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PADM 7060 Quantitative Methods for Public Administration – Unit 2

PADM 7060 Quantitative Methods for Public Administration – Unit 2. Spring 2006 Jerry Merwin. Meier, Brudney & Bohte Part II: Descriptive Statistics. Chapter 4: Frequency Distributions Chapter 5: Measures of Central Tendency Chapter 6: Measures of Dispersion.

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PADM 7060 Quantitative Methods for Public Administration – Unit 2

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  1. PADM 7060 Quantitative Methods for Public Administration – Unit 2 Spring 2006 Jerry Merwin

  2. Meier, Brudney & BohtePart II: Descriptive Statistics • Chapter 4: Frequency Distributions • Chapter 5: Measures of Central Tendency • Chapter 6: Measures of Dispersion

  3. Meier, Brudney & Bohte: Chapter 4 Frequency Distributions • Descriptive statistics: what are they? • How are the following related: • Data • Raw data • Frequency distributions • See Table 4.1 – Arrests per Police Officer • Be sure you know the following: • Variable, class, class boundaries, class midpoints, class intervals, class frequency, total frequency

  4. Meier, Brudney & Bohte: Chapter 4 Frequency Distributions (Page 2) • Be sure you know the following: • variable • class • class boundaries • class midpoints • class intervals • class frequency • total frequency

  5. Meier, Brudney & Bohte: Chapter 4 Frequency Distributions (Page 3) • How is a “Frequency Distribution” constructed? • Step 1 • Step 2 • Step 3 • Tips: • Note tips on page 60 • See table 4.2 • What is a continuous variable?

  6. Meier, Brudney & Bohte: Chapter 4 Frequency Distributions (Page 4) • What is a percentage distribution? • See Tables 4.3 & 4.4 to see how comparison plays a role. • What is a cumulative frequency distribution? • See Table 4.5 • Cumulative percentage distribution • See Table 4.6

  7. Meier, Brudney & Bohte: Chapter 4 Frequency Distributions (Page 5) • How are “Graphic Presentations” important? (See Table 4.7 on page 64) • What is a “Frequency Polygon” and how is it done? • See pages 63-65 for steps. • See figures 4.1, 4.2, & 4.3 • Pay attention to the note at the bottom of page 65.

  8. Meier, Brudney & Bohte: Chapter 4 Frequency Distributions (Page 6) • What is a histogram and under what conditions is it used? (See Table 4.8 on page 66) • See pages 67 for steps. • See figures 4.4, 4.5, 4.6, & 4.7

  9. Meier, Brudney & Bohte: Chapter 4 Frequency Distributions (Page 7) • Summary • Problems 4.2, 4.4, 4.10

  10. Meier, Brudney & BohteChapter 5: Measures of Central Tendency • What are measures of central tendency? • Some examples: • Average starting salary of MPA graduates • What is the average number of MPA graduates per year who accepted job offers in nonprofit organizations? • What was the middle score on the midterm? • What is the average number of employees who report job-related accidents every month?

  11. Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency (Page 2) • What are the three types of average most often calculated and used? (75) • What is the mean? • See formula on page 76. • Remember the symbols we saw at the first of the book? • µ is a Greek letter pronounced “mu” and symbolizes the population mean. • ∑ is symbol for summation of all values X • N is number of items summed.

  12. Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency (Page 3) • More on the mean… • See Table 5.1 on page 76. • What are the important characteristics of the mean? (See page 77) • What is an outlier? • What did you get for the mean in the example?

  13. Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency (Page 4) • What is the median? (See page 69) • Let’s see an example: the city planning office example on pages 78-79 • Note the characteristics on page 79 • Not affected by extreme values • All observations used to determine, but not all calculated. • Only good measure of central tendency if values cluster near median • Usually not unrealistic value • The 50th percentile in distribution of data (GRE)

  14. Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency (Page 5) • Explain the “Mode” as a measure of central tendency. • See Table 5.2 (*unimodal), 5.3 (bimodal), 5.4 • Important characteristics: • Mode is not necessarily near middle of data. • Can take on more than one value, so might be best summary of central tendency with bimodal or trimodal and other complex distributions. (Note: Mean might hide something important about data in these cases.) • With less precise measures, nominal and ordinal, mode is useful. Not so in interval scales.

  15. Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency (Page 6) • How do we get the means for grouped data? • Ideally we use raw data, but might not have it in every situation. • Archival and “sensitive survey” data require grouped data. (Discuss sensitive) • We lose information (frequencies, etc.) with grouped data, so statistics are less accurate.

  16. Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency (Page 7) • How do we get the means for grouped data? (Continued) • Example: Oklahoma Highway Department data in Table 5.5 • How did the analyst calculate the mean? (data grouped by classes or categories) • See steps on pages 82-83 • Table 5.6 with midpoints for each class • Table 5.7 with (∑ F x M) /N • Serious Crimes per Precinct in Metro, TX • Table 5.8

  17. Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency (Page 8) • How do we get the means for grouped data? (Continued) • Serious Crimes per Precinct in Metro, TX • Table 5.8 • How are these data different? • What does the difference mean about the calculation? • Evanapolis Recreation Department • Letters of thanks received by employees • Table 5.9

  18. Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency (Page 9) • What about “Medians” for grouped data? • See steps on pages 84-85 • Table 5.10

  19. Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency(Page 10) • What is the “Crude Mode” for grouped data? • See 86 • The midpoint of the class with the greatest frequency.

  20. Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency(Page 11) • How do we determine when the Median might be better measure of central tendency for numerical data than the mean? • Outliers (Have we talked about this before?) • Skewed – means? • Example: housing prices • More to come in Chapter 6

  21. Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency(Page 12) • How are levels of measurement and measures of central tendency related? • See pages 86-90 • Tables 5.11-5.15 • What is the “Hierarchy of Measurement” used in chapter 5? • See table 5.16 on page 90

  22. Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency(Page 13) • What cautions are provided regarding the levels of measurement and coding of response categories? • See page 91 • Note Table 5.17 • How can we avoid ordinal-interval debate?

  23. Meier, Brudney & Bohte: Chapter 5 Measures of Central Tendency(Page 14) • Summary • Problems 5.2, 5.16

  24. Meier, Brudney & BohteChapter 6: Measures of Dispersion • What do we mean by a measure of dispersion? • See Table 6.1 & Figure 6.1 on page 100 • What are some measures of dispersion?

  25. Meier, Brudney & Bohte Chapter 6: Measures of Dispersion (Page 2) • What is standard deviation? • See Table 6.2, 6.3, & 6.4 • Steps begin on page 101 • Formula for σ of population on page 102 • How is the standard deviation for a sample (s) calculated differently?

  26. Meier, Brudney & Bohte Chapter 6: Measures of Dispersion (Page 3) • How is the standard deviation for grouped data calculated? • See Table 6.5 • Steps are on page 104

  27. Meier, Brudney & Bohte Chapter 6: Measures of Dispersion (Page 4) • What is the importance of the shape of a frequency distribution? • See Figure 6.2 for a symmetric distribution • Figure 6.3 for uniform distribution • Figure 6.4 for a bimodal distribution • Figure 6.5 for a negatively skewed distribution • Figure 6.6 for a positively skewed distribution

  28. Meier, Brudney & Bohte Chapter 6: Measures of Dispersion (Page 5) • What is the importance of the shape of a frequency distribution? • See Figure 6.2 for a symmetric distribution • Figure 6.3 for uniform distribution • Figure 6.4 for a bimodal distribution • Figure 6.5 for a negatively skewed distribution • Figure 6.6 for a positively skewed distribution

  29. Meier, Brudney & Bohte Chapter 6: Measures of Dispersion(Page 6) • Why do we need to use the measures of dispersion and measures of central tendency together? • See page 108

  30. Meier & Brudney: Chapter 6 Measures of Dispersion (Page 7) • Summary • Problems 6.2, 6.4, 6.8

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