Chapter 2 Notes
Math 1680
Math 1680 Assignments
• Look over Chapter 1 and 2 before Wednesday
• Assignment #2: Chapter 2 Exercise Set A (all, but
#7, 8, and 10) due on Monday, January 31st.
• By Wednesday Jan 26th, do Ch 2 review exercises
(not to turn in). Will discuss in class.
• Quiz 1 will be over the reading for Chapter 1
• Don’t forget Prerequisite Verification is due to me
by Friday Jan 28th at 3pm.
• If you want a copy of these notes, email me and I
will reply with them attached.
Section 1
• Controlled experiments vs. observational studies
– In a control experiment, the investigators choose who is
in the control group and who is in the treatment group
– In an observational study the subject assign him or
herself to the treatment or the control group, and the
investigators solely observe what is going on.
– Controlled experiment and observational study still
have both a treatment group and a control group.
Examples of need for
observational vs. controlled
• A study of the effects of smoking
• A study of the effects of sexual promiscuity
• A study of the effects of being an alcoholic
– These are all things that someone is not going to take
part in for 10 years without it being a regular habit, thus
the need for observation study
Causation versus Association
• In an observational study of smokers and
nonsmoker, there is more common
occurrence of heart attacks, lung cancer, and
many other diseases among smokers.
– Thus there is a strong association between
smokers and these diseases.
“Association is circumstantial evidence for
causation. However, the proof is incomplete.”
• There could be confounding factors that are
not being considered
– (In the case of smoking, the idea of other
confounding factors were found implausible
and that if you quitting smoking, you will live
longer.)
Ways to “control” confounding
• Investigate how a control is selected
– Was the control group truly similar to the
treatment group aside from the exposure of
interest?
• Techniques when confounding factors are
identified
– Make comparisons in smaller more
homogeneous groups
Examples in the study of smokers
• Confounding factor: gender
– Men are more susceptible to heart disease than women
– Thus, they compared male smokers to male
nonsmokers
• Confounding factor: age
– Thus, they compared male smokers age 55-59 to male
nonsmokers age 55-59
Section 2
• The Coronary Drug project
– Randomized, controlled double-blind
– One drug tested: Clofibrate
• Death rate: 20% treatment group and 21% control
group, thus Clofibrate does not save lives
• Suggested confounding factor: adherence
• See Table 1 on page 14
Conclusion
• Clofibrate does not have an effect
• Adherers are different from non-adherers
– Remember: comparing adherers to nonadherers is an observation study because the
patients made the decision to adhere or not.
Section 3 (More Examples)
• Pellagra
– Sporadically hit villages
– Sanitary conditions is diseased households was
poor and had many flies
– One such blood-sucking fly (Simulium) had the
same geographic range as Pellagra
– Did pellagra spread through insects?
Conclusion
• “Pellagra was caused by bad diet, and is not
infectious”
– Poorer villages had more restrictive diets
– “The flies were a marker of poverty, not a cause of
Pellagra”
– Association does not imply causation
• Read through next three examples on your own…
Section 4
• Sex Bias at the University of California,
Berkeley Graduate Admissions
– 44% of male applicants admitted
– 35% of female applicants admitted
– Is there discrimination taking place?
• What needs to be done?
• Look at more homogeneous groups….
College Admission Bias
Men
Women
Major
Number of
applicants
Number
admitted
Number of
applicants
Number
admitted
A
825
512
108
89
B
560
353
25
17
C
325
120
593
202
D
417
138
375
131
E
191
53
393
94
F
373
22
341
24
Notice
• Over 50% of the men applied to the first
two majors that were easier to get into
• Over 90% women applied to the later four
that were much harder to get into
• Choice of major was a confounding factor
• Weighted averages show no discrimination
• Simpson’s Paradox
– Relationship between percentages in
subgroups can be reverse when the
subgroups are combined
• Read Section 5 on your own time…
Class Discussion
• Ch 2 review exercises and any other
pertinent questions.