7 - 1 Chapter 7: Data Analysis for Modeling PowerPoint Slides Prepared By: Alan Olinsky Bryant University Management Science: The Art of Modeling with.

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Chapter 7: Data Analysis for Modeling

PowerPoint Slides Prepared By:Alan Olinsky Bryant University

Management Science: The Art of Modeling with Spreadsheets, 2e

S.G. Powell

K.R. Baker

© John Wiley and Sons, Inc.

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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:   The sample variance is calculated as:

and its square root is the sample standard deviation:

nxxn

i i

1

s 2 (xi x )2

n 1i 1

n

s (xi x )2

i 1

n

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 <= <= U) = 1 –

L and U represent the lower and upper limits of the interval.

1 – represents the confidence level. Usually a large percentage like 95 or 99%

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 and standard deviation .

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 and a variance of 2/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:

x / 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 average is:

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.

z x x

x n

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Confidence Intervals for Means

Upper and lower limits on estimate for mean:

n>30 recommended unless original population resembles Normal

z can be computed using NORMSINV(1-/2) Replace 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

x z( / n )

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Interval Estimates for a Proportion

To estimate the sample proportion p, the interval estimate is:

  Sample size should be at least 50 for this

formula to be reliable

p zp(1 p)

n

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Sample Size Determination

Suppose want to estimate mean of sample to within a range of ±R

n = (z/ 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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