2. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall, 2014 Room 120 Integrated Learning Center (ILC) 10:00 - 10:50 Mondays, Wednesdays & Fridays. http://www.youtube.com/watch?v=oSQJP40PcGI

3. Labs continue next week

4. Schedule of readings Before next exam (September 26 th ) Please read chapters 1 - 4 in Ha & Ha 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. Reminder A note on doodling

6. By the end of lecture today 9/19/14 Use this as your study guide Characteristics of a distribution Central Tendency Dispersion Primary types of “measures of central tendency”? Mean Median Mode Measures of variability Range Standard deviation Variance Memorizing the four definitional formulae

7. Homework due – Monday (September 22 nd ) Assignment 6 & 7: Calculating Descriptive Statistics and Presenting Findings in a Memorandum Due: Monday, Sept 22nd Assignment 8 Please read Chapter 4 in our regular Ha & Ha textbook (Renee Ha & James Ha are the authors). Please answer the questions 1 - 18 (page 66-68) Due: Wednesday, September 24th

8. Exam 1 – Week from today – September 26 th Study Guide is online Bring 2 calculators (remember only simple calculators, we can’t use calculators with programming functions) Bring 2 pencils (with good erasers) Bring ID

9. 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

10. 6’ 7’ 5’ 5’6” 6’6” 6’ 7’ 5’ 5’6” 6’6” 6’ 7’ 5’ 5’6” 6’6” The larger the variability the wider the curve the larger the deviations scores tend to be The smaller the variability the narrower the curve the smaller the deviations scores tend to be Variability Review

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

12. 5’8” - 6’0” = - 4” 5’9” - 6’0” = - 3” 5’10’ - 6’0” = - 2” 5’11” - 6’0” = - 1” 6’0” - 6’0 = 0 6’1” - 6’0” = + 1” 6’2” - 6’0” = + 2” 6’3” - 6’0” = + 3” 6’4” - 6’0” = + 4” Deviation scores: The amount by which observations deviate on either side of their mean (x - µ ) = ? Review Mean Mike Shea Preston Diallo 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 ) Based on difference from the mean Remember It’s relative to the mean ( x - µ ) Deviation score

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

14. 5’8” - 6’0” = - 4” 5’9” - 6’0” = - 3” 5’10’ - 6’0” = - 2” 5’11” - 6’0” = - 1” 6’0” - 6’0 = 0 6’1” - 6’0” = + 1” 6’2” - 6’0” = + 2” 6’3” - 6’0” = + 3” 6’4” - 6’0” = + 4” Standard deviation: The average amount by which observations deviate on either side of their mean Σ(x - x) = 0 Σ (x - µ ) = ? Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores Σ(x - µ ) = 0 Review Mean Mike Shea Preston Diallo How far away is each score from the mean? ( x - µ ) Big problem Σ(x - x) 2 Square the deviations Σ(x - µ ) 2 N 2

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

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

18. Standard deviation Standard deviation: The average amount by which observations deviate on either side of their mean Fun Fact: Standard deviation squared = variance Note this is for population

19. Standard deviation Standard deviation: The average amount by which observations deviate on either side of their mean Note this is for sample Fun Fact: Standard deviation squared = variance

20. Standard deviation (definitional formula) - Let’s do one _ X_ 1 2 3 4 5 6 7 8 9 45 Step 1: Find the mean ΣX = 45 ΣX / N = 45/9 = 5 Step 2: Subtract the mean from each score _ 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 0 Step 3: Square the deviations (X - µ ) 2 16 9 4 1 0 1 4 9 16 60 Step 4: Find standard deviation a) 60 / 9 = 6.6667 Σ(x - µ ) = 0 This is the Variance! This is the standard deviation! Each of these are deviation scores b) square root of 6.6667 = 2.5820 This numerator is called “sum of squares”

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

22. Another example: How many kids in your family? 3 4 8 2 2 1 4 2 1 3

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

24. Writing Assignment – Pop Quiz 1. What does this symbol refer to? 2. What does this symbol refer to? 5. What does this symbol refer to? 3. What does this symbol refer to? 4. What does this symbol refer to? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population?

25. Writing Assignment – Pop Quiz 6. What does this refer to? 7. What does this refer to? 8. What do these two refer to? 9. What does this refer to? What are they called? How are they different What is it called? Use it for sample data or population? What are they called? What do they refer to? How are they different What are they called? How are they different

26. Writing Assignment – Pop Quiz 9. What does this refer to? What are they called? What do they refer to? How are they different 10. What does this refer to? What are they called? What do they refer to? How are they different

27. Writing Assignment – Pop Quiz 1. What does this symbol refer to? 2. What does this symbol refer to? 5. What does this symbol refer to? 3. What does this symbol refer to? 4. What does this symbol refer to? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population? What is it called? What does it mean? Is it referring to a sample or population? The standard deviation (population) The mean (population) The mean (sample) The standard deviation (sample) Each individual score sigma population mu x-bar population sample s

28. 6. What does this refer to? 7. What does this refer to? 8. What do these two refer to? 9a. What does this refer to? What are they called? How are they different What is it called? Use it for sample data or population? What are they called? What do they refer to? How are they different What are they called? How are they different Variance population sample Sigma squared S squared Deviation scores population sample Sum of squares population sample Degrees of freedom sample Writing Assignment – Pop Quiz

29. 9b. What does this refer to? What are they called? What do they refer to? How are they different 10. What does this refer to? What are they called? What do they refer to? How are they different Variance population sample Standard Deviation population sample

30. Preview of Homework Worksheet

31. -2 1 3 0 3 – 5 = -2 3 -3 1 6 – 5 = +1 50 -2 2 = 4 1 2 = 1 4191041910 9911199111 36 10 - 1 = 2 2 5 4.5 28 6 4.625 How many errors per hour? 0 Preview of Homework Worksheet

32. 2 3 0 5 – 6 = -1 0 3 1 -5 8 – 6 = +2 60 -1 2 = 1 2 2 = 4 1411914119 0 1 9 1 25 52 10 - 1 = 2.4 2.4 65.5 1 9 8 5.50 How many errors per hour? 6 errors 12 hours Preview of Homework Worksheet

33. Review of Homework Worksheet Must be complete and must be stapled