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ENMA 420/520 Statistical Processes Spring 2007

ENMA 420/520 Statistical Processes Spring 2007. Michael F. Cochrane, Ph.D. Dept. of Engineering Management Old Dominion University. ENMA 420/520 Syllabus. Instructor Michael F. Cochrane, Ph.D. Chief Analyst, US Joint Forces Command, Joint Experimentation Directorate (J9) Phones

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ENMA 420/520 Statistical Processes Spring 2007

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  1. ENMA 420/520Statistical ProcessesSpring 2007 Michael F. Cochrane, Ph.D. Dept. of Engineering Management Old Dominion University statistical processes

  2. ENMA 420/520Syllabus • Instructor • Michael F. Cochrane, Ph.D. • Chief Analyst, US Joint Forces Command, Joint Experimentation Directorate (J9) • Phones • 757-203-5131 (Office) • mcochran@odu.edu • http://www.odu.edu/engr/mcochrane statistical processes

  3. ENMA 420/520Syllabus - Continued • Office hours (by appointment) • Textbooks • Statistics for Engineering and the Sciences • Mendenhall, William and Sincich, Terry • Data Analysis with Microsoft Excel • Berk and Carey statistical processes

  4. ENMA 420/520Syllabus - Continued • Course Objectives • Target audience • Never taken statistics or need refresher • Purpose • Foundation & linkages to engineering applications statistical processes

  5. ENMA 420/520Syllabus - Continued • Spreadsheet software • Excel • Theory  application • Data Analysis add-in to Excel (/Tools/Data Analysis) • Software as an enabling tool • Availability of more powerful statistical sw • JMP, SAS, SPSS, @Risk • Not as prevalent as spreadsheet sw • Targeted to specialized users • Will demo statistical processes

  6. End of course project for 520 students Learn by doing!! ENMA 420/520Syllabus - Continued • Course format • Class schedule in syllabus • Two examinations • Mid term ==> take home • Final ==> in-class • Two quizzes ==> take home • Homework • Assigned but not graded statistical processes

  7. ENMA 420/520Syllabus - Continued • ENMA 520 • Mid-term exam 30 points • Final exam 30 points • Two quizzes 30 points • Course project 10 points • ENMA 420 • Mid-term exam 30 points • Final exam 30 points • Two quizzes 40 points statistical processes

  8. ENMA 420/520Syllabus - Continued Do not copy everything on board!!! • Use the web (www.odu.edu/engr/mcochrane ) statistical processes

  9. ENMA 420/520Syllabus - Continued • The ODU Honor Code statistical processes

  10. Probability & StatisticsGetting Started • Flow of course • Statistics as means of information processing • Introduction to probability • Standard probability models • Statistics as means of inferring population characteristics • Alternative approach to inferential statistics statistical processes

  11. Getting StartedClass 1 • Reading assignments • M & S • Sections 1.1 - 1.4 (Introduction) • Sections 2.1 - 2.8 (Descriptive Statistics) • Recommended Problems • M&S Chapter 2: 45-48, 53-56 The textbook chapters will always be from the syllabus! statistical processes

  12. Statistics Statistics: Principal Branches • Descriptive Statistics • Organizing • Summarizing • Describing • Contrasting • Develop insights into • data sets • Inferential Statistics • Inferring • Estimating • Modeling • Develop insights into populations statistical processes

  13. Data Sets Populations & Samples • Population (universe) • Enumerative data set Examples of population data sets? • Sample • Subset of data from population Examples of sample data sets? Important to distinguish between a population & a sample Parameters - characteristics of population Statistic - characteristic of sample statistical processes

  14. Are All Data the Same?Measurable Data • Quantitative data • Measurable quantity (numerically valued scales) • Example of quantitative data? • Interval data • Distinct units of distance but no zero • Example? • Ratio data • Distinct units of distance and a zero • Example? statistical processes

  15. Types of DataNon-Measurable Data • Qualitative (categorical) data • Non-measurable quantity • Caution: sometimes quantified for convenience • Example of qualitative data? • Nominal data • No meaningful order • Example? • Ordinal • Distinct ranking possible • Example? statistical processes

  16. Recurring Key Concept: A Data Detective • A data detective • Essential for modeling • Understand data & underlying processes • Prerequisite first step • Population or sample? • Type of data? • Data patterns • Data as clue to process • Next step - describing data! statistical processes

  17. Raw Data Information Descriptive Statistics • “Digest” data • Arrange or present data • Develop summary characteristics of data • Communicating with data statistical processes

  18. Topics and Concepts • Describing qualitative data • Various graphical methods • Describing quantitative data • Graphical methods • Numerical descriptions of data sets • Important concepts: • Understand strengths & weaknesses of methods • Suitability of method to specific applications • Present data to highlight insights statistical processes

  19. Describing Qualitative Data • Basic steps • Define categories • Assign observations  categories • Category frequency • Category relative frequency • Present graphically • Key concept • Minimize category ambiguity • Observation  1 & only 1 category • Examples? statistical processes

  20. Categorical DataPrincipal Graphing Techniques • Visualizing categorical data • Histograms • Frequency • Relative frequency • Cumulative frequency • Pie charts • Pictographs • Use common sense • What is message you are communicating? statistical processes

  21. Visualizing Categorical DataExample Problem • Problem: Cause of accidents in Florida (1988) statistical processes

  22. Categorical DataExample Problem • Many different ways to present data • Use good judgment • Which approach highlights yourmessage • What if you had data for 1988 & 1989? • What if you had data for many years? statistical processes

  23. Visualizing Data:Graphing Quantitative Data • Same fundamental purpose • Communicate information • Gain insights into data sets, relationships • Methods to be discussed • Dot plots • Stem & leaf diagrams • Histograms (relative & cumulative frequency) statistical processes

  24. Took sample of home mortgage rates in a neighborhood: Visualizing Quantitative DataExample Data Set statistical processes

  25. Dot PlotA Quick & Dirty Method • Simplest graph • Suitable for small data sets • Single axis  scale that spans data range Range  minimum to maximum values • Each observation is dot on axis • Most statistical software includes • Excel does not provide statistical processes

  26. Dotplot . . . . .. . .:... . . . . . . . -----+---------+---------+---------+---------+---------Rate 6.0 7.0 8.0 9.0 10.0 11.0 Example Dot Plot • Constructed using MiniTab What are strengths & weaknesses? statistical processes

  27. Dot Plot Summary • Advantages • Easy to construct (back of napkin) • Identify range, possible outliers, distribution of data Outlier  highly unusual observation • Disadvantages • Limited to small data sets • May be difficult to reconstruct original data set • Have to be careful with scale statistical processes

  28. .:. . .:::: :.... -----+---------+---------+-------Rate 8.0 12.0 16.0 20.0 Dot Plot: Compressed Scaling • Note contrast with previous dot plot • Lose observation “measurability” • However can now observe data groupings • Before  observations evenly distributed • Now  see mound shaped distribution statistical processes

  29. Leaves in tenths of percent Stems in whole percent Stem & Leaf DiagramsAlternative Graphing Technique • Steps in constructing: • Divide observation into 2 parts • Stem & leaf (choose convenient scales) 8.2 • List stems in order • Proceed through all observations • Arrange leaves in order statistical processes

  30. Stem-and-leaf of Rate Leaf Unit = 0.10 2 6 08 8 7 024579 (6) 8 001235 6 9 025 3 10 058 Stem-and-leaf of Rate Leaf Unit = 0.10 1 6 0 2 6 8 5 7 024 8 7 579 (5) 8 00123 7 8 5 6 9 02 4 9 5 3 10 0 2 10 58 Stretched Stem & leaf Leaves Stems Depth Stem & Leaf DiagramExample Data Set statistical processes

  31. Stem & Leaf Diagrams Summary • Advantages • Visualize data groupings • Can recreate original data set • Simple to construct • Disadvantages • Limited to small data sets statistical processes

  32. Class interval 6  lower class limit (LCL) 7  upper class limit (UCL) Class Mark  (UCL – LCL) / 2 HistogramsDealing With Large Data Sets • Visualizing large data sets • Aggregate observations into classes • Observations lose individual identity • Example data • Possible classes 6 - 7 7 - 8 8 - 9 and so forth statistical processes

  33. HistogramsFour Easy Steps • Determine range of data • Divide range into convenient class intervals • Key step • Consider open intervals for extremes • Text mentions rules of thumb • Excel will do it for you (do not let it!) • Count observations in each interval • Graph statistical processes

  34. HistogramExample Problem Using Excel • Consider home mortgage problem • Build • Histogram • Relative frequency histogram • Cumulative frequency histogram • Also called ogive • Pareto diagram statistical processes

  35. Insert Excel Demo Here statistical processes

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  41. Quantitative DataNumerical Descriptors • Develop numeric characterizations of data • Central tendency • Locate general location (center) of data • Variation • Describe dispersion (spread) of observations in set • Relative standing • Describe observations relative to others in set Note each provides different perspective of data. statistical processes

  42. Measures of Central Tendency • Three most common measures • Mean • Median • Mode • Others exist • Trimmed mean • Truncated mean • Conditional mean statistical processes

  43. Measures of Central Tendency“The Average” statistical processes

  44. Measures of Central TendencyMedian • Median - the middle observation • 50% of observations below, 50% above m median of sample   median of population • A resistant measure • Relatively insensitive to extreme values • Contrast to the mean! statistical processes

  45. Determining the Median statistical processes

  46. Determining the Median: Even Numbered Example statistical processes

  47. Median is resistant to outliers! Determining the Median: Odd Numbered Example statistical processes

  48. Measures of Central TendencyThe Mode • Mode of Y • Value yi that occurs with most frequency • Note • Mode may or may not exist Y={1, 2, 4, 6} • There may be one or more modes • One mode = Unimodal • Two modes = Bimodal • More than two modes = Multimodal statistical processes

  49. Measures of Central TendencyExcel Special Functions • Mean • Average ( … ) • Median • Median ( … ) • Mode • Mode ( … ) statistical processes

  50. Types of Frequency CurvesA Symmetric Frequency Distribution Where are the mean, median and mode? statistical processes

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