Download 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
7-1
7-1
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.
7-2
Topics for Chapter
 Finding facts in databases

Editing, searching, sorting, filtering, and
tabulating
 Sampling
 Estimating parameters

Point estimates and interval estimates
7-3
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.
7-4
Excel Lists
 First row contains names for each field
 Each successive row contains one record.
 Lists may be:




Searched and edited
Sorted
Filtered
Tabulated
7-5
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.
7-6
Database Form
7-7
Criteria Button
 Found under Data – Form
 Allows for searching of records


Enter data into a field.
Click Find Next.
7-8
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
7-9
Sorting: Data – Sort Command
7 - 10
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
7 - 11
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.
7 - 12
Tabulating
 Select Data – Pivot Table.
 Creates summary tables
 Layout button on
third step of wizard
creates the format
for the table
7 - 13
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
7 - 14
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
7 - 15
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
7 - 16
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
7 - 17
(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.
7 - 18
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.
7 - 19
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.
7 - 20
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
7 - 21
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.
7 - 22
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
7 - 23
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
7 - 24
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
7 - 25
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
7 - 26
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.
7 - 27
Copyright 2008 John Wiley & Sons, Inc.
All rights reserved. Reproduction or translation
of this work beyond that permitted in section 117 of the
1976 United States Copyright Act without express
permission of the copyright owner is unlawful. Request
for further information should be addressed to the
Permissions Department, John Wiley & Sons, Inc. The
purchaser may make back-up copies for his/her own use
only and not for distribution or resale. The Publisher
assumes no responsibility for errors, omissions, or
damages caused by the use of these programs or from
the use of the information herein.
7 - 28