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POL 242
Introduction to Research Methods
Assignment One Tutorial
Descriptive Statistics
June 2, 2011
Anthony Sealey
[email protected]
http://individual.utoronto.ca/sealey
Agenda
(1) Introduction
• (2) Review
(i) Types of Variables
(ii) Principal Descriptives
(iii) Webstats
(3) Descriptives in Webstats
(4) Exercise in Webstats
Introduction
Please be sure to sign the
attendance form.
Review of Types of Variables
Research Questions
Review of Principal Descriptives
Research Questions
1. Measures of Central Tendency
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“Pick a number …”
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“… close counts.”
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10
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n
S xi where ‘n’ denotes the
Mean (x) = _______
i=1
_
number of elements
Mean =
n
(1+2+3+4+5+6+7+8+9+10)
Mean = 5.5
10
1, 2, 3, 4, 5, 6, 7, 8, 9, 100
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Median: After arranging the data
from highest to lowest,
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the median
is the value
in the middle.
“… close doesn’t count.”
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1, 2, 2, 3, 4, 5, 6, 7, 8, 9
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Mode: The value that occurs
with the highest frequency
Research
(i.e. theQuestions
value that
appears most often).
2. Measures of Dispersion
Research Questions
1, 2, 3, 4, 5
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_
n
S
(xi –
= _________________
i=1
_
Variance
(s2)
x)2
n–1
Mean =
where ‘x’
denotes
the Mean
(1-3)2+(2-3)2+(3-3)2+(4-3)2+(5-3)2
Mean = 2.5
5–1
Standard
Variance(s) =
Deviation
Variance (s) =
(s2)
2.5
Variance (s) ≈ 1.58114
where ‘s2’
denotes the
Variance
When to use key descriptive statistics:
Descriptive Statistics
Research Questions
Measures of Central Tendency
Mean
Median
Mode
(m)
Variance
Standard
(s2)
Deviation (s)

Nominal
Ordinal
Data Type
Measures of Dispersion


Interval





Ratio





Review of Webstats
Research Questions
• There are four basic steps to the
• analysis of a variable in Webstats:
•(1) Select a dataset.
•(2) Run a ‘frequency’ to understand
how the variable is coded.
•(3) Refine the variable.
•(4) Perform the analysis.
• In today’s tutorial we’ll use the 2006
• CES to consider three variables:
•(1) A citizen’s province.
•(2) Citizen’s preferences for or
against income redistribution.
•(3) Citizen’s evaluations of the
competence of political leaders.
I strongly recommend going to my
site, downloading the ‘code’ file
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and following
along:
http://individual.utoronto.ca/sealey
Step One: Select the dataset
• Go to the course website located at:
http://groups.chass.utoronto.ca/pol242/
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• Go to: Webstats > Start Webstats.
• In section 1, select ‘CES 2006’.
• In section 3, select ‘Syntax Method’.
• Hit <PROCEED>.
Step Two: Run a Frequency
• Let’s begin with the ‘province’ variable.
• To run a frequency, use this code:
fre VAR = province.
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• Given that this variable has no missing
values and does not require a recode, we
can skip the third step (‘refine the
variable’) and go to the fourth (‘perform
the analysis’).
Moving on to the next variable …
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The question wording for ‘cps_f6’
in the 2006 iteration of the Canadian
Elections Study:
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Step Two: Run a Frequency
• Since we’ve already selected the dataset,
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we don’t need to repeat step one.
• To run a frequency, use this code:
fre VAR = cps_f6.
Step Three: Refine the Variable
• Notice the ‘don’t know’ and ‘refused’
responses. These responses take on the
valuesResearch
of ‘8’ and Questions
‘9’ respectively. We’ll
want to code them as missing, and then
rerun the frequency:
missing values cps_f6 (8,9).
fre VAR = cps_f6.
And finally …
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The ‘cps_h2b0’ and ‘cps_h2d0’
variables in the 2006 iteration of the
Canadian Elections Study asks about
respondent’s
perceptions
of
levels
of
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political leaders’ competence. In
today’s tutorial, we’ll focus on the
two most successful political leaders
in the 2011 election.
Smiling Jack
Smiling Stephen
Step Two: Run a Frequency
• Since we’ve already selected the dataset,
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Questions
we don’t need to repeat step one.
• To run frequencies, use this code:
fre VAR = cps_h2b0.
fre VAR = cps_h2d0.
Step Three: Refine the Variables
• Notice the ‘don’t knows’ are coded as
‘98’. To code them as missing, use this
code: Research Questions
missing values cps_h2b0 (98).
fre VAR = cps_h2b0.
missing values cps_h2d0 (98).
fre VAR = cps_h2d0.
Descriptives in Webstats
Research Questions
Once we’ve refined our variables,
the final step is to perform the
analysis.Research
To obtainQuestions
descriptive
statistics, we do this by simply
adding some extra code at the end of
our frequency command.
Step Four: Perform the Analysis
• Suppose we want to find the mode of
the ‘province’ variable; in order to do
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Questions
this, we
simply add
‘/statistics=mode’ at
the end of our frequency command:
fre VAR = province/statistics=mode.
• If we want other descriptive statistics,
simply include the appropriate code at
the end of the frequency command.
• For example, if we want to know the
Questions
median,Research
mean, variance
and
standard devation, simply add
‘/statistics=median mean variance stddev’
at the end of our frequency command.
Use appropriate descriptives for each
level of measurement.
• For nominal variables, find the mode:
fre VAR = province/statistics=mode.
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• For ordinal variables, find the mode
and median:
missing values cps_f6 (8,9).
fre VAR = cps_f6/statistics=mode median.
• For interval/ratio variables, find the
mode, median, mean, variance and
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standard
deviation:
missing values cps_h2b0 (98).
fre VAR = cps_h2b0/statistics = mode median mean
variance stddev.
We can use the means and standard
deviations of similar variables to
compare them.
• For example, if we want to compare
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perceptions
of Jack’s
and Stephen’s
competence, use this code:
missing values cps_h2b0 (98).
fre VAR = cps_h2b0/statistics = mean stddev.
missing values cps_h2d0 (98).
fre VAR = cps_h2d0/statistics = mean stddev.
Once we’ve completed our analysis,
we’ll be prepared to ‘tell the story’.
In other words, what have we
learned from
our analysis?
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QuestionsWhen
doing this, use the information
we’ve gathered from the frequency
distribution as well as from the
appropriate descriptive statistics.
Exercise in Webstats
Research Questions
Exercise
Choose a public opinion dataset that you are
interested in. Find a variable for each of the
nominal, ordinal and (interval or ratio)
levels of measurement. Run frequency
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distributions, refine the variables by
declaring missing values and performing
necessary recodes and calculate
appropriate descriptive statistics for each of
the identified variables. What’s the ‘story’ of
your analysis? What have you learned?