Transcript 7 - 1 - Wiley

Management Science: The Art of
Modeling with Spreadsheets, 3e
7-1
Chapter 7: Data Analysis for
Modeling
S.G. Powell
K.R. Baker
© John Wiley and Sons, Inc.
Power Point Slides Revised By:
Tony Ratcliffe, James Madison University
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Data Analysis in the Context of Modeling
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 Supports the modeling process
 Improves accuracy of model
 Improves usefulness of conclusions
 Modeling is the primary goal.
 Data analysis is a means to that goal.
Topics for Chapter
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 Finding facts in databases
 Editing, searching, sorting, filtering, and tabulating
 Sampling
 Estimating parameters
 Point estimates and interval estimates
Finding Facts from Databases
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 Tables of information
 Each row is a record in the database.
 Each column is a field for the records.
 Excel calls such a table a list.
Excel Lists
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 First row contains names for each field
 Each successive row contains one record.
 Lists may be:
 Searched and edited
 Sorted
 Filtered
 Tabulated
Searching and Editing Lists
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 First assign a range name to entire list.
 Include column titles.
 With list selected Form on the Quick Access
Toolbar.
 Examine records one at a time:
Find Prev.
 Find Next.
 Enter new record with New button.
 Delete record with Delete button.

Database Form
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Criteria Button
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 Selected Form on the Quick Access Toolbar
 Allows for searching of records
 Enter data into a field.
 Click Find Next.
Alternate Excel Search Techniques
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 Highlight entire database.
 Home"Editing►Find&Select►Find.
 Use Find and Replace to edit entries.
 In Find and Replace
 “?” stands for any single symbol
 “*” stands for any sequence of symbols
Sorting: Data – Sort Command
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Filtering
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 Choose Home►Editing►Sort&Filter►Filter.
 Will filter lists based on values
 Found under arrow at the title of each column
 Arrow on title turns blue to remind list is filtered
 Can remove filter by:
 Choose Home►Editing►Sort & Filter►Filter►Clear
More Filtering
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 Top 10 option returns records with smallest or
largest value of a numerical record
 Custom option allows filtering with compound
criteria
 More complicated compound criteria can be
achieved by clicking Custom Filter option under
Number Filters or Text Filters.
Tabulating
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 Select Data – Pivot Table.
 Creates summary tables
 Layout button on
third step of wizard
creates the format
for the table
Analyzing Sample Data
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 Data is unlikely to cover whole population
 Work with sample from population
 Statistics are summary measures about sample
 Want to construct statistics that represent population
 Convenience sampling
 Have easy access to information on subset of population
 Subset may not be representative
 Random sampling
 All objects in population have equal chance of appearing
in sample
Descriptive Statistics
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 Summarizes information in sample
 Gives numerical picture of observations
 Excel Tools – Data Analysis
 Descriptive Statistics table produced based on data given as
input
Inferential Statistics
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 Use information in sample to make inferences
about population
 Systematic Error
If sample not representative of population
 Avoid by careful sampling

 Sampling Error
 Sample is merely subset of population
 Mitigated by taking large samples
Estimating Parameters: Point Estimates
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 The sample average is calculated as:
x x n
n
i 1
 The sample variance is calculated as:
(xi  x )2
s 
n 1
i 1
2
n
 and its square root is the sample standard
deviation:
n
s
2
(x

x
)
 i
i 1
n 1
i
(Optional) Estimating Parameters: Interval
Estimates
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 We can estimate parameters in two ways, with
point estimates and with interval estimates.
 The interval estimate approach produces a range of
values in which we are fairly sure that the
parameter lies, in addition to a single-value point
estimate.
 A range of values for a parameter allows us to
perform sensitivity analysis in a systematic
fashion, and it provides input for tornado charts or
sensitivity tables.
Interval Estimates for the Mean
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 P(L <= m <= U) = 1 – a.
 L and U represent the lower and upper limits of the
interval.
 1 – a represents the confidence level.


Usually a large percentage like 95 or 99%
m represents the (unknown) true value of the
parameter.
Sampling Theory
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 Working with a population described by a Normal
probability model

Mean m and standard deviation s.
 Take repeated samples of n items from population
 Calculate the sample average each time
 The sample averages will follow a Normal
distribution with a mean of m and a variance of
s2/n.
Estimates
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 Standard error: the standard deviation of some
function being used to provide an estimate.
 Use the sample average to estimate the population
mean.
 The standard deviation of the sample average is
called the standard error of the mean:
sx  s / n
Z-scores
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 The z-score measures the number of standard
deviations away from the mean.
 The z-score corresponding to any particular
sample average is:
 Tells how
xm
xm

 errors
manyzstandard
sx
s n
from the mean
 90% of the sample averages will have z-scores
between –1.64 and +1.64.

The chances are 90% that the sample average will fall no
more than 1.64 standard errors from the true mean.
Confidence Intervals for Means
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 Upper and lower limits on estimate for mean:
 n>30 recommended unless original population
x  z(s / n )
resembles Normal
 z can be computed using NORMSINV(1-a/2)
 Replace s by the sample standard deviation s

Provided that sample is larger than n = 30
 Excel Descriptive Statistics also will calculate half-
width of confidence interval
Interval Estimates for a Proportion
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 To estimate the sample proportion p, the interval
estimate is:
p(1 at
 p)
 Sample size should
be
least 50 for this formula to
pz
be reliable
n
Sample Size Determination
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 Suppose we want to estimate mean of sample to
within a range of ±R
n = (zs / R)2
 Assumes:


Sampling from Normal distribution
Known variance – can begin with small sample to estimate
standard deviation
Sample Size Determination for Proportions
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 Suppose want to estimate a proportion to within a
range of ±R
n = z2p(1 – p) / R2
 Value maximized at p = 0.5
 Conservative value:
n = (z/2)2 / R2
Summary
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 Data collection and analysis support the modeling task




where appropriate.
When early sensitivity testing indicates that certain
parameters must be estimated precisely, we turn to data
analysis for locating relevant information and for
estimating model parameters.
The process of finding facts in data is aided by a facility
with Excel and in particular with its database capabilities.
Excel provides an array of commands for searching,
sorting, filtering, and tabulating data.
Excel’s Data Analysis tool for calculating descriptive
statistics enables rapid construction of point estimates and
interval estimates from raw data.
Copyright 2011 John Wiley & Sons, Inc.
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