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POL322 Lecture #4 .docx
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University of Toronto St. George
Political Science
POL101Y1
Agria
Fall
Description
POL322 Lecture #4
How Do We Make Sense of Our Data? Descriptive Statistics and Visualization
Descriptive Statistics
 the sample population must be at random
3 Classifications of Variables
Continuous Variables
 values of a variable take an infinite continuum of possible real numbers in a certain
interval
o party vote share, percentage support to policy, economic growth rate
Discrete Variables
 values of a variables take a set of separate numbers (integers), such as 0, 1, 2
o vote choice, number of military causalities, answer to multiplechoice
questions
o discrete variables taking many, many values, are often treated as continuous
variables
campaign spending, number of days in office .. etc
Quantitative Variables
 the measurement scale of a variable is numerical values (naturally expressed in
numbers)
o annual income, vote share, age, number of siblings, growth rate … etc
Categorical (or Qualitative Variables)
 the measurement scale of a variable is a set of categories (but will assign numbers)
o Vote choice (Rep or Dem)
o Religious affiliation (Christian, Protestant, Catholic)
o Answer to multiplechoice questions (Stongly Agree, Agree, Neutral .. etc)
What kind of scale are we using to express our variable?
Interval Scale
 values of a variable has a specific numerical distance or interval between each value
o number, percentage, share, rate, amount … etc
Nominal Scale
 values of a variable take unordered multiple categories
o vote choice (Rep or Dem)
o religious affiliation (Christian, Protestant, Catholic)
Ordinal Scale
 values of a variable take ordered multiple categories
4 Types of Variables
1. Continuous, Interval, Quantitative Variable
2. Discrete, Interval, Quantitative Variables
3. Discrete, Ordinal, Categorical/Quantitative Variables
4. Discrete, Nominal, Categorical Variables
Using different statistical methods for each variable Descriptive Statistics
When we describe our data, we want to know:
1. Distribution of Data
a. How the values of a variable are distributed across observations
2. Center of data
a. The value of a variable o a typical observation in data
3. Variability of data
a. How the values of a variable are spread from the center
The center and variability of data can be numerical
Categorical Variables
1. Distribution of Data
a. Relative frequency distribution
b. Frequency table
c. Visualization: bar graph or pie chart
2. Center of Data: the value of a typical observation
a. Mode: The value that occurs most frequently
i. It indicates he most common outcome
b. Median, if a variable is ordinal: the value of the observation that falls in the
middle of the ordered sample
i. It splits the sample into two parts with equal number of observations
Quantitative Variables
Distribution of Data
 (Relative) Frequency Distribution
 Frequency Table
 Visualization: Histogram (X axis has the intervals of the values of a variable)
Center of Data
 Mode could be meaningful if a variable is discrete and takes a relatively small
number of values: Most common value
 Median: Middle value
 Mean: Average value, the sum of the values of all observations divided by the
number of observations
o
Variability of Data
 Standard Deviation, Variance
 Percentile, Quartile

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