Date post: | 21-Jan-2016 |
Category: |
Documents |
Upload: | oswald-pierce |
View: | 217 times |
Download: | 0 times |
Univariate Statistics PSYC*6060
Peter Hausdorf
University of Guelph
Agenda
• 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
• Lectures
• Discussions
• Exercises
• Lab
Terminology
• Random sample• Population• External validity• Discrete• Parameter
• Random assignment• Sample• Internal validity• Continuous• Statistic
Terminology (cont’d)
• Descriptive vs inferential statistics
• Independent vs dependent variables
Measurement Scales
• Nominal
• Ordinal
• Interval
• Ratio
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
Measures of Central Tendency: The Mean
X =N
Mean=Sum of all scores
Total number ofscores
• Is the most common score (or the score obtained from the largest number of subjects)
Measures of Central Tendency: The Mode
• 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
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
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
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
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
Another Example
Mean = 18.9
Median = 21
Mode = 32
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
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
Describing Distributions
• Normal
• Bimodal
• Negatively skewed
• Positively skewed
• Platykurtic (no neck)
• Leptokurtic (leap out)
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
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
Measure of Variability
Variance =s
Standarddeviation
2
N - 1
2
(X-X)
SDN - 1
2
(X-X)=
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
• Sufficiency
• Unbiasedness
• Efficiency
• Resistance
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