5af395135f8da61a449226b606e325f1.pdf
大小:(9.56 MB)

只需: 20 个论坛币  马上下载

Basic Business Statistics: A Casebook
Dean P. Foster, Robert A. Stine, Richard P. Waterman (auth.)
Springer New York
Class 1. Overview and Foundations
The notes for this class offer an overview of the main application areas of statistics. The
key ideas to appreciate are data, variation, and uncertainty.
Topics
Variability
Randomness
Replication
Quality control
Overview of Basic Business Statistics
The essential difference between thinking about a problem from a statistical perspective as
opposed to any other viewpoint is that statistics explicitly incorporates variability. What do we
mean by the word "variability"? Take your admission to the MBA program as an example. Do
you believe there was an element of uncertainty in it? Think about your GMA T score. If you took
the test again, would you get exactly the same score? Probably not, but presumably the scores
would be reasonably close. Your test score is an example of a measurement that has some
variability associated with it. Now think about those phone calls to the Admissions Office. Were
they always answered immediately, or did you have to wait? How long did you wait? Was it a
constant time? Again, probably not. The wait time was variable. If it was too long, then maybe
you just hung up and contemplated going to a different school instead. It isn't a far leap from this
example to see the practical relevance of understanding variability -
after all, we are talking about
customer service here. How are you paying for this education? Perhaps you have invested some
money; maybe you purchased some bonds. Save the collapse of the government, they are pretty
certain, nonvariable, riskless investments. Perhaps, however, you have invested in the stock
market. This certainly is riskier than buying bonds. Do you know how much your return on these
stocks will be in two years? No, since the returns on the stock market are variable. What about
car insurance? If you have registered your car in Philadelphia then you have seen the insurance
market at work. Why is the insurance so high? Most likely the high rates are the result of large
numbers of thefts and uninsured drivers. Is your car certain to be stolen? Of course not, but it
might be. The status of your car in two years, either stolen or not stolen, is yet another "variable"
displaying uncertainty and variation.
The strength of statistics is that it provides a means and a method for extracting,
quantifying, and understanding the nature of the variation in each of these questions. Whether the underlying issue is car insurance, investment strategies, computer network traffic, or educational
testing, statistics is the way to describe the variation concisely and provide an angle from which to
base a solution.
What This Material Covers
A central theme of these case studies is variability, its measurement and exploitation in
decision-making situations. A dual theme is that of modeling. In statistics, modeling can be
described as the process by which one explains variability.
For an example, let's go back to the question about car insurance. Why are the rates high?
We have already said that it's probably because there are many thefts and lots of uninsured drivers.
But your individual insurance premium depends on many other factors as well, some of which you
can control while others are outside your reach. Your age is extremely important, as is your prior
driving history. The number of years you have had your license is yet another factor in the
equation that makes up your individual insurance premium. International students face real
challenges! These factors, or variables as we are more likely to call them, are ways of explaining
the variability in individual insurance rates. Putting the factors together in an attempt to explain
insurance premiums is an example of "building a model." The model-building process -
how to
do it and how to critique it -
is the main topic of this text. In this course, you will learn about
variability. In our sequel, Business Analysis Using Regression you can learn about using models
to explain variability.
What Is Not Covered Here
A common misconception about statistics is that it is an endless list of formulas to be
memorized and applied. This is not our approach. We are more concerned about understanding the
ideas on a conceptual level and leveraging the computational facilities available to us as much as
possible. Virtually no formulas and very little math appears. Surprisingly, rather than making our
job easier, it actually makes it far more of a challenge. No more hiding behind endless
calculations; they will happen in a nanosecond on the computer. We will be involved in the more
challenging but rewarding work of understanding and interpreting the results and trying to do
something useful with them!
Key Application
Quality control. In any manufacturing or service-sector process, variability is most often
an undesirable property. Take grass seed, for example. Many seed packets display the
claim "only 0.4% weed seed." The manufacturer has made a statement; for the
consumer to retain confidence in the manufacturer, the statement should be at least
approximately true. Ensuring that the weed content is only 0.4% is a quality control
problem. No one believes that it will be exactly 0.4000000% in every packet, but it
better be close. Perhaps 0.41 % or 0.39% is acceptable. Setting these limits and
ensuring adherence to them is what quality control is all about. We accept that there is
some variability in the weed content, so we want to measure it and use our knowledge
of the variability to get an idea of how frequently the quality limits will be broken.
Quality applies equally well to service-sector processes. How long you wait for the
telephone to be answered by the admissions office is such a process. The variability of
wait times needs to be measured and controlled in order to avoid causing problems to
people that must wait inordinate amounts of time.
Definitions
Variability, variation. These represent the degree of change from one item to the next, as in
the variability in the heights, weights, or test scores of students in a statistics class.
The larger the variation, the more spread out the measurements tend to be. If the
heights of all the students were constant, there would be no variability in heights.
Randomness. An event is called "random", or said to display "randomness," if its outcome
is uncertain before it happens. Examples of random events include
• the value of the S&P500 index tomorrow afternoon (assuming it's a weekday!),
• whether or not a particular consumer purchases orange juice tomorrow,
• the number of a-rings that fail during the next space shuttle launch.
Replication. Recognizing that variability is an important property, we clearly need to
measure it. For a variability measure to be accurate or meaningful, we need to repeat
samples taken under similar conditions. Otherwise we are potentially comparing apples
with oranges. This repetition is called "replication." In practice it is often not clear that
the conditions are similar, and so this similarity becomes an implicit assumption in a
statistical analysis.
Heuristics
Heuristics are simple descriptions of statistical concepts put into everyday language. As
such, they are not exact statements or even necessarily technically correct. Rather, they are meant
to provide an illuminating and alternative viewpoint.
Variability. One way of thinking about variability is as the antithesis of information. You
can think about an inverse relationship between variability and information. The more
variability in a process the less information you have about that process. Obtaining a
lot of information is synonymous with having low variability.
Information is also close to the concept of precision. The more information you
have, the more precise a statement you can make. Engineers love precision;
components manufactured with high precision have low variability. So an alternative
way of thinking about variability is by considering the way it is inversely related to
information and precision. That is, as variability increases, information and precision
decrease. Conversely, as variability decreases, information and precision increase.
Potential Confusers
What's the difference between a "variable" and "variability"?
A variable is a measurement or value that displays variability across the sampled items.
For example, the number of chocolate chips in a cookie is a variable, and the range in
counts seen for different cookies is a measure of the variability.
Class 2. Statistical Summaries of Data
This class introduces simple, effective ways of describing data. All of the computations
and graphing will be done by JMP. Our task -
and it is the important task -
is to learn how to
selectively interpret the results and communicate them to others. The priorities are as follows: flIst,
displaying data in useful, clear ways; second, interpreting summary numbers sensibly.
The examples of this class illustrate that data from diverse applications often share
characteristic features, such as a bell-shaped (or normal) histogram. When data have this
characteristic, we can relate various summary measures to the concentration of the data, arriving at
the so-called empirical rule. The empirical rule is our flIst example of a useful consequence of a
statistical model, in this case the normal model for random data. Whenever we rely upon a model
such as this, we need to consider diagnostics that can tell us how well our model matches the
observed data. Most of the diagnostics, like the normal quantile plot introduced in this lecture, are
graphical.
Topics
Pictures:
Histograms, boxplots, and smooth density plots
Diagnostic plot for the normal model (normal quantile plot)
Time series plots
Summaries:
Measures of location: sample mean, median
Measures of scale: standard deviation, interquartile range, variance
Concepts: Normal distribution
Empirical rule
Skewness and outliers
Examples
GMATscores
Fundamental numerical and graphical summaries, smoothing
Returns on General Motors stock
Time series, trends, and the transformation to percentage change
Skewness in executive compensation
All data are not normal, but transformations can remedy some of the
deviations from normality