STATISTICS 226, Winter 1997, Homework 1
1
TAs notes
Whenever possible, parts of a question will be graded conditionally on how you answered the preceding part(s). Be consistent throughout your problem solving. You may feel free to discuss homework with o
Biostatistics 695 HW # 1
Jian Kang
September 20, 2007
3. CDA 1.1, 1.2, 1.3, 1.6, 1.15, 1.17 (for 1.1 give a short explanation for each answer).
1.1 Identify each variable as nominal, ordinal, or interval.
a. UK political party preference (Labour, Conserva
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Solution to Tutorial 8
1. (a) We rst t the loglinear model of independence between educational aspiration (E)
and income (I):
log ij = + E + I , i = 1, , 4, j = 1, 2, 3.
i
j
The deviance of the tte
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Solution to Tutorial 2
1. (a) Belief in after life (Y ) is the response variable and Race (X ) is the explanatory variable.
(b) To measure the association, we can use odds ratio. Then the sample od
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Solution to Tutorial 5
1. (a) For treatment A, x = 0 and we have log A = . For treatment B, x = 1,and we have
log B = + Therefore, log B log A = ( + ) = The estimated model t is:
log = 1.6094 + 0.5
Biostatistics 695 HW # 5
Jian Kang
October 25, 2007
4.1 In the 2000 U.S. presidential election, Palm Beach County in Florida was the
focus of unusual voting patterns including a large number of illegal double votes.
apparently caused by a confusing butter
Biostatistics 695 HW # 9
Jian Kang
December 2, 2007
7.1 For Table 7.13, let Y = belief in life after death, x1 = gender (1 = females,
0 = males), and x1 = race (1 = whites, 0 = blacks). Table 7.14 shows the t of
the model
G
R
log(j /3 ) = j + j x1 + j x2
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Tutorial 2
1. The following table was taken from the 1991 General Social Survey.
Belief in Afterlife
Race
Yes
No or Undecided
White
Black
621
89
239
42
(a) Identify each classication as a response
Biostatistics 695 HW # 2
Jian Kang
September 26, 2007
1. CDA 1.9, 1.10, 1.30
1.9 Table 1.3 contains Ladislaus von Bortkiewiczs data on deaths of soldiers in
the Prussian army from kicks by army mules (Fisher 1934; Quine and Seneta
1987) The data refer to
Biostatistics 695 HW # 10
Jian Kang
December 9, 2007
8.1 The 1988 General Social Survey compiled by the National Opinion Research
Center asked: Do you support or oppose the following measures to deal with
AIDS?(1) Have the government pay all of the health
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Tutorial 5
1. An experiment analyzes imperfection rates for two processes used to fabricate silicon wafers
for computer chips. For treatment A applied to 10 wafers, the numbers of imperfections
are
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ST3241 Categorical Data Analysis I
Two-way Contingency Tables
Odds Ratio and Tests of Independence
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%
1
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Inference For Odds Ratio (p. 24)
For small to moderate sample size, the distribution of sample
odds ratio is highly skewed.
For = 1, cannot
STATISTICS 226, Winter 1997, Homework 2
1
TAs notes
To receive full credits, you must show the work by which you reach the answer(s). Interpretation of results should be phrased in the context of question(s) and as detailed as possible. Numbers themselve
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Tutorial 8
1. A study on educational aspirations of high school students (S. Crysdale, Int. J. Compar.
Sociol.,16:19 - 36 (1975) measured aspirations using the scale (some high school, high
school
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Tutorial 7
1. The following table is taken from a report on the relationship between aspirin use (X ) and
myocardial infarction (Y ) by the Physicians Health Study Research Group at Harvard
Medical
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Tutorial 6
1. The U.S. National Collegiate Athletic Association (NCAA) conducted a study of graduation rates for student athletes who were freshmen during the 1984/1985 academic year.
The following
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Tutorial 4
1. For baseball national league games during nine decades, the following table shows the
percentage of times that the starting pitcher pitched a complete game.
Decade
Percent
Complete
19
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Tutorial 3
1. In murder trials in 20 Florida counties during 1976 and 1977, the death penalty was given
in 19 out of 151 cases in which a white killed a white, in 0 out of 9 cases in which a white
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Tutorial 1
1. Which scale of measurement is most appropriate for the following variables - nominal, or
ordinal?
(a) Political party aliation (Democrat, Republican, unaliated).
(b) Highest degree ob
ST3241 Categorical Data Analysis
Midterm Examination
6:30-8:00 pm, March 04, 2011
(Total 5 problems, 100 pts)
NAME:
Key
Major:
Student ID:
PLEDGE:
I have neither given nor received any unauthorized aid in completing this exam.
SIGNATURE:
Problem
Full pts
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Solution to Tutorial 7
1. (a) We rst t the independence model
log ij = + X + Y , i = 1, 2, j = 1, 2.
i
j
The parameter estimates are = 9.2956, X = 0.0003, X = 0.0,Y = 4.3085 and
1
2
1
Y = 0.0. The
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Solutions to Tutorial 6
1. Let be the probability of graduation of a student athlete and let G denotes the gender
and R denotes the race.
(a) The logistic regression model for the homogeneous assoc
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Solution to Tutorial 4
1. (a) 0.7578 and -0.0695 are the intercept and slope of the tted straight line, respectively.
We can interpret it as for x = 0 (i.e. in the decade 1890-1899), the estimated
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Solution to Tutorial 3
1. (a) The three-contingency table is given below:
Victims
Defendants
Death Penalty
Race
Race
Yes
No
Total
White
White
Black
19
11
132
52
151
63
Black
White
Black
0
6
9
97
9
ST3241 Categorical Data Analysis I
Semester II, 2010-2011
Solution to Tutorial 1
1. (a) Nominal.
(b) Ordinal.
(c) Ordinal.
(d) Nominal.
(e) Nominal.
2. As the student selects one answer randomly out of four possible choices, the prob- ability
that the stu
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ST3241 Categorical Data Analysis I
Multicategory Logit Models
Logit Models For Nominal Responses
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1
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Models For Nominal Responses
Y is nominal with J categories.
Let cfw_1 , , J denote the response probabilities with
1 + + J = 1 .
If we have
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ST3241 Categorical Data Analysis I
Loglinear Models
2 2 Models For Contingency Tables
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Two-way Tables
Consider an I J contingency table that crossclassies a
sample of n subjects on two categorical responses.
Let Yij be the observed cell fre