1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2017 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays.
Welcome

2. A note on doodling

3. Schedule of readings Before next exam (February 10)
Please read chapters in OpenStax textbook
Please read Appendix D, E & F online On syllabus this is referred to as online readings 1, 2 & 3
Please read Chapters 1, 5, 6 and 13 in Plous
Chapter 1: Selective Perception
Chapter 5: Plasticity
Chapter 6: Effects of Question Wording and Framing
Chapter 13: Anchoring and Adjustment

4. Homework Assignment 7 & 8 Please complete the worksheet by hand
Please complete the memorandum
Due: Friday, February 3rd

5. Homework Assignment 7 & 8 Please complete the worksheet by hand
Please complete the memorandum
Due: Friday, February 3rd

6. By the end of lecture today 1/30/17
Use this as your
study guide
By the end of lecture today 1/30/17
Characteristics of a distribution
Central Tendency
Dispersion
Measures of variability
Range
Standard deviation
Variance
Memorizing the four definitional formulae

7. Lab sessions Everyone will want to be enrolled
in one of the lab sessions
Labs continue
this week

8. Project 1 - Likert Scale - Correlations - Comparing two means (bar graph)
Questions?

11. Overview Frequency distributions
The normal curve
Mean, Median,
Mode, Trimmed Mean
Standard deviation,
Variance, Range
Mean Absolute Deviation
Skewed right, skewed left
unimodal, bimodal, symmetric

12. Frequency distributions
The normal curve

13. Some distributions are more
Variability
What might this be?
Some distributions are more
variable than others
Let’s say this is our distribution of heights of men on U of A baseball team 5’
5’6” 6’
6’6” 7’ 5’
5’6” 6’
6’6” 7’
Mean is 6 feet tall
What might this be? 5’
5’6” 6’
6’6” 7’

14. Dispersion: Variability
Some distributions are more variable
than others 6’ 7’ 5’
5’6”
6’6” A
The larger the variability
the wider the curve tends to be
The smaller the variability
the narrower the curve tends to be B
Range: The difference between
the largest and smallest
observations C
Range for distribution A?
Range for distribution B?
Range for distribution C?

15. 84” – 71” = 13” Wildcats Basketball team:
Tallest player = 84” (same as 7’0”) (Lauri Markkanen and Dusan Ristic)
Shortest player = 71” (same as 5’11”)
(Parker Jackson-Cartwritght)
Fun fact:
Mean is 78
Range:
The difference
between the largest
and smallest scores
84” – 71” = 13”
xmax - xmin = Range
Range is 13”

16. No reference is made to numbers between the min and max
Baseball
Fun fact:
Mean is 72
Wildcats Baseball team:
Tallest player = 77” (same as 6’5”)
(Kevin Ginkel)
Shortest player = 68” (same as 5’8”)
(Justin Behnke and Cody Ramer & Zach Gibbons)
Range:
The difference between the largest and smallest score
77” – 68” = 9”
xmax - xmin = Range
Range is 9” (77” – 68” )
Please note:
No reference is made to numbers between the min and max

17. Let’s build it up again… U of A Baseball team
Deviation scores
Let’s build it up again… U of A Baseball team
Diallo is 0”
Diallo is 6’0”
Diallo’s deviation score is 0
6’0” – 6’0” = 0
Diallo
5’8” 5’10” 6’0” 6’2” 6’4”

18. Let’s build it up again… U of A Baseball team
Deviation scores
Diallo is 0”
Let’s build it up again… U of A Baseball team
Preston is 2”
Diallo is 6’0”
Diallo’s deviation score is 0
Preston is 6’2”
Preston
Preston’s deviation score is 2”
6’2” – 6’0” = 2
5’8” 5’10” 6’0” 6’2” 6’4”

19. Let’s build it up again… U of A Baseball team
Deviation scores
Diallo is 0”
Let’s build it up again… U of A Baseball team
Preston is 2”
Mike is -4”
Hunter is -2
Diallo is 6’0”
Diallo’s deviation score is 0
Hunter
Preston is 6’2”
Mike
Preston’s deviation score is 2”
Mike is 5’8”
Mike’s deviation score is -4”
5’8” – 6’0” = -4
5’8” 5’10” 6’0” 6’2” 6’4”
Hunter is 5’10”
Hunter’s deviation score is -2”
5’10” – 6’0” = -2

20. Let’s build it up again… U of A Baseball team
Deviation scores
Diallo is 0”
Let’s build it up again… U of A Baseball team
Preston is 2”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
Diallo’s deviation score is 0
David
Preston’s deviation score is 2”
Mike’s deviation score is -4”
Shea
Hunter’s deviation score is -2”
Shea is 6’4”
Shea’s deviation score is 4”
5’8” 5’10” 6’0” 6’2” 6’4”
6’4” – 6’0” = 4
David is 6’ 0”
David’s deviation score is 0
6’ 0” – 6’0” = 0

21. Let’s build it up again… U of A Baseball team
Deviation scores
Diallo is 0”
Let’s build it up again… U of A Baseball team
Preston is 2”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
Diallo’s deviation score is 0
David
Preston’s deviation score is 2”
Mike’s deviation score is -4”
Shea
Hunter’s deviation score is -2”
Shea’s deviation score is 4”
David’s deviation score is 0”
5’8” 5’10” 6’0” 6’2” 6’4”

22. Let’s build it up again… U of A Baseball team
Deviation scores
Diallo is 0”
Let’s build it up again… U of A Baseball team
Preston is 2”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
5’8” 5’10” 6’0” 6’2” 6’4”

23. Standard deviation: The average amount
Deviation scores
Standard deviation: The average amount
by which observations deviate on either side
of their mean
Diallo is 0”
Preston is 2”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
5’8” 5’10” 6’0” 6’2” 6’4”

24. Standard deviation: The average amount
Deviation scores
Standard deviation: The average amount
by which observations deviate on either side
of their mean
Diallo is 0”
Preston is 2”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
5’8” 5’10” 6’0” 6’2” 6’4”

25. How far away is each score from the mean?
Diallo is 0”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
Preston is 2”
Deviation scores
(x - µ)
Deviation scores: The amount by which observations
deviate on either side of their mean
(x - µ)
How far away is each score from the mean?
Mean
Diallo
Deviation
score
Mike
Preston
Shea
(x - µ) = ?
Hunter
Mike
5’8” ’0” = - 4”
5’9” ’0” = - 3”
5’10’ - 6’0” = - 2”
5’11” - 6’0” = - 1”
6’0” ’0 = 0
6’1” ’0” = + 1”
6’2” ’0” = + 2”
6’3” ’0” = + 3”
6’4” ’0” = + 4”
Diallo
How do we find each deviation score?
(x - µ)
Preston
Hunter
Diallo
Mike
Preston
Find distance of each person from the mean (subtract their score from mean)

26. How far away is each score from the mean?
Diallo is 0”
Mike is -4”
Hunter is -2
Shea is 4
David is 0”
Preston is 2”
Deviation scores
(x - µ)
Deviation scores: The amount by which observations
deviate on either side of their mean
(x - µ)
How far away is each score from the mean?
Mean
Diallo
Deviation
score
Preston
Shea
(x - µ) = ?
Mike
5’8” ’0” = - 4”
5’9” ’0” = - 3”
5’10’ - 6’0” = - 2”
5’11” - 6’0” = - 1”
6’0” ’0 = 0
6’1” ’0” = + 1”
6’2” ’0” = + 2”
6’3” ’0” = + 3”
6’4” ’0” = + 4”
Remember
It’s relative
to the mean
Based on difference from the mean

27. How far away is each score from the mean?
Standard deviation: The average amount by which
observations deviate on either side of their mean
Deviation scores
(x - µ)
Diallo is 0”
Preston is 2”
How far away is each score from the mean?
Mike is -4”
Hunter is -2
Shea is 4
Mean
David is 0”
Add up
Deviation scores
Diallo
Preston
Σ (x - µ) = ?
Shea
Mike
5’8” ’0” = - 4”
5’9” ’0” = - 3”
5’10’ - 6’0” = - 2”
5’11” - 6’0” = - 1”
6’0” ’0 = 0
6’1” ’0” = + 1”
6’2” ’0” = + 2”
6’3” ’0” = + 3”
6’4” ’0” = + 4”
How do we find the average height? N Σx
= average height
How do we find the average spread?
Σ(x - x) = 0
Σ(x - µ) N
= average deviation
Σ(x - µ) = 0

28. How far away is each score from the mean?
Standard deviation: The average amount by which
observations deviate on either side of their mean
Deviation scores
(x - µ)
Diallo is 0”
Preston is 2”
How far away is each score from the mean?
Mike is -4”
Hunter is -2
Shea is 4
Mean
David is 0”
Diallo
Preston
Σ (x - µ) = ?
Shea
Mike
5’8” ’0” = - 4”
5’9” ’0” = - 3”
5’10’ - 6’0” = - 2”
5’11” - 6’0” = - 1”
6’0” ’0 = 0
6’1” ’0” = + 1”
6’2” ’0” = + 2”
6’3” ’0” = + 3”
6’4” ’0” = + 4”
Square the deviations
Big problem
Σ(x - x) 2 2
Σ(x - x) = 0
Σ(x - µ) N
Σ(x - µ) 2
Σ(x - µ) = 0

29. Writing Assignment: Let’s try two problems

30. Standard deviation (definitional formula) - Let’s do one
This numerator is called “sum of squares”
Each of these are deviation scores
_ X - µ _
1 - 5 = - 4
(X - µ)2 16
Step 1: Find the mean
_ X_ 1 2 3 4 5 6 7 8 9 45
Step 2: Subtract the mean from
each score
Step 3: Square the deviations
Step 4: Find standard deviation

31. Standard deviation (definitional formula) - Let’s do one
This numerator is called “sum of squares”
Each of these are deviation scores
_ X - µ _
1 - 5 = - 4
2 - 5 = - 3
3 - 5 = - 2
4 - 5 = - 1
5 - 5 = 0
6 - 5 = 1
7 - 5 = 2
8 - 5 = 3
9 - 5 = 4
(X - µ)2 16 9 4 1 60
Step 1: Find the mean
_ X_ 1 2 3 4 5 6 7 8 9 45
ΣX = 45
ΣX / N = 45/9 = 5
Step 2: Subtract the mean from
each score
Step 3: Square the deviations
Step 4: Find standard deviation
This is the Variance!
a) 60 / 9 =
b) square root of =
Σ(x - µ) = 0
This is the standard deviation!

32. Standard deviation - Let’s do one
Definitional formula
How many kids?
Step 1: Find the mean
X - µ_
3 - 3 = 0
(X - µ)2
_ X_ 3 2 1 4 8
Step 2: Subtract the mean from
each score (deviations)
Step 3: Square the deviations
Step 4: Add up the squared deviations
Step 5: Find standard deviation
Σ(x - µ) = 0
Σx = 30
Σ(x - µ)2 = 38

33. Standard deviation - Let’s do one
Definitional formula
How many kids?
Step 1: Find the mean
X - µ_
3 - 3 = 0
2 - 3 = -1
1 - 3 = -2
4 - 3 = 1
8 - 3 = 5
(X - µ)2 1 4 25
_ X_ 3 2 1 4 8
= 30
= 30/10 = 3
Step 2: Subtract the mean from
each score (deviations)
Step 3: Square the deviations
Step 4: Add up the squared deviations
Step 5: Find standard deviation
Σ(x - µ) = 0
Σx = 30
Σ(x - µ)2 = 38
This is the Variance!
a) 38 / 10 = 3.8
b) square root of 3.8 = 1.95
This is the standard deviation!

34. Thank you!
See you next time!!