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Skewness
9/27/2012
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)
Homework
• Homework Due: Chapter 2 Pollock Workbook
(10/2)
– 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
OPPORTUNITIES TO DISCUSS
COURSE CONTENT
Office Hours For the Week
• When
– Friday and
Monday 11-1
– Tuesday 8-12
– And
appointment
• Santa wears
blublockers
Course Learning Objectives
• Students will learn the research methods
commonly used in behavioral sciences and will
be able to interpret and explain empirical
data.
• Students will achieve competency in
conducting statistical data analysis using the
SPSS software program.
THE NORMAL CURVE
Different Kinds of Distributions
Different Kinds of Curves
Rectangular
Camel Humps
Dromedary (one hump)
Bactrian (bi-modal)
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
SKEWNESS
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.
How to describe skewness
The Mean or the Median?
• In a normal distribution, the mean is the
preferred measure
• In a skewed distribution, you go with the
median
Testing for Skewness
In the Descriptives Command
Click
Here
In the Frequencies Command
Deviate from the norm?
1. Divide the skewness
value
2. By the std. error of
skewness
A distribution is said to be skewed if
the magnitude of
(Skewness value/ St. Error of Skew) is
greater than 2 (in absolute value)
If the Value is Two or More
Median
Skewness Value
Standard error of Skewness
If the Value Is Two or Less
Mean
Skewness Value
Standard error of Skewness
Baseball Salaries again
• Divide the Skewness by
its standard error
– .800/.427
= 1.87
• This value is less than 2
so we use the mean (92
million)
• What does the positive
skew value mean???
Lets Try another One (Per Capita
income in the states)
• Divide the Skewness by its
standard error
– .817/.337
= 2.42
• The value is greater than
two, and the skewness
value is positive
• What is the better
measure and what might
cause this distribution
shape?
CO2 Emissions by State
Percent Hispanic
World Urban Population
MAKING BAR CHARTS IN SPSS
Simple Bar Charts
• In SPSS
• OPEN GSS 2008
• Analyze
– Descriptive Statistics
• Frequencies
STATISTICAL 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
# 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?
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