SIPA U6500 Quantitative Analysis for International and Public
Course Overview and Objectives
This course introduces students to the fundamentals of statistical analysis. We will examine the principles and basic
methods for analyzing quantitative data, with a focus on applications to problems in public policy, management, and
the social sciences. We will begin with simple statistical techniques for describing and summarizing data and build
toward the use of more sophisticated techniques for drawing inferences from data and making predictions about the
social world.
The course will assume that students have little mathematical background beyond high school algebra. The for-
mal mathematical foundation of statistics is downplayed; students who expect to make extensive and customized use
of advanced statistical methods may be better served by a different course. This course also offers less practice in
writing research papers using quantitative analysis than some courses (e.g., Political Science 4910). Most SIPA stu-
dents, however, should benefit from our emphasis on generating and interpreting statistical results in many different
practical contexts.
Students will be trained on STATA, which is supported in the SIPA computer lab. This powerful statistical
package is frequently used to manage and analyze quantitative data in many organizational/institutional contexts. A
practical mastery of a major statistical package will be an important proficiency for many of you down the road. You
can obtain more information about your lab sticker at the SIPA lab, which is located on the 5th floor of IAB.
Requirements and Recommendations
Students are required to attend class. Lectures will sometimes cover matters related directly to the homework
assignments that are not covered fully in the assigned readings. Students are also required to actively participate
in the learning process - paying attention, taking notes, asking question, solving in-class exercises, etc. The use of
laptops during the class is strongly discouraged.
Students are required to review and obtain any relevant material (e.g., weekly handouts) in advance of each
class by going to Courseworks at https://courseworks.columbia.edu. This site will include all course
materials including: the syllabus, weekly class handouts, class summaries, homework assignments, answer keys for
assignments, policy papers discussed in class, midterm and final exam review sheets, and information on data as
well as downloadable datasets.
Students are required to come to class having already completed the assigned readings for that class. The purpose
of this requirement is to ensure that lectures focus on learning how to bring statistical concepts and methods to life
in an applied context. Class will be conducted in a manner that assumes this advance preparation has been done.
Students are recommended to download, print, and bring to class the weekly class handout. The weekly class
handout is integrated with the lecture and is meant to serve two purposes. First, it allows students to take notes
during the class and organize these notes within the flow of the lecture. Second, it provides a preview of the topics to
be covered in class. At the minimum, students must absolutely read the handout slides labeled “Read Before Class”
and attempt or think about the “In-Class Exercises” before attending the lecture.
Students are required to attend one weekly lab session in addition to the regular lecture. These labs will be
important supplements to each lecture, where concepts and methods will be reviewed and students will receive
direction and support as they learn STATA. In certain weeks, some concepts we did not have time to cover in class
will be taught in the labs.
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Grading
The three components to the final course grade will include weekly homework (problem sets and quizzes) (30%),
a midterm exam, and a final exam. The exam with a larger score will get a 40% weight and the other exam a
30% weight. In “borderline” cases, the quality of your class attendance and participation will be considered in
determining your final grade.
Problem Sets
The role of the homework is both to solidify concepts covered in the previous lectures, by providing students with
opportunities to practice their applications, as well as to prepare students for the concepts to be covered in future
lectures. As such, the problem sets will cover both the topics covered in the previous lectures and the readings for
the upcoming lecture.
Problem sets will be assigned at least a week in advance of their due dates. Late problem sets will not be
accepted for credit. You are encouraged to be actively engaged in the completion of every problem set since hands-
on work (computer-based or otherwise) is essential to fully understanding the material presented in this course.
Problem sets may be done individually or in groups of up to three students. Groups may be formed or dissolved as
students see fit throughout the semester.
Problem sets will be turned in as hard copy at the beginning of a lecture on Monday. Only one hard copy of the
problem set must be turned in by students in a group.
Quizzes
Throughout the semester there will be opportunities to earn extra credit points through optional quizzes. The quizzes
are due on Mondays at 10am. The points earned on quizzes will be counted toward the score on problem sets.
Exams
The Midterm Exam will take place on Friday, March 3rd, at a time to be determined later. The Final Exam will take
place on Monday, May 8th, at a time to be determined later.
Students must take both the midterm exam and the final exam. Failure to do so may result in failing the course.
We will do our best to provide reasonable accommodations to conflicts with the exam, but that is not guaranteed in
all cases.
STATA Use
SIPAIT is pleased to announce that it has signed a one year Stata BE 17 site license for use by SIPA students only.
You can find more information here: https://www.sipa.columbia.edu/information-technology/
software-download/stata-students .
SIPA Computer Lab Policy 2022 - 2023
The SIPA computer lab accommodates a maximum of 44 students per session. All students taking classes or at-
tending recitations in the computer lab must adhere to this limit. Additional students will not be allowed to share
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computer stations, sit on the floor, or sit in the back of the room. Instructors, TAs, and computer lab staff will enforce
this policy.
All SIPA students must have a valid SIPA Lab ID to access the SIPA lab resources. Validating the Columbia
University ID can be done in room 510 IAB each semester. All registered SIPA students are billed automatically a
fee each semester during the academic year based on their program.
Non-SIPA students are issued a guest ID for access to attend a class in the SIPA instructional lab. Guest IDs are
issued after information is received from the Office of Student Affairs in the second week of classes.
Non-SIPA students who wish to use the SIPA computer lab outside of regular class/recitation time must
pay $180 per semester (payable by check or cash in 510 IAB). Non-SIPA students who choose not to pay this fee
should consult their course instructor and the IT office at their own school about any special software required for
the course. SIPA IT is not equipped to provide technical support to non-SIPA students who have not paid the $180
per semester fee.
For more information: https://www.sipa.columbia.edu/information-technology/it-policies-procedures/
computing-guidelines-sipa
Academic Integrity Statement
The School of International & Public Affairs does not tolerate cheating and/or plagiarism in any form. Those students
who violate the Code of Academic & Professional Conduct will be subject to the Dean’s Disciplinary Procedures.
Please familiarize yourself with the proper methods of citation and attribution. The School provides some useful
resources online; we strongly encourage you to familiarize yourself with these various styles before conducting your
research.
You are requested to view the Code of Academic & Professional Conduct here: http://new.sipa.columbia.
edu/code-of-academic-and-professional-conduct
Violations of the Code of Academic & Professional Conduct will be reported to the Associate Dean for Student
Affairs.
Readings
The required and recommended textbooks may be purchased at Book Culture (536 West 112th Street).
Required Texts:
D. Moore, G. McCabe, and B. Craig “Introduction to the Practice of Statistics” 9th edition (2017), W. H. Freeman
and Company
C. Lewis-Beck and M. Lewis-Beck, “Applied Regression” 2nd edition (2015) SAGE
Recommended Texts:
Lawrence C. Hamilton “Statistics with STATA: Version 12”
X. Wang “Performance Analysis for Public and Nonprofit Organizations”
E. Berman and X. Wang “Essential Statistics for Public Managers and Policy Analysts”
Supplemental Texts:
T. Wonnacott and R. Wonnacott “Introductory Statistics” 5th edition (1990)
C. Achen “Interpreting and Using Regression” (1982)
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Course Outline
Session 1: Orientation and Research Design
Monday, January 23rd
Orientation
– Introduction of course, teaching style, expectations
– Discussion of the syllabus
– Roadmap of the material
Research design
– Causality and Observational Studies
– Two-group randomized comparative experiment
– Other experiment designs (matched pairs, blocked design)
Readings:
Syllabus and Syllabus FAQ
Why Study Quantitative Analysis?
M&M Chapter 2.7 - The Question of Causation
M&M Chapter 3.1 - Sources of Data
M&M Chapter 3.2 - Design of Experiments
Session 2: Sampling and Exploratory Data Analysis
Monday, January 30th
Sampling
– Representative samples
– Simple random sample
– Introduction to statistical inference
Classification of variables
Graphical and numerical summaries of one variable
– Bar Charts, Pie Charts, Histograms
– Measures of central tendency (mean, median, mode)
– Measures of dispersion (Range, Quartiles, Boxplots, Variance, Standard Deviation)
Association between two quantitative variables
– Scatterplot and correlation coefficient
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Readings:
M&M Chapter 1.1 - Data
M&M Chapter 1.2 - Displaying Distributions with Graphs M&M Chapter 1.3 - Displaying Distributions with Numbers
M&M Chapter 2.1 - Relationships
M&M Chapter 2.2 - Scatterplots
M&M Chapter 2.3 - Correlations
M&M Chapter 3.3 - Sampling Design
Focus before class: M&M pages 9-11, 14-20, 28-38, 86, 88-89, 101, 189, 191
Session 3: Density curves, Normal density, and Introduction to Probability
Monday, February 6th
Density curves
– Population parameters: mean, standard deviation, median, skewness
Normal density curves
– Properties of normal density (shape, rule of 68-95-99.7)
– Standard normal and Z-tables
– Other Normal distributions
Introduction to probability
Readings:
M&M Chapter 1.4 - Density Curves and Normal Distributions
M&M Chapter 4.1 - Randomness
Focus before class: M&M pages 54-56, 59-63, 216-218
Session 4: Probability and Random Variables
Monday, February 13th
Probability
– Probability models
– Rules for probability
– Conditional probability
Random variables
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– Mean and variance of random variables
– Sums and differences of random variables
Readings:
M&M Chapter 4.1 - Randomness
M&M Chapter 4.2 - Probability Models
M&M Chapter 4.3 - Random Variables
M&M Chapter 4.4 - Means and Variances of Random Variables
Focus before class: M&M pages 221-225, 228-229, 232, 236, 241, 246-248, 254, 256-258
Session 5: Sampling Distributions and Statistical Inference
Monday, February 20th
Introduction to sampling distributions
– Statistics
– Sample mean as random variable
– The sampling distribution of the sample mean
Statistical Inference
– Confidence intervals
Readings:
M&M Chapter 5.1 - Toward Statistical Inference M&M Chapter 5.2 - The Sampling Distribution of a Sample Mean
M&M Chapter 6.1 - Estimating with Confidence
Focus before class: M&M pages 297-300, 307, 346-347, 349
Session 6: Hypothesis Testing
Monday, February 27th
Hypothesis Testing
– One-tailed test of significance
– Two-tailed test of significance
Readings: M&M Chapter 6.2 - Tests of Significance
Focus before class: M&M pages 363-366, 371-372, 375, 379
Session 7: The t-distribution and Comparing two population means
Monday, March 6th
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? Difference in differences as a tool to answer policy questions using observational data
? Statistical inference when the standard deviation is not known
– The t-distribution
– Confidence intervals and hypothesis testing using the t-distribution
? Comparing the means of two populations
Readings:
? M&M Chapter 7.1 - Inference for the Mean of a Population
? M&M Chapter 7.2 - Comparing Two Means
Focus before class: M&M pages 408-413, 433-437, 440
Session 8: Ordinary Least Squares Regressions
Monday, March 20th
? Comparing the means of two populations with the same standard deviation
? Ordinary Least Squares Regression
– Formal statistical model
– OLS regression properties
? Comparing the means of two populations
Readings:
? M&M Chapter 2.4 - Least Square Regressions
? M&M Chapter 10.1 - Simple Linear Regression
Focus before class: M&M pages 107-112, 115, 556-560, 567
Session 9: Statistical Inference in Regressions
Monday, March 21st
? Properties of regression coefficients
? Statistical inference in regressions
? Assumptions of OLS models
– Residual plots
– Normal quantile plots
Readings:
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? M&M Chapter 1.4 - Density Curves and Normal Distribution
? M&M Chapter 11.1 - Inference for Multiple Regressions
Focus before class: M&M pages 66-69, 567-569, 608-613
Session 10: Multivariate Regressions
Monday, April 3rd
? Multivariate regression
? Interaction terms
? Difference-in-differences
Readings: Handout
Focus before class: Handout
Session 11: Analysis of Variation
Monday, April 10th
Dummy variables
Analysis of Variation
– Goodness of fit
– R squared and adjusted R squared
– F-test
Readings:
M&M Chapter 11.1 - Inference for Multiple Regressions
M&M Chapter 12.1 - Inference for One-Way Analysis of Variance
Focus before class: M&M pages 613-616, 651-653, 656, 660-662
Session 12: Predictions in regression
Monday, April 17th
Prediction in regression
– Predicted values
– Confidence intervals for the mean predicted values
– Forecast intervals for predicted values
Categorical response variables
– Binomial distribution
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Readings: M&M Chapter 10.1 - Simple Linear Regression
Focus before class: M&M pages 570-573
Session 13: Sampling distribution and Inference for one proportion
Monday, April 24th
Sampling distribution for proportions and counts
Inference for a population proportion
Readings:
M&M Chapters 5.3 - Sampling Distributions for Counts and Proportions
M&M Chapters 8.1 - Inference for a Single Proportion
Focus before class: M&M pages 312-314, 317-322, 332-333, 486, 491, 500
Session 14: Comparison of Two Population Proportions
Monday, May 1st
Inference for the difference between two population proportion
Linear probability model regressions
Readings: M&M Chapter 8.2 - Comparing Two Proportions
Focus before class: M&M pages 506-507, 511-513