Transcript 7 - 1 - Wiley

Management Science: The Art of
Modeling with Spreadsheets, 2e
Chapter 7: Data Analysis for
Modeling
S.G. Powell
K.R. Baker
© John Wiley and Sons, Inc.
PowerPoint Slides Prepared By:
Alan Olinsky
Bryant University
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Data Analysis in the
Context of Modeling
 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.
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Topics for Chapter
 Finding facts in databases

Editing, searching, sorting, filtering, and
tabulating
 Sampling
 Estimating parameters

Point estimates and interval estimates
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Finding Facts from Databases
 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.
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Excel Lists
 First row contains names for each field
 Each successive row contains one record.
 Lists may be:




Searched and edited
Sorted
Filtered
Tabulated
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Searching and Editing Lists
 First assign a range name to entire list.

Include column titles.
 With list selected choose Data – Form.
 Examine records one at a time:




Find Prev.
Find Next.
Enter new record with New button.
Delete record with Delete button.
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Database Form
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Criteria Button
 Found under Data – Form
 Allows for searching of records


Enter data into a field.
Click Find Next.
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Alternate Excel Search
Techniques
 Highlight entire database.
 Use Edit – Find to search.
 Use Find and Replace to edit entries.
 In Find and Replace


“?” stands for any single symbol
“*” stands for any sequence of symbols
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Sorting: Data – Sort Command
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Filtering
 Select database then Data – Filter – AutoFilter.
 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:


Select (All) using the list arrow; or
Selecting Show All under Data – Filter
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More Filtering
 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 with Data – Filter – Advanced
Filter submenu.
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Tabulating
 Select Data – Pivot Table.
 Creates summary tables
 Layout button on
third step of wizard
creates the format
for the table
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Analyzing Sample Data
 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
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Descriptive Statistics
 Summarizes information in sample
 Gives numerical picture of observations
 Excel Tools – Data Analysis

Descriptive Statistics table produced based on
data given as input
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Inferential Statistics
 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
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Estimating Parameters: Point
Estimates
 The sample average is calculated as: x   x n
n
i 1
i
 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
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(Optional) Estimating Parameters:
Interval Estimates
 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.
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Interval Estimates for the Mean
 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.
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Sampling Theory
 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.
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Estimates
 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
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Z-scores
 The z-score measures the number of standard
deviations away from the mean.
 The z-score corresponding to any particular sample
xm xm
average is:
z
sx

s
n
 Tells how many standard errors 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.
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Confidence Intervals for Means
 Upper and lower limits on estimate for mean:
x  z(s / n )
 n>30 recommended unless original population
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 halfwidth of confidence interval
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Interval Estimates for a
Proportion
 To estimate the sample proportion p, the
interval estimate is:
p(1  p)
pz
n
 Sample size should be at least 50 for this
formula to be reliable
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Sample Size Determination
 Suppose 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
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Sample Size Determination for
Proportions
 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
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Summary
 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.
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