2. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Fall 2015 Room 150 Harvill Building 10:00 - 10:50 Mondays, Wednesdays & Fridays. 9/11/15

3. Everyone will want to be enrolled in one of the lab sessions Lab continue next week, Project 1 should be collected

4. Homework Assignment No new homework assignments (Time to get caught up if you’ve fallen behind )

5. More information on registering clickers coming soon

6. Schedule of readings Before next exam (September 25 th ) Please read chapters 1 - 5 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

7. Overview Frequency distributions The normal curve Mean, Median, Mode, Trimmed Mean 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 Skewed right, skewed left unimodal, bimodal, symmetric

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

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

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

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

16. 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

17. 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

18. Frequency distributions The normal curve

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

20. 6’ 7’ 5’ 5’6” 6’6” 6’ 7’ 5’ 5’6” 6’6” 6’ 7’ 5’ 5’6” 6’6” Dispersion: Variability Some distributions are more variable than others Range: The difference between the largest and smallest observations Range for distribution A? Range for distribution B? Range for distribution C? A B C The larger the variability the wider the curve tends to be The smaller the variability the narrower the curve tends to be

21. Range: The difference between the largest and smallest scores 84” – 70” = 14” Tallest player = 84” (same as 7’0”) (Kaleb Tarczewski and Dusan Ristic) Shortest player = 70” (same as 5’10”) (Parker Jackson-Cartwritght) Wildcats Basketball team: Range is 14” Fun fact: Mean is 78 x max - x min = Range

22. Range: The difference between the largest and smallest score 77” – 69” = 8” Tallest player = 77” (same as 6’5”) (Austin Schnabel) Shortest player = 69” (same as 5’9”) (Justin Behnke and Ernie DeLaTrinidad ) Wildcats Baseball team: Range is 8” (77” – 69” ) Fun fact: Mean is 72 x max - x min = Range Please note: No reference is made to numbers between the min and max Baseball

23. Variability Standard deviation: The average amount by which observations deviate on either side of their mean Mean is 6’ Generally, (on average) how far away is each score from the mean?

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

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

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

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

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

29. 5’8” 5’10” 6’0” 6’2” 6’4” Diallo is 0” Mike is -4” Hunter is -2 Shea is 4 David is 0” Preston is 2” Deviation scores Let’s build it up again… U of A Baseball team

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

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

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

33. 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 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

34. 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 ) = ? 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

35. 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? Mean Mike Shea Preston Diallo How far away is each score from the mean? ( x - µ ) Add up Deviation scores

36. 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 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

37. 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

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

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

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