1. Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2019 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays.
February 4

2. Even if you have not yet registered your clicker you can still participate
The
Green
Sheets

3. Schedule of readings Before next exam (February 8)
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

7. 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
Review

8. 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)
Review

9. 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
Won’t Work
= average deviation
Σ(x - µ) = 0
Review

10. 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
Review

11. 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
Step 1
Find the mean
David is 0”
Diallo
Step 2
Find each deviation score
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”
Step 3
Square each deviation score
And add them up
Step 4
Divide by n and take square root
Σ(x - x) 2 2
Σ(x - x) = 0
Σ(x - µ) N
Σ(x - µ) 2
Σ(x - µ) = 0
Review

12. You know by heart – you’ve memorized
Standard deviation: The average amount by which
observations deviate on either side of their mean
“Sum of Squares”
You know by heart – you’ve memorized
these formula
Review

13. You know by heart – you’ve memorized
Standard deviation: The average amount by which
observations deviate on either side of their mean
“degrees of freedom”
You know by heart – you’ve memorized
these formula
Review

14. Standard deviation squared = variance
Standard deviation: The average amount by which
observations deviate on either side of their mean
Both are called “standard deviation”
Both are called “variance”
What do these two formula have in common?
Standard deviation squared = variance
Fun Fact:

15. Standard deviation: The average amount by which
observations deviate on either side of their mean
Both are for sample
Both are for population
What do these two formula have in common?

16. 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?
Review

17. Raw scores, z scores & probabilities
Please note spatially where 1 standard deviation falls on the curve
Review

18. Raw scores, z scores & probabilities
Please note spatially where 1 standard deviation falls on the curve
68%
95%
99.7%
Review

19. Raw scores, z scores & probabilities
1 sd above and below mean
68%
z = +1
z = -1
Mean = 50
σ = 10
If we go up one standard deviation
z score = +1.0 and raw score = 60
If we go down one standard deviation
z score = -1.0 and raw score = 40

20. Raw scores, z scores & probabilities
2 sd above and below mean
95%
z = -2
z = +2
Mean = 50
σ = 10
If we go up two standard deviations
z score = +2.0 and raw score = 70
If we go down two standard deviations
z score = -2.0 and raw score = 30

21. Raw scores, z scores & probabilities
3 sd above and below mean
99.7%
z = +3
z = -3
Mean = 50
σ = 10
If we go up three standard deviations
z score = +3.0 and raw score = 80
If we go down three standard deviations
z score = -3.0 and raw score = 20

22. z score = raw score - mean standard deviation
If we go up one standard deviation
z score = +1.0 and raw score = 105
z = -1
z = +1
68%
If we go down one standard deviation
z score = -1.0 and raw score = 95
If we go up two standard deviations
z score = +2.0 and raw score = 110
z = -2
95%
z = +2
If we go down two standard deviations
z score = -2.0 and raw score = 90
If we go up three standard deviations
z score = +3.0 and raw score = 115
99.7%
z = -3
z = +3
If we go down three standard deviations
z score = -3.0 and raw score = 85
z score: A score that indicates how many standard deviations
an observation is above or below the mean of the distribution
z score = raw score - mean
standard deviation

23. Summary of 7 facts to memorize

25. Writing Assignment – Pop Quiz Distance from the mean X Taller 2 inches
Preston is 2” taller than the mean (taller than most)
Taller
2 inches
Shorter X
Mike is 4” shorter than the mean (shorter than most)
Shorter
4 inches
Taller X
Equal to mean
Diallo is exactly same height as mean (half taller half shorter)
0 inches
Half are Shorter

26. Writing Assignment – Pop Quiz Sigma – standard deviation - population
Parameter
mu – a mean – an average - population
Parameter
x-bar – a mean – an average - sample
statistic
s – standard deviation - sample
statistic
The number of “standard deviations” the score is from the mean
population
Sigma squared and s squared - variance
Sigma is parameter (population) s is statistic (sample)
Deviation scores
(x-µ) for population (parameter) (x-x) is statistic (sample)
Sum of squares
On left is statistic on right is parameter
Standard deviation
s is statistic sigma is parameter
Degrees of freedom
sample

27. Homework Assignment # 7 Due: Wednesday, February 6
Worksheet with Memorandum
Due: Wednesday, February 6

28. Step 2 Find each deviation score
Step 1 Find the mean
Step 2 Find each deviation score
Step 3 Square each deviation score
and add them up
Step 4 Divide by n
and take square root

29. Preview of Homework Worksheet
Each of these are deviation scores
3 – 5 = -2
-22= 4
6 – 5 = +1 -2 1 3 -1 4 1 9
12= 1 3 -3 -1 1 9 1
Σ(x - µ) = 0 50 36 36
= 2 2
10 - 1
This is the standard deviation! 5 4
4.5 2 8 6

30. Preview of Homework Worksheet
-12= 1
5 – 6 = -1 -1 2 3 1 4 9
22= 4
8 – 6 = +2 -1 3 1 -5 1 9 25 60 52 52
2.4
= 2.4
10 - 1 6
5.5 5 1 9 8

31. Homework Assignment # 7 Due: Wednesday, February 6
Worksheet with Memorandum
Due: Wednesday, February 6

32. Thank you!
See you next time!!