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Univariate Statistics
PSYC*6060
Peter Hausdorf
University of Guelph
Agenda
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Overview of course
Review of assigned reading material
Sensation seeking scale
Howell Chapters 1 and 2
Student profile
Course Principles
• Learner centered
• Balance between theory, math and
practice
• Fun
• Focus on knowledge acquisition and
application
Course Activities
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Lectures
Discussions
Exercises
Lab
Terminology
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Random sample
Population
External validity
Discrete
Parameter
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Random assignment
Sample
Internal validity
Continuous
Statistic
Terminology (cont’d)
• Descriptive vs inferential statistics
• Independent vs dependent variables
Measurement Scales
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Nominal
Ordinal
Interval
Ratio
Sensation Seeking Test
Defined as:
“the need for varied, novel and
complex sensations and experiences
and the willingness to take physical
and social risks for the sake of such
experiences”
Zuckerman, 1979
Measures of Central
Tendency: The Mean
Mean =
Sum of all scores
Total number of
scores
X =
EO
N
Measures of Central
Tendency: The Mode
• Is the most common score (or the score
obtained from the largest number of
subjects)
Measures of Central
Tendency: The Median
• The score that corresponds to the point
at or below which 50% of the scores fall
when the data are arranged in
numerical order.
Median Location
=
N+1
2
Advantages
Mean
– can be manipulated algebraically
– best estimate of population mean
Mode
– unaffected by extreme scores
– represents the largest number in sample
– applicable to nominal data
Median
– unaffected by extreme scores
– scale properties not required
Disadvantages
Mean
– influenced by extreme scores
– value may not exist in the data
– requires faith in interval measurement
Mode
– depends on how data is grouped
– may not be representative of entire results
Median
– not entered readily into equations
– less stable from sample to sample
Bar Chart
10
Median
Modes
8
6
4
Count
2
0
7.00
15.00
12.00
TOT ALSSS
19.00
17.00
23.00
21.00
27.00
25.00
31.00
29.00
33.00
Histogram
Mode
=14+15+16
16
14
12
10
8
6
4
2
Std. Dev = 6.20
0
N = 74.00
Mean = 21.6
7.5
12.5
10.0
TOTALSSS
17.5
15.0
22.5
20.0
27.5
25.0
32.5
30.0
35.0
Another Example
Mean = 18.9
Median = 21
Mode = 32
Bar Chart
10
8
6
4
Count
2
0
2.00
6.00
4.00
BIMODAL
13.00
8.00
19.00
16.00
24.00
22.00
28.00
26.00
32.00
30.00
35.00
Histogram
Histogram
14
12
10
8
6
Frequency
4
Std. Dev = 11.73
Mean = 18.9
N = 74.00
2
0
2.5
7.5
5.0
BIMODAL
12.5
10.0
17.5
15.0
22.5
20.0
27.5
25.0
32.5
30.0
35.0
Describing Distributions
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Normal
Bimodal
Negatively skewed
Positively skewed
Platykurtic (no neck)
Leptokurtic (leap out)
16
N = 74.00
Mean = 21.6
Median = 22
Mode = 23
14
12
10
8
6
4
2
Std. Dev = 6.20
0
7.5
12.5
10.0
17.5
15.0
TOTALSSS
22.5
20.0
27.5
25.0
32.5
30.0
35.0
Histogram
30
N = 74.00
Mean = 21.6
20
Median = 22
Frequency
10
Mode = 23
Std. Dev = 1.16
0
19.0
20.0
SAMEMEAN
21.0
22.0
23.0
Measures of Variability
• Range - distance from lowest to highest
score
• Interquartile range (H spread) - range
after top/bottom 25% of scores removed
|X-X|
E
• Mean absolute deviation =
N
Measure of Variability
Variance
Standard
deviation
(X-X)
E
s =
N-1
2
2
SD =
E(X-X)
N-1
2
Degrees of Freedom
• When estimating the mean we lose one
degree of freedom
• Dividing by N-1 adjust for this and has a
greater impact on small sample sizes
• It works
Mean & Variance as
Estimators
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Sufficiency
Unbiasedness
Efficiency
Resistance
Linear Transformations
• Multiply/divide each X by a constant
and/or add/subtract a constant
Rules
• Adding a constant to a set of data adds to the
mean
• Multiplying by a constant multiplies the mean
• Adding a constant has no impact on variance
• Multiplying by a constant multiplies the
variance by the square of the constant