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graphs
Measurement
Univariategraphs
Multivariategraphs
References
Approaches to Analysing PoliticsVariables & graphs
Johan A. Elkink
School of Politics & International Relations
University College Dublin
6–8 March 2017
graphs
Measurement
Univariategraphs
Multivariategraphs
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1 Measurement
2 Univariate graphs
3 Multivariate graphs
graphs
Measurement
Univariategraphs
Multivariategraphs
References
Outline
1 Measurement
2 Univariate graphs
3 Multivariate graphs
graphs
Measurement
Univariategraphs
Multivariategraphs
References
graphs
Measurement
Univariategraphs
Multivariategraphs
References
Measurement
A variable is an attribute that has two or more divisions,characteristics, or categories. The opposite is a constant,which is “an attribute that does not vary.”
A sample is a subset of the population, the population is theset of all cases of interest.
A case is an entity that displays or possesses the traits of agiven variable. The unit of analysis refers to the level or classof the cases.
Measurement is the process of determining and recordingwhich of the possible traits of a variable an individual caseexhibits or possesses.
(Argyrous, 1997, 3–4)
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Variables: example
Hypothesis: “Countries with high levels of inequality are morelikely to experience civil war.”
Unit of analysis: countries
– possibly a time-series, i.e. theunit of analysis is a country-year
Population: e.g. all countries
– from 1945 to 2010
Independent variable: inequality
– e.g. the ratio-level Ginicoefficient
Dependent variable: civil war
– e.g. a nominal variable, 1 =civil war, 0 = no civil war
Example of a case: Kenya
– Kenya in 1993
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Measurement
Univariategraphs
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References
Variables: example
Hypothesis: “Countries with high levels of inequality are morelikely to experience civil war.”
Unit of analysis: countries
– possibly a time-series, i.e. theunit of analysis is a country-year
Population: e.g. all countries
– from 1945 to 2010
Independent variable: inequality – e.g. the ratio-level Ginicoefficient
Dependent variable: civil war – e.g. a nominal variable, 1 =civil war, 0 = no civil war
Example of a case: Kenya
– Kenya in 1993
graphs
Measurement
Univariategraphs
Multivariategraphs
References
Variables: example
Hypothesis: “Countries with high levels of inequality are morelikely to experience civil war.”
Unit of analysis: countries – possibly a time-series, i.e. theunit of analysis is a country-year
Population: e.g. all countries – from 1945 to 2010
Independent variable: inequality – e.g. the ratio-level Ginicoefficient
Dependent variable: civil war – e.g. a nominal variable, 1 =civil war, 0 = no civil war
Example of a case: Kenya – Kenya in 1993
graphs
Measurement
Univariategraphs
Multivariategraphs
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Variables: example
Hypothesis: “Voters with low trust in politicians are more infavour of binding referendums.”
Unit of analysis: voters / individual
Population: e.g. all Dutch voters
Sample: e.g. Dutch Parliamentary Election Study sample of1,200 respondents
Independent variable: trust
– e.g. an ordinal Likert-scale oflow, medium, high trust
Dependent variable: support for referendums
– e.g. anordinal Likert-scale of disagree, neutral, agree
Example of a case: an individual voter
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Measurement
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Variables: example
Hypothesis: “Voters with low trust in politicians are more infavour of binding referendums.”
Unit of analysis: voters / individual
Population: e.g. all Dutch voters
Sample: e.g. Dutch Parliamentary Election Study sample of1,200 respondents
Independent variable: trust – e.g. an ordinal Likert-scale oflow, medium, high trust
Dependent variable: support for referendums – e.g. anordinal Likert-scale of disagree, neutral, agree
Example of a case: an individual voter
graphs
Measurement
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Levels of measurement
Categorical Nominal categories
Ordinal ... in particular order
Scale Interval ... with meaningful distance
Ratio ... with meaningful zero
Examples:
graphs
Measurement
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Multivariategraphs
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Levels of measurement
Categorical Nominal categories
Ordinal ... in particular order
Scale Interval ... with meaningful distance
Ratio ... with meaningful zero
Examples:
Binary: treaty signed; war initiated; gender; participated inprotest; democracy-autocracyMultiple categories: electoral system; party family; urban-rural
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Levels of measurement
Categorical Nominal categories
Ordinal ... in particular order
Scale Interval ... with meaningful distance
Ratio ... with meaningful zero
Examples:
Likert-scales: disagree-neutral-agree; never-sometimes-oftenOther: democracy-anocracy-autocracy;peace-skirmish-war-world war
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Levels of measurement
Categorical Nominal categories
Ordinal ... in particular order
Scale Interval ... with meaningful distance
Ratio ... with meaningful zero
Examples:
Polity democracy scale; sympathy scores; attitude scales
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Measurement
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Levels of measurement
Categorical Nominal categories
Ordinal ... in particular order
Scale Interval ... with meaningful distance
Ratio ... with meaningful zero
Examples:
war duration; exports; Gini coefficient; battle deaths
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Example data set
DistrictSystem Magnitude Seats Threshold Proportionality
1 PR 10 80 Yes 0.82 PR 150 150 No 0.93 STV 9 100 No 0.84 FPTP 1 300 No 0.45 FPTP 1 600 No 0.56 PR 3 200 Yes 0.77 STV 5 125 No 0.78 PR 10 100 Yes 0.89 MIXED 15 500 Yes 0.6
PR = proportional representation; STV = single transferablevote; FPTP = first past the post; MIXED = mixed electoralsystem
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Example data set
party education gender leftRight ageFianna Fail below 2nd level Female 7 70Other 3rd level Female 5 61Fianna Fail below 2nd level Female 6 61Fianna Fail 2nd level Male 5 31Fianna Fail 2nd level Male 5 53Independent 3rd level Female 5 40Other 3rd level Female 5 30Labour 3rd level Female 5 41Sinn Fein 2nd level Male 7 60Sinn Fein 2nd level Male 5 39
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Outline
1 Measurement
2 Univariate graphs
3 Multivariate graphs
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Measurement
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Main graph types
univariatecategorical pie-charts
barplotsscale time plot
histogramboxplot
multivariatescale by scale scatterplotscale by categorical boxplots
barplotcategorical by categorical barplot
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Categorical variables
For categorical variables, it is often useful to look at thenumber of cases or the proportion of cases in a particularcategory.
Barplots and pie charts are useful for this.
0
50
100
150
Fianna Fail Fine Gael Labour Other Sinn Fein
party
coun
t
Fianna Fail
Fine Gael
Labour
Other
Sinn Fein
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Pie chart
Fianna Fail
Fine Gael
Independent
Labour
Other
Sinn Fein
Party of 1st preference vote
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Pie chart
Using a 3D projection leads to misleading interpretations.
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Bar chart (univariate)
Fianna Fail
Fine Gael
Independent
Labour
Other
Sinn Fein
Party of 1st preference vote
0.00
0.05
0.10
0.15
0.20
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Bar chart (univariate)
Labour
Independent
Sinn Fein
Other
Fianna Fail
Fine Gael
Party of 1st preference vote
0.00
0.05
0.10
0.15
0.20
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Bar chart (univariate)
Labour
Independent
Sinn Fein
Other
Fianna Fail
Fine Gael
Party of 1st preference vote
0.0
0.2
0.4
0.6
0.8
1.0
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Time plot
When data is measured over time, another useful plot is a time plot,
to see trends over time.
1800 1850 1900 1950 2000
0.0
0.2
0.4
0.6
0.8
1.0
Year
Pro
port
ion d
em
ocra
cie
s
Polity IV (Marshall and Jaggers, 2002)
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Time plot
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Time plot
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Distributions
For graphs of distributions (histogram, density plot, boxplot,etc.) you want to get an impression of:
• the shape of the distribution;
• the center and spread of the distribution;
• the presence of outliers.
(Moore, 2003, 12)
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Histogram
For continuous (or scale) variables, we often want to get anidea of the distribution of values. How many low, medium,high values?
Histograms are useful to get an impression.
• bin the data using equal-distance cut-off points• then produce a barplot of the number in each bin.
Probability ever vote for Labour
Fre
quency
2 4 6 8 10
050
100
150
200
250
300
(Irish National Election Study 2011)
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Histogram
0
25
50
75
100
125
25 50 75
age
coun
t
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Box plot
20
40
60
80
0.6 0.8 1.0 1.2 1.4
1
age
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Boxplot
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Outline
1 Measurement
2 Univariate graphs
3 Multivariate graphs
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Scatter plot
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20 40 60 80
Age
Left−
Rig
ht s
elf−
plac
emen
t
Left−right self−placement by age
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graphs
Measurement
Univariategraphs
Multivariategraphs
References
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Left−right self−placement by age
graphs
Measurement
Univariategraphs
Multivariategraphs
References
Bar charts
Barcharts can be used to visualise the distribution of avariable—using the proportions in each category of acategorical variable—but also for relationships between twovariables:
With another categorical variable: by displaying the proportionsin a different variable.
With another scale variable: by displaying the mean or otherstatistics of a different variable.
graphs
Measurement
Univariategraphs
Multivariategraphs
References
Bar chart
Sinn Fein
Other
Labour
Independent
Fianna Fail
Fine Gael
Average left−right self−placement by party
0 2 4 6 8 10
graphs
Measurement
Univariategraphs
Multivariategraphs
References
Bar chart
Sinn Fein
Other
Labour
Independent
Fianna Fail
Fine Gael
Average left−right self−placement by party
3.5
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graphs
Measurement
Univariategraphs
Multivariategraphs
References
Bar chart
Fianna Fail
Fine Gael
Other
Labour
Independent
Sinn Fein
Percentage of young voters by party
0 20 40 60 80 100
graphs
Measurement
Univariategraphs
Multivariategraphs
References
Bar chart
graphs
Measurement
Univariategraphs
Multivariategraphs
References
Bar chart
graphs
Measurement
Univariategraphs
Multivariategraphs
References
Box plots
Box plots can also be split by category on a different variable,to visualise the relationship between a categorical and a scalevariable.
graphs
Measurement
Univariategraphs
Multivariategraphs
References
Box plot
20
40
60
80
Fianna Fail Fine Gael Independent Labour Other Sinn Fein
party
age
graphs
Measurement
Univariategraphs
Multivariategraphs
References
Conclusion
• Remember keywords of measurement: levels ofmeasurement, sample vs population, unit of analysis.
• Understanding the relation between measurement,variables, and data sets.
• Understanding the variation in types of graphs—and hownot to use them.
• Understanding the difference between univariate andmultivariate graphs.
graphs
Measurement
Univariategraphs
Multivariategraphs
References
Argyrous, George. 1997. Statistics for social research. Basingstoke: MacMillan.
Marshall, M.G. and K. Jaggers. 2002. “Polity IV project: political regime characteristics and transitions,1800-2002.”.URL: http://www.bsos.umd.edu/cidcm/polity/
Moore, David S. 2003. The basic practice of statistics. 3rd ed. New York: W.H. Freeman.
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