1. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Spring 2016 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays
Welcome

2. By the end of lecture today 2/5/16
Use this as your
study guide
By the end of lecture today 2/5/16
Characteristics of a distribution
Central Tendency
Dispersion
Measures of variability
Range
Standard deviation
Variance
Memorizing the four definitional formulae
Empirical Rule for Normal Curve
(68% vs 95% vs 99.7%)

4. Schedule of readings Before next exam (February 12th)
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. Lab sessions Everyone will want to be enrolled
in one of the lab sessions
Labs continue
next week

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

7. Homework due Monday, Feb 8th
On class website: please print and complete homework worksheet # 7 & 8
Calculating Descriptive Statistics
And Presenting Findings in a Memorandum

8. Review From the lab review
IV:
Nominal
IV: Nominal Ordinal Interval or Ratio?
Independent
Variable?
Type of
Cow Chow
Mariska works at a cattle ranch, and wants cattle to gain as much weight as possible. Mariska wants to know if the new feed makes a difference in how much weight the cattle gain.
She gathers the first 100 cows that she finds in the meadow, and then randomly assigns those 100 cows into two groups (50 each group)
One group gets the new feed for 6 months, while the other group of cattle gets the old feed. She is not looking for any trends over time, but is just looking for a difference between the two types of cow chow (feed).
IV: Continuous or discrete?
IV:
Discrete
Random
Sampling?
No, only convenience sampling
Random Assignment
(True Expt)
Random
Assignment?
DV:
Ratio
DV: Nominal Ordinal Interval or Ratio?
Dependent Variable?
Weight
DV: Continuous or discrete?
DV: Continuous
Between or within?
Between Participant Design
Cross
Sectional
Cross Sectional or Time Series
Review

10. 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

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
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
Review

12. 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

13. 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
Review

14. 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?
Review

15. 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?
Review

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. 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!

18. “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
“n-1” is
“Degrees of Freedom”
“n-1” is
“Degrees of Freedom”
Remember, it’s relative to the mean
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

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

20. These would be helpful to know by heart – please memorize areas
1 sd above and below mean
68%
2 sd above and below mean
95%
3 sd above and below mean
99.7%
These would be helpful to know by heart – please memorize areas

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

22. Summary of 7 facts to memorize

23. Writing Assignment – Pop Quiz
1. What is a “deviation score”
2. Preston has a deviation score of 2: What does that tell us about Preston?
Is he taller or shorter than the mean? And by how much?
Are most people in the group taller or shorter than Preston
Mike has a deviation score of -4: What does that tell us about Mike?
Are most people in the group taller or shorter than Mike
Diallo has a deviation score of 0: What does that tell us about Diallo?
Are most people in the group taller or shorter than Diallo?
Please write the formula for the standard deviation of a population
Please draw 3 curves showing 1, 2 & 3 standard deviations from mean

24. Writing Assignment – Pop Quiz 1. What is a “deviation score”
2. Preston has a deviation score of 2: What does that tell us about Preston?
Is he taller or shorter than the mean? And by how much?
Are most people in the group taller or shorter than Preston
Mike has a deviation score of -4: What does that tell us about Mike?
Are most people in the group taller or shorter than Mike
Diallo has a deviation score of 0: What does that tell us about Diallo?
Are most people in the group taller or shorter than Diallo?
Please write the formula for the standard deviation of a population
Please draw 3 curves showing 1, 2 & 3 standard deviations from mean
How far away is each score from the mean?
Preston is 2” taller than the mean (taller than most)
Mike is 4” shorter than the mean (shorter than most)
Diallo is exactly same height as mean (half taller half shorter)

25. Thank you!
See you next time!!