STAT 110 - Section 5
Lecture 9
Professor Hao Wang
University of South Carolina
Spring 2012
Thought Question 1:
In a study to relate two conditions, researchers
often define one as the explanatory variable
and other as the outcome or response variable.
In a study to determine whether surgery or
chemotherapy results in higher survival rates for
a certain type of cancer, whether the patient
survived is one variable, and whether he or she
received surgery or chemotherapy is the other.
Which is the explanatory variable and which is
the response variable?
Thought Question 2:
In an experiment, researchers assign
“treatments” to participants, whereas in
an observational study, they simply observe
what the participants do naturally.
Give an example of a situation where
an experiment would not be feasible
for ethical reasons.
Thought Question 3:
Interested in determining whether a daily dose
of vitamin C helps prevent colds. Recruit 20
volunteers, want half to take vitamin C and
other half to agree not to take it. Ask each
which they prefer, and ten say take vitamin
and other ten say not. Ask each to record how
many colds he or she gets during the next ten
weeks. At end of time, compare the results
reported from the two groups.
Give 3 reasons why this is not a good
experiment.
Thought Question 4:
When experimenters want to compare two
treatments, such as an old and a new drug, they
use randomization to assign the participants to
the two conditions.
If you had 50 people participate in such a study,
how would you go about randomizing them?
Why do you think randomization is necessary?
Why shouldn’t the experimenter decide which
people should get which treatment?
Defining a Common Language
Explanatory variable is one that may
explain or may cause differences in a
response variable (or outcome
variable).
Example:
Study found that overall left-handed people die
at a younger age than right-handed people.
Explanatory = Handedness
Response = Age at death
A treatment is one or a combination
of categories of the explanatory
variable(s) assigned by the
experimenter.
Example: meditators/vegetarian and speed of aging process
Two Explanatory Var. = meditator or not; vegetarian or not;
Four treatments: (Med,Veg) (Med, Non-veg)
(Non-med, non-veg), (Not Med, Non-veg)
Response = speed of aging
Example
You are planning an experiment to study the effect
of gasoline brand and vehicle weight on the gas
mileage (miles per gallon) of sport utility
vehicles. In this study,
A. Gas mileage is the response variable.
B. Gas mileage is an explanatory variable.
Example
You are planning an experiment to study the effect
of gasoline brand and vehicle weight on the gas
mileage (miles per gallon) of sport utility
vehicles. In this study, the explanatory
variable(s) is(are)
A. Miles per gallon
B. Sport utility vehicles
C. Gasoline brand
D. vehicle weight
E. (C) and (D)
The study includes three vehicle weights and three
brands of gasoline, so there are:
A. Two treatments and six explanatory variables
B. Two treatments and nine explanatory variables
C. Two explanatory variables and six treatments
D. Two explanatory variables and nine treatments
Problems in Experiments
lurking variable – a variable that has an important
effect on the relationship among
the variables in a study but is not
one of the explanatory variables
studied
confounding – two variables are confounded when
their effects on a response variable
cannot be distinguished from each
other
 confounded variables can be either
explanatory or lurking
Example: Lurking Variables
Study of the relationship between smoking
during pregnancy and child’s subsequent IQ
a few years after birth.
• Explanatory variable: whether or not the
mother smoked during pregnancy
• Response variable: subsequent IQ of the child
• Women who smoke also have poor nutrition,
lower levels of education, or lower income.
• Possible Lurking Variables: Mother’s
nutrition, education, and income.
Example: Lurking variable
• Consider wanting to compare the effectiveness of
online business calculus classes to traditional in-class
business calculus classes.
• Two sections of the course, one online and on in-class,
are scheduled for the semester. The students choose
which class to sign up for.
• The two classes are taught by the same teacher and
take the same final exam at the end of the semester.
The class with the higher average on the final will be
declared to have had the better method.
Example
• What if the students who are less confident in their
mathematical ability also dislike computers more (or
want to see the instructor in person).
• Maybe the average scores on a pre-calculus test for
the two groups are
online – 40.70 vs traditional – 27.64
which group do you think should do better?
•The effect of online vs traditional instruction is mixed up
with influences lurking in the background.
• Here, student preparation (a lurking variable) is
confounded with the explanatory variable.
Example
online vs
traditional
(explanatory
variable)
Causes?
student
preparation
(lurking
variable)
test score
after course
(response
variable)
The influence of course
setting can’t be
distinguished from the
influence of student
preparation.
Randomized Comparative Experiment
randomized comparative experiment – compare
the effects of a treatment
on an experimental group
to a control group
• Subjects are randomly assigned to two groups –
experimental and control.
Randomized Comparative Experiment
group 1
n1 subjects
random
allocation
treatment 1
compare
response
group 2
n2 subjects
treatment 2
The Logic of Experimental Design
• Randomization produces groups of subjects that
should be similar in all respects before we apply
the treatments.
• Comparative design ensures that influences
other than the experimental treatments operate
equally on all groups.
• Therefore, differences in the response variable
must be due to the effects of the treatments.
Principles of Experimental Design
• Control the effects of lurking variables on the
response, most simply by comparing two or
more treatments.
• Randomize – use impersonal chance to assign
subjects to treatments.
• Use enough subjects in each group to reduce
chance variation in the results.
placebo – a dummy treatment with no active
ingredients that is used to control for
psychological effects, especially in
medical experiments
placebo effect – the response of patients to a
placebo
• Some subjects improve when taking placebo!
Example: Quitting Smoking with Nicotine
Patches
Study Details:
• 240 smokers recruited (all met entry criteria).
• Randomly assigned to either nicotine patch or
placebo patch for 8 weeks. All received counseling.
• Why can not let them volunteer ?
• After 8 weeks: 46% of nicotine group quit, only 20%
of placebo group quit.
• After 1 year: 27.5% of nicotine group quit, only 14.2%
of placebo group quit.
Source: Hurt et al., 23 February
1994
“What if we can’t Experiment?”
or “How to Live with Observational Studies”
• Good studies are comparative even when
they’re not experiments.
• We can use matching to control for lurking
variables.
• We can measure and adjust for confounding
variables (by using statistical techniques).
Example: Observational study
Study of the relationship between smoking
during pregnancy and child’s subsequent IQ
a few years after birth.
• Explanatory variable: whether or not the
mother smoked during pregnancy
• Response variable: subsequent IQ of the child
• Women who smoke also have poor nutrition,
lower levels of education, or lower income.
• Possible Lurking Variables: Mother’s
nutrition, education, and income.