psc200 3. descriptive statistics. level of measurement 1.nominal 2.ordinal 3.interval
TRANSCRIPT
PSC2003. Descriptive Statistics
Level of Measurement
1. Nominal
2. Ordinal
3. Interval
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
Frequency Distribution of Age in NES 2000
1820 22 24 26 28 30 32 34 36 3840 42 44 46 48 50 52 54 56 5860 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 95 97. 97 and older
Respondent age
0
10
20
30
40
50
Co
un
t
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?
Nominal DataMeasure of Central Tendency: Mode
• What is typical?
1. Northeast 2. North Central 3. South 4. West
Census region of interview
0
100
200
300
400
500
600
700
Co
un
t
Nominal Data
• SPSS: =>Analyze =>Descriptive Stats=>Frequencies…
• What measures of central tendency & disperson can you identify?
• What’s the difference between percent and valid percent?
Statistics
career59
2
Valid
Missing
N
career
22 36.1 37.3 37.3
17 27.9 28.8 66.1
14 23.0 23.7 89.8
6 9.8 10.2 100.0
59 96.7 100.0
2 3.3
61 100.0
law
politics
business
academic/edu
Total
Valid
.Missing
Total
Frequency Percent Valid PercentCumulative
Percent
Nominal DataDisplay matters!
law politics business academic/edu
career
0
10
20
30
40
Pe
rc
en
t
career
Charts
Bar Charts
Percentage
Nominal Data
Would vote for ___?
9 14.8 15.3 15.3
11 18.0 18.6 33.9
3 4.9 5.1 39.0
20 32.8 33.9 72.9
2 3.3 3.4 76.3
13 21.3 22.0 98.3
1 1.6 1.7 100.0
59 96.7 100.0
2 3.3
61 100.0
Clark
Kerry
Sharpton
Bush
Kucinich
Dean
0
Total
Valid
.Missing
Total
Frequency Percent Valid PercentCumulative
Percent
Clark Kerry Sharpton Bush Kucinich Dean Edwards
Would vote for ___?
0
10
20
30
40
Pe
rce
nt
Would vote for ___?
Your Presidential Preference
“If the presidential election were today, for whom would you vote?”
Nominal Data
Primary Reason for Attending UR
9 14.8 15.0 15.0
19 31.1 31.7 46.7
3 4.9 5.0 51.7
29 47.5 48.3 100.0
60 98.4 100.0
1 1.6
61 100.0
Reputation
Financial Package
Safety School
Quality of Education
Total
Valid
.Missing
Total
Frequency Percent Valid PercentCumulative
Percent
Reputation Financial Package Safety School Quality of Education
Primary Reason for Attending UR
0
10
20
30
40
50
Pe
rce
nt
Primary Reason for Attending UR
Why UR?
“What was your primary reason for coming to UR?”
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. APPROVE5. DISAPPROVE 8. DON'T KNOW --> SKIP TO B1 9. RF 0. NA
1 5 8 9Count 1177 565 55 10
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
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
Summary Approval/Disapproval Clinton Job
1. Approve strongly 2. Approve not strongly 4. Disapprove not strongly
5. Disapprove strongly
Summary app/disapp Clinton job
0
200
400
600
800C
ou
nt
Ordinal DataMeasure of Central Tendency: Median
jobclint Summary app/disapp Clinton job
745 41.2 43.0 43.0
425 23.5 24.5 67.6
162 9.0 9.4 76.9
400 22.1 23.1 100.0
1732 95.8 100.0
75 4.2
1807 100.0
1 1. Approve strongly
2 2. Approve not strongly
4 4. Disapprove notstrongly
5 5. Disapprove strongly
Total
Valid
SystemMissing
Total
Frequency Percent Valid PercentCumulative
Percent
Ordinal DataMeasure of Central Tendency: Median
1. Never permit 2. Rape, incest, health only
3. Clear need 4. Always permit
Abortion scale
0
200
400
600
800
Co
un
t
Ordinal DataMeasure of Central Tendency: Median
Abortion scale
215 11.9 12.2 12.2
525 29.1 29.9 42.1
265 14.7 15.1 57.2
753 41.7 42.8 100.0
1758 97.3 100.0
49 2.7
1807 100.0
1 1. Never permit
2 2. Rape, incest,health only
3 3. Clear need
4 4. Always permit
Total
Valid
SystemMissing
Total
Frequency Percent Valid PercentCumulative
Percent
Nominal Data
Party ID
14 23.0 23.0 23.0
24 39.3 39.3 62.3
15 24.6 24.6 86.9
4 6.6 6.6 93.4
4 6.6 6.6 100.0
61 100.0 100.0
Republican
Democrat
Independent
Other
Don't Know
Total
ValidFrequency Percent Valid Percent
CumulativePercent
Republican Democrat Independent Other Don't Know
Party ID
0
10
20
30
40
Perc
en
t
Party ID
Party Identification
“Generally speaking, do you usually consider yourself as a Republican, a Democrat, an Independent, or what?”
Interval Data
• Continuous: numbers on the real line• Mean (arithmetic):
• Example: 2, 3, 3, 5, 5, 6, 7, 7, 10, 201, 987– Mean =(2+3+3+5+5+6+7+7+10+201+987)/11 = 112.36
– Median?
– Modes?
Dichotomous or Dummy Variables• Nominal Data: Two Values• Can be treated as interval data
1. Male 2. Female
Gender
0
200
400
600
800
1,000
1,200
Co
un
t
Interval DataSkewed Distributions
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
31
3
)1(
)(
sN
YYN
ii
Y
• Median = 45• Mean = 47.2• Modes = 37, 42
1820 22 24 26 28 30 32 34 36 3840 42 44 46 48 50 52 54 56 5860 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 95 97. 97 and older
Respondent age
0
10
20
30
40
50
Co
un
t
Interval Data Grouped Into Categories for Visual Presentation
Variance
How dispersed or spread out the data is
Variance is the average squared deviation from the mean
1
)(1
2
2
n
XXs
n
ii
Standard Deviation = square root of variance = s
Use and Abuse of Descriptive Stats
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
Measures of House Partisanship
House Party Members and Leaders
Conclusion: leaders not necessarily centrist but drawn from party mode.
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…
Incumbent Vote Share in House, 1952-82
Incumbents seem to be winning more votes in later years…
… but are incumbents winning more often?
All House Incumbents
Are incumbents winning more often?
Freshman Incumbents
Do Incumbents Win More Often?
Senior Incumbents
Jacobson’s 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