Download Political Research and Statistics

Skewness and Curves
10/1/2013
Readings
• Chapter 2 Measuring and Describing Variables
(Pollock) (pp.37-44)
• Chapter 6. Foundations of Statistical Inference
(128-133) (Pollock)
• Chapter 3 Transforming Variables (Pollock
Workbook)
OPPORTUNITIES TO DISCUSS
COURSE CONTENT
Office Hours For the Week
• When
– Wedesday10-12
– Thursday 8-12
– And by appointment
Homework
• Chapter 2
– Question 1: A, B, C, D, E
– Question 2: B, D, E (this requires a printout)
– Question 3: A, B, D
– Question 5: A, B, C, D
– Question 7: A, B, C, D
– Question 8: A, B, C
Course Learning Objectives
1. Students will learn the basics of research
design and be able to critically analyze the
advantages and disadvantages of different
types of design.
2. Students Will be able to interpret and explain
empirical data.
MEASURES OF DISPERSION
The Normal/Bell Shaped curve
• Symmetrical around the
mean
• It has 1 hump, it is
located in the middle,
so the mean, median,
and mode are all the
same!
Why we use the normal curve
• To determine skewness
• The Normal Distribution
curve is the basis for
hypothesis/significance
testing
What is skewness?
• an asymmetrical
distribution.
• Skewness is also a
measure of symmetry,
• Most often, the median
is used as a measure of
central tendency when
data sets are skewed.
A distribution is said to be skewed if
the magnitude of
(Skewness value/ St. Error of Skew) is
greater than 2 (in absolute value)
World Urban Population
STATISTICAL SIGNIFICANCE
Testing
• Causality
• Statistical Significance
• Practical Significance
Statistical Significance
• A result is called statistically significant if it is unlikely to
have occurred by chance
• You use these to establish parameters, so that you can
state probability that a parameter falls within a
specified range called the confidence interval (chance
or not).
• Practical significance says if a variable is important or
useful for real-world. Practical significance is putting
statistics into words that people can use and
understand.
Curves & Significance Testing
What this Tells us
• Roughly 68% of the scores
in a sample fall within one
standard deviation of the
mean
• Roughly 95% of the scores
fall 2 standard deviations
from the mean (the exact
# for 95% is 1.96 s.d)
• Roughly 99% of the scores
in the sample fall within
three standard deviations
of the mean
A Practice Example
• Assuming a normal curve
compute the age (value)
– For someone who is +1 s.d,
from the mean
– what number is -1 s.d. from the
mean
• With this is assumption of
normality, what % of cases
should roughly fall within this
range (+/-1 S.D.)
• What about 2 Standard
Deviations, what percent
should fall in this range?
Life Expectancy in Latin America and
Caribbean
• Compute the estimated
values for Average Life
Expectancy for +/- 2
standard deviations
from the mean.
• With this is assumption
of normality, what % of
cases should fall within
this range (+/-2 s.d).
If you find this amusing or annoying,
you get the concept
STANDARD DEVIATION AND
CHARTS IN SPSS
Standard Deviation (open GSS)
For Ratio Variables
Step 2
Step 1
Step 4
Step 3
Testing for Skewness
In the Descriptive Command
Click
Here
In the Frequencies Command
Simple Bar Charts
• In SPSS
• OPEN GSS 2008
• Analyze
– Descriptive Statistics
• Frequencies
PRINTING OUTPUTS
SPSS Printing
• SPSS outputs can be
very large
• Much of the
information is useless
• Please be smart in
printing outputs
Step 1: Change your settings
Change from portrait to landscape
Step 2: Highlight only the output you
want
Step 3: Click on “selected output”
Step 4: Choose ok
Research Design
What is a Research Design
• It is a plan for research
• It guides the researcher
through all aspects of
the study
What it Includes: Your Unit of Analysis
• Unit of Analysis
• What is it that you are
trying to study?
• What kind of data will
you need
What it includes: Variables
• The Variables
– Dependent (only 1)
– The Independent(s)
(additive)
• How you intend to
measure each
(operational definitions)
What it Includes: Hypotheses
• What is your null
hypotheses for each
relationship .
• What are your alternate
hypotheses (for each
relationship)
• Make sure these
hypothesis are “good”
What it includes: Statistical Analysis
• What statistics you plan
to use
• And Why
The Goal of A Research Design is to
create a study that can demonstrate
causality
Working for Causality
INTERNAL VALIDITY OF DESIGN
Internal Validity
• Setting up Research
Designs Properly
• Having control over
the experiment.
Especially the
independent variable.
• This can be
threatened
Threat 1:History
• You cannot account for
all previous knowledge
and events
• You cannot control for
all potential
independent variables
An Example
Threat 2: Maturation
• We get older
• We get wiser
• We get tired (short
term)
• These are natural
changes
Threat 3: Experimental Mortality
• Participants leave the
research study
• The world changes
• Those who remain, may
not be like the target
group
Threat 4: Selection Bias
• Choosing the wrong
sample
• Picking Respondents to
favor your results
• Excluding cases or
respondents that do not
fit your goals
• Using volunteers!
Threat 5: Instrumentation
A Bad Measure
Changing a Measure to Fit your
Needs
Threat 6: Design Contamination
• People intentionally or
unintentionally act
differently
• “Instrument Reactivity”
• We Guess the test, we
share information
Hawthorne Effect
Which of these are Most Common?
• History
• Maturation
• Selection
• Contamination is the worst!