Univariate Statistics PSYC*6060 Peter Hausdorf University of Guelph.
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Transcript of Univariate Statistics PSYC*6060 Peter Hausdorf University of Guelph.
![Page 1: Univariate Statistics PSYC*6060 Peter Hausdorf University of Guelph.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bff11a28abf838cbb852/html5/thumbnails/1.jpg)
Univariate Statistics PSYC*6060
Peter Hausdorf
University of Guelph
![Page 2: Univariate Statistics PSYC*6060 Peter Hausdorf University of Guelph.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bff11a28abf838cbb852/html5/thumbnails/2.jpg)
Agenda
• Overview of course
• Review of assigned reading material
• Sensation seeking scale
• Howell Chapters 1 and 2
• Student profile
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Course Principles
• Learner centered
• Balance between theory, math and practice
• Fun
• Focus on knowledge acquisition and application
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Course Activities
• Lectures
• Discussions
• Exercises
• Lab
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Terminology
• Random sample• Population• External validity• Discrete• Parameter
• Random assignment• Sample• Internal validity• Continuous• Statistic
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Terminology (cont’d)
• Descriptive vs inferential statistics
• Independent vs dependent variables
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Measurement Scales
• Nominal
• Ordinal
• Interval
• Ratio
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Sensation Seeking Test
“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”
Defined as:
Zuckerman, 1979
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Measures of Central Tendency: The Mean
X =N
Mean=Sum of all scores
Total number ofscores
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• Is the most common score (or the score obtained from the largest number of subjects)
Measures of Central Tendency: The Mode
![Page 11: Univariate Statistics PSYC*6060 Peter Hausdorf University of Guelph.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bff11a28abf838cbb852/html5/thumbnails/11.jpg)
• The score that corresponds to the point at or below which 50% of the scores fall when the data are arranged in numerical order.
Measures of Central Tendency: The Median
Median Location =N + 1
2
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Advantages
– can be manipulated algebraically– best estimate of population mean
– unaffected by extreme scores– represents the largest number in sample– applicable to nominal data
– unaffected by extreme scores– scale properties not required
Mean
Mode
Median
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Disadvantages
– influenced by extreme scores– value may not exist in the data– requires faith in interval measurement
– depends on how data is grouped– may not be representative of entire results
– not entered readily into equations– less stable from sample to sample
Mean
Mode
Median
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Bar Chart
TOTALSSS
33.00
31.00
29.00
27.00
25.00
23.00
21.00
19.00
17.00
15.00
12.00
7.00
Co
un
t
10
8
6
4
2
0
Median Modes
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Histogram
TOTALSSS
35.0
32.5
30.0
27.5
25.0
22.5
20.0
17.5
15.0
12.5
10.0
7.5
16
14
12
10
8
6
4
2
0
Std. Dev = 6.20
Mean = 21.6
N = 74.00
=14+15+16Mode
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Another Example
Mean = 18.9
Median = 21
Mode = 32
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Bar Chart
BIMODAL
35.00
32.00
30.00
28.00
26.00
24.00
22.00
19.00
16.00
13.00
8.00
6.00
4.00
2.00
Co
un
t
10
8
6
4
2
0
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Histogram
BIMODAL
35.0
32.5
30.0
27.5
25.0
22.5
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5
Histogram
Fre
qu
en
cy
14
12
10
8
6
4
2
0
Std. Dev = 11.73
Mean = 18.9N = 74.00
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Describing Distributions
• Normal
• Bimodal
• Negatively skewed
• Positively skewed
• Platykurtic (no neck)
• Leptokurtic (leap out)
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TOTALSSS
35.032.5
30.027.5
25.022.5
20.017.5
15.012.5
10.07.5
16
14
12
10
8
6
4
2
0Std. Dev = 6.20
Mean = 21.6
N = 74.00
SAMEMEAN
23.022.021.020.019.0
Histogram
Fre
quen
cy
30
20
10
0Std. Dev = 1.16
Mean = 21.6
N = 74.00
Median = 22Mode = 23
Median = 22
Mode = 23
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Measures of Variability
• Range - distance from lowest to highest score
• Interquartile range (H spread) - range after top/bottom 25% of scores removed
• Mean absolute deviation = |X-X|
N
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Measure of Variability
Variance =s
Standarddeviation
2
N - 1
2
(X-X)
SDN - 1
2
(X-X)=
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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
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Mean & Variance as Estimators
• Sufficiency
• Unbiasedness
• Efficiency
• Resistance
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Linear Transformations
• Multiply/divide each X by a constant and/or add/subtract a constant
• 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
Rules