7 - 1 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.

7 - 2 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 - 3 Topics for Chapter  Finding facts in databases Editing, searching, sorting, filtering, and tabulating  Sampling  Estimating parameters Point estimates and interval estimates

7 - 4 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 - 5 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 - 6 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 - 7 Database Form

7 - 8 Criteria Button  Found under Data – Form  Allows for searching of records Enter data into a field. Click Find Next.

7 - 9 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

Sorting: Data – Sort Command

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

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.

Tabulating  Select Data – Pivot Table.  Creates summary tables  Layout button on third step of wizard creates the format for the table

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

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

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

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:

(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.

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.

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.

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:

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 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  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

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

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

Sample Size Determination for Proportions  Suppose want to estimate a proportion to within a range of ±R n = z 2 p(1 – p) / R 2  Value maximized at p = 0.5  Conservative value: n = (z/2) 2 / R 2

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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