1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Fall 2016 Room 150 Harvill Building 10: :50 Mondays, Wednesdays & Fridays.
Welcome

2. By the end of lecture today 9/14/16
Use this as your
study guide
By the end of lecture today 9/14/16
Characteristics of a distribution
Central Tendency
Dispersion
Measures of variability
Range
Standard deviation
Variance
Memorizing the four definitional formulae

3. Homework Assignments 7 & 8 Please complete the homework worksheets
Calculating Descriptive Statistics
And Presenting Findings in a Memorandum
Due: Friday, September 16th

4. Schedule of readings Before next exam (September 23rd)
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

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

6. Overview Frequency distributions
The normal curve
Challenge yourself as we work through characteristics of distributions to try to categorize each concept as a measure of
1) central tendency
2) dispersion or 3) shape
Mean, Median,
Mode, Trimmed Mean
Skewed right, skewed left
unimodal, bimodal, symmetric

7. A little more about frequency distributions
An example of a normal distribution

8. A little more about frequency distributions
An example of a normal distribution

9. A little more about frequency distributions
An example of a normal distribution

10. A little more about frequency distributions
An example of a normal distribution

11. A little more about frequency distributions
An example of a normal distribution

12. Measure of central tendency: describes how scores tend to
Measure of central tendency: describes how scores tend to cluster toward the center of the distribution
Normal distribution
In all distributions:
mode = tallest point
median = middle score
mean = balance point
In a normal distribution:
mode = mean = median

13. Measure of central tendency: describes how scores tend to
Measure of central tendency: describes how scores tend to cluster toward the center of the distribution
Positively skewed distribution
In all distributions:
mode = tallest point
median = middle score
mean = balance point
In a positively skewed distribution:
mode < median < mean
Note: mean is most affected by outliers or skewed distributions

14. Measure of central tendency: describes how scores tend to
Measure of central tendency: describes how scores tend to cluster toward the center of the distribution
Negatively skewed distribution
In all distributions:
mode = tallest point
median = middle score
mean = balance point
In a negatively skewed distribution:
mean < median < mode
Note: mean is most affected by outliers or skewed distributions

15. Mode: The value of the most frequent observation
Bimodal distribution: Distribution with two most
frequent observations (2 peaks)
Example: Ian coaches two boys baseball teams. One team is made up of 10-year-olds and the other is made up of 16-year-olds. When he measured the height of all of his players he found a bimodal distribution

16. 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

17. Frequency distributions
The normal curve

18. 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’

19. 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?

20. 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”

21. 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

22. 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”

23. 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”

24. 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

25. 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

26. 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”

27. 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”

28. 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”

29. 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”

30. 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”

31. 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)

32. 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

33. 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

34. These would be helpful to know by heart – please memorize
Standard deviation: The average amount by which
observations deviate on either side of their mean
These would be helpful to know by heart – please memorize
these formula

35. What do these two formula have in common?
Standard deviation: The average amount by which observations
deviate on either side of their mean
What do these two formula have in common?

36. What do these two formula have in common?
Standard deviation: The average amount by which observations
deviate on either side of their mean
What do these two formula have in common?

37. How do these formula differ?
Standard deviation: The average amount by which observations
deviate on either side of their mean
“n-1” is
Degrees of Freedom”
How do these formula differ?

38. “Sum of Squares” “Sum of Squares” “Sum of Squares” “Sum of Squares”
Standard deviation: The average amount by
which observations deviate on either side of their mean
“Sum of Squares”
“Sum of Squares”
“Sum of Squares”
“Sum of Squares”
Diallo is 0”
Mike is -4”
Hunter is -2
Shea is 4
David 0”
Preston is 2”
Deviation scores
Remember, it’s relative to the mean
“n-1” is
“Degrees of Freedom”
“n-1” is
“Degrees of Freedom”
Generally, (on average) how far away is each score from the mean?
Based on difference from the mean
Mean
Remember, We are thinking in terms of “deviations”
Diallo
Please memorize these
Preston
Shea
Mike

39. 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!

40. Thank you!
See you next time!!