PSC200 3. Descriptive Statistics

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PSC2003. Descriptive Statistics
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Level of Measurement

1. Nominal
2. Ordinal
3. Interval

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Lecture OverviewDescriptive Statistics

• Frequency Distribution
• Data Information but too much information.
  How do we summarize data?
• Central Measure of Tendency
• Mode Nominal, Ordinal, Interval
• Median Ordinal, Interval
• Mean Interval
• Measures of Dispersion
• Variance Interval

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Frequency Distribution of Age in NES 2000
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Understanding Distributions

• What is typical?? Mode? Median? Mean?
• Example 2, 2, 2, 4, 6, 8, 8
• Mode 2
• Median 4
• Mean 4.57
• Where does each measure of central tendency apply?

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Nominal DataMeasure of Central Tendency Mode

• What is typical?

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Nominal Data

• SPSS
• gtAnalyze
• gtDescriptive Stats
• gtFrequencies
• What measures of central tendency disperson can
  you identify?
• Whats the difference between percent and valid
  percent?

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Nominal DataDisplay matters!

• Charts
• Bar Charts
• Percentage

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Nominal Data
Your Presidential Preference
If the presidential election were today, for
whom would you vote?
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Nominal Data
Why UR?
What was your primary reason for coming to UR?
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Ordinal Data

• Sequence matters, e.g. rankings
• Median now has meaning
• Example
• A12. Approve/disapprove Clinton job
  
• Do you approve or disapprove of the way Bill
  Clinton is handling his job as president?
• 1. APPROVE
• 5. DISAPPROVE
• 8. DON'T KNOW --gt SKIP TO B1
• 9. RF
• 0. NA
• 1 5 8 9
• Count 1177 565 55 10

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A12a. Strength of approval/disapproval of Clinton

• IF R APPROVES CLINTON HANDLING JOB AS PRESIDENT/
  
• IF R DISAPPROVES CLINTON HANDLING JOB AS
  PRESIDENT
• Strongly or not strongly?
• 1. STRONGLY
• 5. NOT STRONGLY
• 8. DK
• 9. RF
• 0. NA INAP, 8,9,0 in A12
• 0 1 5 8
  9
• Count 65 1145 587 8
  2

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Summary Approval/Disapproval of Clinton Job as
President

• Do you approve or disapprove of the way Bill
  Clinton is handling his job as president?
• Strongly or not strongly?
• SUMMARY APPROVAL/ DISAPPROVAL OF CLINTON JOB AS
  Built from A12 and A12a.
• 1. Approve strongly
• 2. Approve not strongly
• 4. Disapprove not strongly
• 5. Disapprove strongly
• 8. DK (in A12 or A12a)
• 9. RF (in A12 or A12b)
• 0. NA

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Summary Approval/Disapproval Clinton Job
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Ordinal DataMeasure of Central Tendency Median
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Ordinal DataMeasure of Central Tendency Median
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Ordinal DataMeasure of Central Tendency Median
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Nominal Data
Party Identification
Generally speaking, do you usually consider
yourself as a Republican, a Democrat, an
Independent, or what?
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Interval Data

• Continuous numbers on the real line
• Mean (arithmetic)
• Example 2, 3, 3, 5, 5, 6, 7, 7, 10, 201, 987
• Mean (2335567710201987)/11 112.36
• Median?
• Modes?

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Dichotomous or Dummy Variables

• Nominal Data Two Values
• Can be treated as interval data

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Interval DataSkewed Distributions
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Skewed Distributions

• Skewness
• For data Y1, Y2,YN
• Skewness
• Where is the mean, s is the standard
  deviation, and N is the number of data points

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• Median 45
• Mean 47.2
• Modes 37, 42

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Interval Data Grouped Into Categories for Visual
Presentation
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Variance

• How dispersed or spread out the data is
• Variance is the average squared deviation from
  the mean

• Standard Deviation square root of variance s

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Use and Abuse of Descriptive Stats
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Grofman, Koetzle, McGann. LSQ 2002. Congressional
Leadership, 1965-96

• Are congressional leaders more extreme than their
  followers?
• Discern between theories that claim that
• leaders are more extreme
• leaders are more centrist

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Measures of House Partisanship
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House Party Members and Leaders
Conclusion leaders not necessarily centrist but
drawn from party mode.
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Gary Jacobson. 1987. The Marginals Never
Vanished. AJPS.

• Marginal competitive elections
• Do incumbents have a growing advantage in
  elections?
• Do they win elections more easily than in the
  past?
• Has electoral competition declined? Incumbent
  behavior changed?
• Implications for democracy

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Incumbent Vote Share in House, 1952-82
Incumbents seem to be winning more votes in later
years
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but are incumbents winning more often?
All House Incumbents
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Are incumbents winning more often?
Freshman Incumbents
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Do Incumbents Win More Often?
Senior Incumbents
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Jacobsons Conclusion

• No net change in overall security for incumbents
  (same proportion, ca. 6-7, lose)
• Marginals do increase but so does vote swing.
• First-term incumbents safer, senior incumbents
  not
• Explains absence of change in incumbent behavior