(18 points possible)
Unit 1 Homework - Question Set 1
A doctor examines a group of healthy adults (presenting to clinic for their annual physical
exams) and records their respiratory rates, shown in the following table.
Outcome
(RR in breaths Frequency
pe
(12 points possible)
This week, we discussed a 2000 study in the New England Journal of Medicine (NEJM) that
compared patients with rheumatoid arthritis who were randomly assigned to take either
Vioxx or a conventional pain reliever, naproxen. In 2005, it
Overview
Statistics for Health Care
n
Statistics in Medicine @ Stanford University
Basic study designs; measures of
disease frequency and association
Unit 2:
Overview
Teaser 1, Unit 2
Teaser 2, Unit 2
2000 NEJM study on rofecoxib vs.
naproxen, Randomized
Overview
n
Statistics for Health Care
Introduction to probability and
conditional probability; Bayes Rule;
diagnostic testing
Unit 3:
Overview/Teasers
Teaser 1, Unit 3
n
A classic statistics problem: The Monty Hall
Problem
Teaser 1, Unit 3
n
You are on th
Statistics for Health Care
Unit 6:
Overview/Teasers
Overview
Type I and Type II errors and statistical
power; pitfalls of p-values
Overview of statistical tests
Teaser 1, Unit 6
A prospective cohort study of 34,079 women found
that women who exercised >21
Statistics in Healthcare
Unit 7:
Overview/Teasers
Overview
Tests for comparing groups
unadjusted analyses!
Common statistics for various
types of outcome data
Outcome
Variable
Are the observations independent or
correlated?
Alternatives
(assumptions
viola
UNIT 9 HOMEWORK
The following table comes from a paper that examined the relationship between the duration of breast feeding as an
infant and the presence of overweight or obesity at age 18 years (in men). (The p-value for linear trend was
calculated by r
Statistics in Healthcare
Unit 9:
Overview/Teasers
Overview
Regression II: Logistic regression; Cox
regression
Common statistics for various
types of outcome data
Outcome
Variable
Are the observations independent or
correlated?
Alternatives
(assumptions
vi
Statistics for Health Care
Statistics in Medicine @ Stanford University
Unit 2:
Overview
Overview
n
Basic study designs; measures of
disease frequency and association
1
Teaser 1, Unit 2
2000 NEJM study on rofecoxib vs.
naproxen, Randomized Trial
Teaser 2,
Statistics for Health Care
Unit 3:
Overview/Teasers
Overview
n
Introduction to probability and
conditional probability; Bayes Rule;
diagnostic testing
1
Teaser 1, Unit 3
n
A classic statistics problem: The Monty Hall
Problem
Teaser 1, Unit 3
n
You are on
Statistics for Health Care
Statistics in Medicine @ Stanford University
Unit 1
Overview/Teasers
First rules of statistics
n
n
Use common sense!
Draw lots of pictures!
1
Whats wrong with this?
n
n
Study with sample size of 10 (N=10)
Results: Objective scor
UNIT 4 HOMEWORK
For some problems, you will need a normal probability calculator or chart. Here are some links:
Graphical standard normal calculator/chart:
http:/www.mathsisfun.com/data/standard-normal-distribution-table.html
Simple standard normal calcul
UNIT 3 HOMEWORK
Question 1:
In 1980 (before the era of in-vitro fertilization), there were 3,612,258 births in the United States
(according to the U.S. Census Bureau), of which 68,339 births were to twins and 1,337 births
were to triplets or more.
What wa
Statistics in Healthcare
Unit 8:
Overview/Teasers
Overview
Regression I: Linear regression
Common statistics for various
types of outcome data
Outcome
Variable
Are the observations independent or
correlated?
Alternatives
(assumptions
violated)
independent
Statistics for Health Care
Unit 5:
Overview/Teasers
Overview
Statistical inference: confidence
intervals, hypothesis tests, and p-values
Teaser 1, Unit 5, polls
New York Times/CBS News Poll (Feb. 2012) found:
59 percent said the health insurance plans of
300699 Discrete Structures and Complexity, Spring 2012
Tutorial Week 7 (Solutions)
On the role of tutorials in this unit:
The purpose of the tutorials is to reinforce what you have learnt in lectures; they are not meant
to, and cannot, replace attending o
300699 Discrete Structures and Complexity, Spring 2012
Tutorial Week 6 (Solutions)
On the role of tutorials in this unit:
The purpose of the tutorials is to reinforce what you have learnt in lectures; they are not meant
to, and cannot, replace attending o
300699 Discrete Structures and Complexity, Spring 2012
Tutorial Week 8 (Solutions)
On the role of tutorials in this unit:
The purpose of the tutorials is to reinforce what you have learnt in lectures; they are not meant
to, and cannot, replace attending o
300699 Discrete Structures and Complexity, Spring 2012
Tutorial Week 10 (Solutions)
On the role of tutorials in this unit:
The purpose of the tutorials is to reinforce what you have learnt in lectures; they are not meant
to, and cannot, replace attending
Table of Logical Equivalences
p q q p
p q q p
Associative
(p q) r p (q r)
(p q) r p (q r)
Distributive
p (q r) (p q) (p r)
p (q r) (p q) (p r)
Identity
p T p
p F p
Negation
p p T
p p F
Double Negative
( p) p
Commutative
Idempotent
p p p
p p p
Universal B
TABLE 6 Logical Equivalences.
Equivalence
Name
p AT=.p
Identity laws
p VF=.p
Domination laws
p vT=.T
pAF=.F
pvp=.p
Idempotent laws
p Ap=.p
-.(-.p) =. p
Double negati on law
p vq=.q Vp
Commutative laws
p Aq=.q Ap
(p
q) V r
V
(p A q) A r
p V (q A r)
p A (q
COT3100: Propositional Equivalences
Logic and Proofs
COT3100: Applications of Discrete Structures COT3100: Propositional Equivalences
1 Translating from Natural Languages
EXAMPLE. Translate the following sentence into a logical expression:
I met my ex
CLASS TEST 2 (Version B) (Solutions)
SPRING SESSION 2011
SCHOOL OF COMPUTING AND MATHEMATICS
Unit Name:
Discrete Structures and Complexity
Unit Number:
300699
Time Allowed:
40 minutes
Number of Questions: Five (5)
Lecturers Names:
Question 1
Dr James East
CLASS TEST 1 (Version A) (Solutions)
SPRING SESSION 2011
SCHOOL OF COMPUTING AND MATHEMATICS
Unit Name:
Discrete Structures and Complexity
Unit Number:
300699
Time Allowed:
40 minutes
Number of Questions: Six (6)
Lecturers Names:
Dr James East, Dr Volker
CLASS TEST 1 (Version B) (Solutions)
SPRING SESSION 2011
SCHOOL OF COMPUTING AND MATHEMATICS
Unit Name:
Discrete Structures and Complexity
Unit Number:
300699
Time Allowed:
40 minutes
Number of Questions: Six (6)
Lecturers Names:
Dr James East, Dr Volker
CLASS TEST 2 (Version A) (Solutions)
SPRING SESSION 2011
SCHOOL OF COMPUTING AND MATHEMATICS
Unit Name:
Discrete Structures and Complexity
Unit Number:
300699
Time Allowed:
40 minutes
Number of Questions: Five (5)
Lecturers Names:
Question 1
Dr James East
Business statistics practice
Assignment (1)
2.4
2.8
a.
(a and b)
Category / Class
A
B
C
D
Frequency
100
25
75
50
Frequency
0.40
0.10
0.30
0.20
Relative
Frequency
40%
10%
30%
20%
Tally for Discrete Variables: Sports League
Sports
Rel.
League
Count
Freq.
Pe