. Sample answer:
Maybe gender.]
o “What would help control confounding variables best: having very
similar groups or very different groups?” [Answer: Groups should
be similar to each other.]
Question 5
•
Students work together to devise a strategy for creating groups that
are similar. Students tend to answer questions like this by saying
something like “randomly divide participants into groups.” While this is
correct, it is not specific as to how it is to be done. Encourage them to
design a specific method to accomplish the grouping. Will they toss a
coin? Maybe they will draw names out of a hat. There are many
ideas that would work.
•
Remember that we want to make an inference about a treatment in
this study, so a representative sample is less important than having
groups that are similar. Still, representative samples are nice when
we can have them, and larger samples are always a good thing.
•
Students sometimes have trouble deciding what the variables are in a
study, especially when they are categorical. The explanatory variable,
chocolate eating, is easy enough, but they may say that the response
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Suggested Instructor Notes 15.B, All things in moderation
variable is stroke risk. Remind them that the response variable is
measured for each member in the sample. We do not measure rates
from single individuals.
•
Guiding
Questions
In Part C, students practice making a statistical inference. Because
confounding variables were controlled, it is appropriate to make a
conclusion that indicates a causal relationship between chocolate
eating and lower rates of stroke. Check with them to verify that their
conclusion indicates cause.
o “Is this an experimental or observational study?” [Answer:
Experimental.]
o “What type of statistical study allows us to make a cause and
effect conclusion?” [Answer: Experimental.]
Wrap-up/transition
(5 minutes)
Wrap-up
•
Take a few moments to go over the main ideas of this lesson and be
sure the statistics dictionary is complete.
o In experiments, we attempt to control confounding variables by
holding them constant from group to group. This is done by
making groups as similar as possible.
o One way that researchers can make groups similar is to randomly
assign subjects to groups. A method of assignment is random if
each group has an equal chance of receiving any member.
Transition
•
Ask students to reflect on Lesson 15, Parts A and B, and write their
reflections on a 3x5 card. List one concept that is clear (or not clear)
after the two lessons.
•
Have students refer back to the Objectives for the lesson and check
the ones they recognize from the activity. Alternatively, checking
objectives may be done throughout the lesson.
Suggested assessment, assignments, and reflections
•
Give Practice Assignment 15.B.
•
Give the Preview Assignments, if any, for the lesson activities you plan to
complete in the next class meeting.
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Lesson 15, Part B
All Things in Moderation – ANSWERS
Chocolate has been a favorite food of humans for over 3,000 years, originating from
Central America and Mexico, where it was enjoyed as a drink. It was thought to have
certain medicinal properties and was even considered valuable enough to be used as
money.1
Lately, studies have emerged that also promote the
health benefits of chocolate.
1) Have you heard of any health benefits from
eating chocolate? If so, what were they?
Answers will vary.
Sample answer: Chocolate is an antioxidant;
lower cholesterol; reduce cognitive decline as you
age; reduce risk of cardiovascular problems,
heart disease, stroke.
Credit: ThinkStock
Objectives for the lesson
You will understand that:
o Conclusions about cause and effect cannot be made in observational studies
because of confounding variables.
o Conclusions about cause and effect can be made in experimental studies where
confounding is controlled.
o Experimental groups created through random assignment can usually control
variability among confounding variables.
You will begin to be able to:
o Analyze a statistical study and identify possible confounding variables.
o Decide when confounding variables restrict conclusions about cause and effect.
o Design an experiment that allows conclusions about cause and effect.
In this lesson, we consider how conclusions in statistical studies can be uncertain when
researchers do not know why a particular outcome has happened.
2) A research study in Sweden asked the research question: “Does chocolate reduce
the risk of stroke?”2
1
Benson, A. (2008, March 1.) A brief history of chocolate. Retrieved November 24, 2014, from
http://www.smithsonianmag.com/arts-culture/a-brief-history-of-chocolate-21860917/?no-ist.
2
Larsson, S. C., Virtamo, J., & Wolk, A. (2012). Chocolate consumption and risk of stroke: A prospective
cohort of men and meta-analysis. Neurology, 79(12), 1223-–1229.
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A sample of 37,000 Swedish men were divided into four groups based on their
normal chocolate consumption, ranging from those who ate no chocolate to the
group who ate the most (63 grams per week). It is important that the study included
so many people because it makes the results more reliable. Participants were
followed for 10 years.
The study concluded that men who ate more chocolate had a lower risk of
experiencing a stroke.
Part A: Did this study prove that eating chocolate causes a lower risk of stroke?
Explain your response.
Answer: No.
Sample explanation: This is an observational study so we cannot infer causation.
There may be other variables that can explain lowered risk of stroke among
chocolate eaters.
Part B: Offer an alternate explanation for this lowered risk among chocolate eaters.
Answers will vary.
Sample answer: Maybe people who ate more chocolate also tended to eat
something else that could be contributing to lower risk of stroke, or maybe they
tended to not eat something that may contribute to a higher risk of stroke.
3) In Preview Assignment 15.B, you read about confounding variables, or factors that
give alternate explanations for an effect. When there are confounding variables,
researchers cannot make inferences about cause and effect.
Another article3 pointed out some important facts in the study described above. The
men who ate the most chocolate tended to be younger, were more educated, and
were less likely to smoke or high blood pressure. They also reported eating more
vegetables and drinking more wine. All of these factors have positive health benefits.
Part A: Explain how this information sheds light on the study that says that eating
chocolate lowers the risk for stroke? Does it make us more or less certain
about the effects of eating chocolate?
Answers will vary.
3
Goodman, B. (2013, January 7). Don’t fudge the facts on chocolate studies. Retrieved November 24,
2014, from http://healthjournalism.org/blog/2013/01/dont-fudge-the-facts-on-chocolate-studies.
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Sample answer: It tells us that chocolate eaters have other attributes, which may
also contribute to lower stroke risk. These other factors make us less certain about
the effects of chocolate eating.
Part B: Chocolate eaters tended to be more highly educated. What other
confounding variables arise from this fact that may also cause a lowered
risk of stroke? (What other things do people who are better educated tend to
have in common?)
Answers will vary.
Sample answer: People who are more educated often make more money and thus
have better health care. More educated people may eat better and exercise more.
Education can lead to many behaviors that are beneficial for good health. All of
these are confounding variables.
Cause and effect conclusions cannot be made in observational studies because of
confounding variables. Experiments allow such conclusions by holding confounding
variables constant among several groups. To do this, researchers make sure that
groups are similar in terms of education, age, eating habits, and so on. When groups
are similar, confounding variables are controlled (not varying), and it becomes easier to
argue that a treatment (like chocolate) is the cause of an observed effect (like fewer
people having a stroke).
To control for the confounding variables, researchers divide participants into similar
groups. Some groups are treatment groups—they receive a real treatment. Other
groups are control groups—they receive a placebo (a fake treatment) or nothing at all.
Control groups are used as a basis for comparison to the treatment groups.
4) We want to design a new study to infer whether eating chocolate drinking causes
lowered risk of stroke. To do this, we compare a large group of chocolate eaters with
another large group of non-chocolate eaters.
Part A: Which is the control group? Which is the treatment group?
Answer: Control group: Non-chocolate eaters. Treatment group: Chocolate eaters.
Part B: Would it make sense to allow the study participants to choose which group
they are in? Explain the possible consequences of such an approach.
Answer: No.
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Suggested Instructor Notes 15.B, All things in moderation
Sample explanation: Allowing participants to choose their group would be a mistake.
Chocolate eaters would choose the chocolate-eating (treatment) group, and nonchocolate eaters would pick the other (control) group. Chocolate eaters probably
have other factors in common that could make the causes of any observed results
unclear.
Part C: As researchers, it is our job to create control and treatment groups so that
confounding variables, such as education or income, do not interfere with
the outcome. What should be our goal as we decide how to assign subjects
to groups?
Answer: Our goal should be to make the groups similar so that the confounding
variables are held constant from group to group.
In controlled statistical experiments, researchers try to minimize the effects of
confounding variables by creating treatment and control groups that are as similar as
possible. Groups are similar when confounding variables are held constant (on average)
from group to group.
5) You have gathered a group of volunteers who are all in their early 20s. They come
from various socioeconomic backgrounds, and none eat chocolate, but they are all
willing to try it for the sake of the experiment. You want to divide them into two
groups (control and treatment), and you will monitor their health for four decades.
Part A: Devise a method for dividing the volunteers into groups that will minimize
confounding in the long-term results. Be specific.
Answers may vary.
Sample answer: Use a random number generator to separate them into two groups.
Volunteers who get an odd number will be in the control (no-chocolate) group; those
with an even number will be in the treatment group.
Sample answer: Carefully design the groups to be similar by matching them
regarding diet, exercise habits, etc., Then randomly assign one person of each
similar pair to the treatment group and the other to the control group.
Part B: What are the explanatory and response variables in this study? Are they
quantitative or categorical?
Answer: The explanatory variable is eating chocolate (yes or no). The response
variable is stroke (yes or no). Both variables are categorical.
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Part C: With your method of dividing the volunteers into groups, suppose that the
decades-long study concludes with a significantly lower rate of stroke
among those who ate chocolate. Write a sentence that infers a conclusion
for the study.
Answer: With this carefully designed experimental study, we can state that there is
evidence that eating chocolate is the cause of lower risk for stroke.
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Practice Assignment 15.B
Practice Assignment 15.B
1) Researchers conducted a study to learn how early childhood education relates to a
child’s future earning potential. They gathered a random sample of 200 5-year-old
children and divided them into two groups. Children who had preschool education
were gathered into the first group. All other children were placed in the second group.
By age 30, the subjects who received preschool education were 80% less likely to
have received welfare in their 20s.
Part A: This study was ___________.
a) Observational
b) Experimental
Part B: Having a preschool education (yes or no) is one variable in this study.
Which is it?
a) Response
b) Explanatory
Part C: Receiving welfare in one’s 20s (yes or no) is another variable in this study.
Which is it?
a) Response
b) Explanatory
Part D: List possible confounding variables.
Part E: Can researchers conclude from this study that preschool education causes
people to be less likely to receive welfare in their 20s?
a) Yes
b) No
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Practice Assignment 15.B
Part F: Explain your answer to Part E.
2) The damaging effects of drinking too much alcohol have been observed for
centuries. Only lately have statistical studies shown that drinking alcohol in moderate
amounts is associated with positive health benefits.1 These studies do not always
explain why these benefits occur.
In one study focusing on the effects of drinking wine, a representative sample of
adults was divided into three groups: non-wine drinkers, moderate wine drinkers,
and heavy wine drinkers. Participants were tracked for decades recording wine
consumption and heart disease. The moderate wine drinkers had the lowest risk of
heart disease.
Part A: Did this study prove that moderate wine drinking causes a lower risk of heart
disease?
a) Yes
b) No
Part B: Offer an alternate explanation for this lowered risk among moderate wine
drinkers.
1
Mayo Clinic. (2014, February 11.) Alcohol use: If you drink, keep it moderate. Retrieved November 23,
2014, from http://www.mayoclinic.org/healthy-living/nutrition-and-healthy-eating/in-depth/alcohol/art20044551.
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Practice Assignment 15.B
Part C: In 2001, Danish researchers observed that moderate wine drinkers are
better educated, on average.2 Explain how this information sheds light on
the study that says that moderate wine drinkers have lower risk for heart
disease. Does it make us more or less certain about the effects of moderate
wine drinking?
a) This observation makes us more certain that drinking a moderate
amount of wine lowers the risk for heart disease.
b) This observation makes us less certain that drinking a moderate amount
of wine lowers the risk for heart disease.
Part D: Besides education, think of other confounding variables that might cause a
lowered risk of heart disease among moderate wine drinkers.
3) We want to design an experimental study to infer whether moderate wine drinking
causes lowered risk of heart disease. To do this, we plan to compare participants
who drink a moderate amount of wine with participants who do not drink wine.
Part A: Which is the control group? Which is the treatment group?
a) Non-wine drinkers are the control group, and moderate drinkers are the
treatment group.
b) Moderate wine drinkers are the control group, and non-wine drinkers are
the treatment group.
Part B: Would it make sense to allow the study participants to choose which group
they are in?
a) Yes
b) No
2
Mortensen, E. L., Jensen, H. H., Sanders, S. A., & Reinisch, J. M. (2001). Better psychological
functioning and higher social status may largely explain the apparent health benefits of wine. Archives of
Internal Medicine, 161(15), 1844-1848.
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Practice Assignment 15.B
Part C: As researchers, it is our job to create control and treatment groups so that
confounding variables, such as education or income, do not interfere with
the outcome. What should be our goal as we decide how to assign subjects
to groups?
a) To make sure that everyone in the control group is similar to one another
and that everyone in the treatment group is similar to one another.
b) To make sure that the composition of the control group is similar to the
composition of the treatment group.
Part D: You have gathered a group of volunteers that are all in their early 20s. They
come from various socioeconomic backgrounds, and none drink wine, but
they are all willing to try it for the sake of the experiment. You want to divide
them into two groups (control and treatment), and you will monitor their
health for four decades.
Which of the following is an acceptable method for dividing the volunteers
into groups that will minimize confounding in the long-term results.
a) Put all of the men into the treatment group and all of the women into the
control group.
b) Put all of the women into the treatment group and all of the men into the
control group.
c) Put all of the participants under the age of 40 in the treatment group and
all of the participants over the age of 40 in the control group.
d) Put all of the participants under the age of 40 in the control group and all
of the participants over the age of 40 in the treatment group.
e) Randomly assign each participant to either the treatment group or the
control group.
Part E: With your method of dividing the volunteers into groups, suppose that the
decades-long study concludes with a significantly lower rate of heart
disease among those who drank moderate amounts of wine. Write a
sentence that infers a conclusion for the study.
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