Transcript Feb. 2 Statistic for the day:

Feb. 2 Statistic for the day:
Percent of the time, since 1887, that
Punxsutawney Phil has correctly predicted the
length of winter: 39
Source: http://www.stormfax.com/ghogday.htm
Assignment: Exercise #1, p. 63; Exercise
#11, p. 124; Exercise #4, p. 136
These slides were created by Tom Hettmansperger and in some cases
modified by David Hunter
Research question: Does a chemical QS when added
to sun tan lotion enhance tanning when mixed with
Coppertone?
Response: Tanning index
Explanatory Variable: QS or not.
What sort of study?
•Randomized Experiment?
•Observational Study?
Randomized Experiment.
W/O QS
8.0
8.3
8.4
8.7
9.2
9.3
9.7
10.8
10.9
11.0
QS
8.8
9.3
9.1
9.6
10.0
10.4
10.6
11.6
11.7
12.0
Tanning Index
12
11
10
9
8
W/O QS
With QS
There is a lot of overlap between the boxplots.
This suggests that there is NOT a significant
difference between QS and W/O QS.
The problem:
Too much variability within the two groups
due to variation in tanning ability.
We need to eliminate some of the within
variability.
Then we may be able to detect the difference
across the two groups.
The answer is to let each subject be his/her own
control.
RANDOMLY assign QS or not to left or right side
of the body.
The experimental design is called
PAIRED DATA DESIGN.
Tan for 3 hours.
Measure the tanning index.
Record the difference between QS and W/O QS
QS – W/O QS
0.8
1.0
0.7
0.9
0.8
0.9
0.9
0.8
0.8
1.0
Notice that the treatments are only compared within a subject.
Differences within Subjects
1.0
0.9
0.8
0.7
Boxplot of 10 differences within subjects.
Note that the entire data set is above 0.
This means QS had higher index than W/O QS for all subjects.
W/O
Quaker
State
8.0
8.3
8.4
8.7
9.2
9.3
9.7
10.8
10.9
11.0
Quaker
State
QS – W/O QS
8.8
9.3
9.1
9.6
10.0
10.4
10.6
11.6
11.7
12.0
0.8
1.0
0.7
0.9
0.8
0.9
0.9
0.8
0.8
1.0
Tanning Index
12
11
Unpaired
10
9
8
W/O QS
With QS
Differences within Subjects
1.0
Paired
0.9
0.8
0.7
Research question: How prevalent is
cheating at PSU?
Imagine the following study:
Individual students taking an exam in a particular
course are filmed and observed closely by a team of
extra observers, who then record the number of
instances of cheating they observe.
Any problems with this?
Hawthorne Effect!
Research question: Do cell phones cause
cancer?
What sort of a study could be used to answer this?
•Observational Study?
•Randomized Experiment?
Observational Study
If we cannot establish cause and effect,
can we establish an association between
cell phones and cancer?
Observational Study:
Response Variable: whether or not a subject
gets cancer.
Explanatory Variable: whether or not the subject
uses a cell phone.
Randomly select people who use cell phones and
record the % who get cancer.
Randomly select people who never use cell phones
and record the % who get cancer.
This may require a very long time.
A special kind of observational study:
SWITCH RESPONSE AND EXPLANATORY VARIABLES
Response Variable: whether a subject uses a cell phone or not
Explanatory Variable: whether a subject has cancer or not.
1. Select a sample of cancer patients (Cancer Case)
2. Develop a group of people who match the
cancer patients but do not have cancer. (Control)
3. Compute the % who use cell phones in each group.
Called a Case-Control Study
Also Called: Retrospective Case-Control Study
Retrospective because we asked subjects if they
have been using cell phones in the past.
Note that since we only look for an association
it does not matter which variable is the response
and which is the explanatory.
Suppose we take 100 cancer patients and then take
200 non-cancer patients in the same hospital as controls.
Data:
Cancer
No
Cancer
Yes
No
Cell Phone Cell
Phone
30
70
100
------------ ----------30%
70%
ME=10% ME=10%
50
150
200
------------ ----------25%
75%
ME=7%
ME=7%
Plot with Margins of Error
Percentages and Margins of Error
Note the large overlap.
40
30
20
Cancer
No
Cancer
We would probably conclude that there is little or no
association between using cell phones and cancer.
Research question: How does
putting a smiley face on the bill
influence a waitperson’s tip?
Interacting variable: Sex of waitperson
 Female waitress: Drawing a smiley face
increased tip significantly
 Male waiter: Drawing a smiley face
decreased tip, though not significantly

Source: Journ. Appl. Soc. Psych, 1996
Interaction plot: Smiley-face
experiment