Chuck Stull
Winter 2002
Quant II introduces statistical methods used
in economics and business. It is not a continuation of quantitative
methods I, but instead a course on statistics, probability, estimation, empirical
studies, and related issues. The class will emphasize quantitative reasoning
over proofs and mathematical formalism. We will work extensively with
numbers (bring a calculator to class) and we will use Microsoft Excel for
some assignments. A good understanding of statistical analysis is crucial
to understand how the world works (which is why it is covered on the comprehensive
exam.)
Gambling involves uncertain outcomes and gambling
was a primary motivation for early studies of probability. Games of
chance are easily analyzed using classical probability methods. Casino
gambling and online gambling are both growing industries, despite the fact
that the games they offer are not fair bets. (The expected value of
the bet is negative; if you play long enough you will lose all of your money.)
This edge to the house makes possible the gambling palaces
of Las Vegas, as well as good returns to the stockholders. (See the
investor relations pages from Harrah
's, Trump
, or
MGM Grand
for examples.)
A number of websites offer basic analysis of casino games but they are so
gimmicked with pop-up windows and promotions that I'm reluctant to include
them here. Try
Yahoo's gambling section
for a selection. For analysis of the social and economic impact of
gambling see The National Opinion Research Center report on gambling to the
National Gambling Impact Study Commission
. The Wager
is on online journal of gambling addiction from Harvard Medical School.
Life expectancy is an another interesting example of expected value. See this website for a simple life expectancy calculator. Since expected values are based on probabilities, we can improve these calculations with more information. In other words, we can use conditional probabilities to more accurately estimate lifespans. Northwestern Mutual Insurance has a fun website: try their Longevity Game .
Financial markets also display large amounts of uncertainty. The theory of efficient markets concludes that changes in stock prices should be random and unpredictable. This means returns from a portfolio will be more uncertain than a salesman at a brokerage would like you to believe. T. Rowe Price has an interesting retirement income calculator that uses probabilities.
II. Summary Statistics
Descriptive statistics are the most familiar
part of statistical analysis. Averages-- mean, median, mode-- sometimes
called measures of central tendency; percentages; and measures of spread or
dispersion -- variance, standard deviation-- are very common. We won't
belabor these because most students have had some exposure to them.
For an explanation of the basics, see
Statistics Every Writer Should Know.
While calculations for Samples and Populations look similar, it's important to remember that a sample is only an estimate and we'll need to use probability theory to relate it to the true population parameter.
Graphs are often a useful supplement to descriptive statistics.
III. Collecting Data
Whenever you read a statistic, a question should pop
into your mind, "where did this number come from?" Not all numbers
are created equally, even if they are printed on really nice glossy paper.
Methodology and definition are truly important.
Samples need to be random. Getting a true random
sample requires real effort. Try this online source of
random numbers
.
Lots of good data is available online. See
Finding Data on the Internet
for links to some sources.
IV. Analyzing data
Numbers by themselves are boring. They only have interest in the context of a research question. Hypothesis testing is a statistical way to answer questions like, "does Energizer last longer? " or "do tax cuts increase consumer spending?" For some questions we can compare populations. For other questions we want to relate variables using correlation or regression. Sometimes we will look for trends and cycles using time series analysis .
V. What else can we do?
Regressions are frequently used for forecasting. Many economic variables
are interconnected, so forecasters build systems of equations to make forecasts.
Fairmodel
is a large macromodel (US or international) available for free, online.
Tests and projects
Exam 1: Wednesday Jan 30, 8:00pm
Exam 2: Wednesday Feb 27, 8:00 pm
Final Exam: Wednesday March 20, 8:00 am, as scheduled by registrar
We will have two midterms and a final-- each with a variety of types of questions. The material on each exam will be discussed in class.
We'll also have assignments and problem sets throughout the term.
At the end of the quarter we will do original
research projects
. I'm including links to previous class projects below. (please
note: these are web summaries of the project-- the papers were longer and
more complete.) Statistical Studies, Winter 2000
and More Statistical Studies,
Fall 2000,
and Statistical Studies,
Winter 2001
, Studies Winter 2002
links
a few statistical sources:
Kalamazoo Statistics-- study results
The Gallup Poll
Federal Statistics (from 70 agencies)
A website to accompany Statistics: Concepts and Controversies has some fun java applets illustrating various statistical concepts.
Dr. B's Wide World of Web Data
the EconData service
The Data and Story Library
Community Research and Survey Design .
The Journal of Statistics Education .
Statistics and Survey Research Courses
My Statistics and Information
Literacy links
Department of Economics homepage
Questions, problems, or comments?
email: cstull@kzoo.edu