Download PADM 7060

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
Meier, Brudney & Bohte: Chapter 4
Frequency Distributions
 Descriptive statistics: what are they?
 How are the following related:
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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
Meier, Brudney & Bohte: Chapter 4
Frequency Distributions (Page 2)
 Be sure you know the following:
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variable
class
class boundaries
class midpoints
class intervals
class frequency
total frequency
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?
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
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.
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
Meier, Brudney & Bohte: Chapter 4
Frequency Distributions (Page 7)
 Summary
 Problems 4.2, 4.4, 4.10
Meier, Brudney & Bohte Chapter 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?
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.
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?
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)
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.
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.
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
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
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
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.
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?
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Outliers (Have we talked about this before?)
Skewed – means?
Example: housing prices
More to come in Chapter 6
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
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?
Meier, Brudney & Bohte: Chapter 5
Measures of Central Tendency
 Summary
 Problems 5.2, 5.16
(Page 14)
Meier, Brudney & Bohte Chapter 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?
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?
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
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
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
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
Meier & Brudney: Chapter 6
Measures of Dispersion (Page 7)
 Summary
 Problems 6.2, 6.4, 6.8