2. Stage Screen Row B 13 121110 20191817 14 13 121110 19181716 1514 Gallagher Theater 16 65879 Row R 6 58 7 9 Lecturer’s desk Row A Row B Row C 4 3 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 3 21 3 2 43 21 Row A 17 16 15 Row A Row C 131211 10 1514 6 58 7 9 Row D 13121110 1514 16 6 58 7 9 20191817 Row D Row E 131211 10 1514 6 58 7 9 19181716 Row E Row F 13121110 1514 16 6 58 7 9 20191817 Row F Row G 13121110 1514 6 58 7 9 19181716 Row G Row H 13121110 1514 16 6 58 7 9 20191817 Row H Row I 13121110 1514 6 58 7 9 19181716 Row I Row J 13121110 1514 16 6 58 7 9 20191817 Row J Row K 13121110 1514 6 58 7 9 19181716 Row K Row L 13121110 1514 16 6 58 7 9 20 191817 Row L Row M 13121110 1514 6 58 7 9 19181716 Row M Row N 13121110 1514 16 6 5879 20191817 Row N Row O 13121110 1514 6 58 7 9 19181716 Row O Row P 13121110 1514 16 6 5879 20191817 Row P Row Q 13121110 6 5879 161514 Row Q 4 4 Row R 10 879 Row S Row B Row C Row D Row E Row F Row G Row H Row I Row J Row K Row L Row M Row N Row O Row P Row Q 26Left-Handed Desks A14, B16, B20, C19, D16, D20, E15, E19, F16, F20, G19, H16, H20, I15, J16, J20, K19, L16, L20, M15, M19, N16, P20, Q13, Q16, S4 5 Broken Desks B9, E12, G9, H3, M17 Need Labels B5, E1, I16, J17, K8, M4, O1, P16 Left handed

3. Stage Screen 2213 121110 Row A Row B Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 17 Row C Row D Row E Projection Booth 65 4 table Row C Row D Row E 30 27 26252423 282726 2524 23 3127262524 23 R/L handed broken desk 16 1514 13 12 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 Social Sciences 100 Row N Row O Row P Row Q Row R 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 8 7 9 65 4 8 7 9 3 2 6 5 48793 2 1 6 5 48793 2 1 Row F Row G Row H Row J Row K Row L Row M Row N Row O Row P Row Q Row R 6 5 48793 2 1 6 5 48793 2 1 Row I 2213 121110 2019181716151421 Row I 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 Lecturer’s desk 6 5 48793 2 1 262524 23 302928 Row F Row G Row H Row J Row K Row L Row M Row N Row O Row P Row Q Row R Row I 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 Row B 2928 27

4. MGMT 276: Statistical Inference in Management Fall, 2014 Green sheets

6. Just a reminder Talking or whispering to your neighbor can be a problem for us – please consider writing short notes. A note on doodling

7. Homework due - (September 23 rd ) Assignment 5 & 6 Calculating Descriptive Statistics And Presenting Findings in a Memorandum Due: Tuesday, September 23 rd

8. Schedule of readings Before next exam: September 25 th Please read chapters 1 - 4 & Appendix D & E in Lind 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

9. By the end of lecture today 9/18/14 Use this as your study guide Characteristics of a distribution Standard Deviation Variance Empirical Rule (areas under the curve) Measures of variability Understanding and memorization of the following four definitional formulae Standard Deviation for sample Standard Deviation for population Variance for sample Variance for population

10. Review of Homework Worksheet.10.08 22 35 25 8 100,000 10.22.35.25 80,000 250,000 350,000 220,000 Notice Gillian asked 1300 people 130+104+325+455+286=1300 130/1300 =.10.10x100=10.10 x 1,000,000 = 100,000

11. Review of Homework Worksheet.10.08 22 35 25 8 100,000 10.22.35.25 80,000 250,000 350,000 220,000

12. Review of Homework Worksheet

13. 10 2030 40 50 Age 1 2 3 4 5 6 7 8 9 Dollars Spent Strong Negative Down -.9

14. Review of Homework Worksheet =correl(A2:A11,B2:B11) =-0.9226648007 Strong Negative Down -0.9227

15. Review of Homework Worksheet =correl(A2:A11,B2:B11) =-0.9226648007 Strong Negative Down -0.9227 This shows a strong negative relationship (r = - 0.92) between the amount spent on snacks and the age of the moviegoer Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Correlation r (actual number)

16. Height of Daughters (inches) Height of Mothers (in) 48 52 56 60 64 68 72 76 48 52 5660 64 68 72 This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Both axes and values are labeled Both axes have real numbers listed 1. Describe one positive correlation Draw a scatterplot (label axes) 2. Describe one negative correlation Draw a scatterplot (label axes) 3. Describe one zero correlation Draw a scatterplot (label axes) 4. Describe one perfect correlation (positive or negative) Draw a scatterplot (label axes) 5. Describe curvilinear relationship Draw a scatterplot (label axes) Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) Hand in Homework and Correlation worksheet

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 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

18. Another example: How many kids in your family? 3 4 8 2 2 1 4 1 14 2 Number of kids in family 1414 3232 1818 4242 214

19. Measures of Central Tendency (Measures of location) The mean, median and mode Mean: The balance point of a distribution. Found by adding up all observations and then dividing by the number of observations Mean for a sample: Mean for a population: ΣX / N = mean = µ (mu) Note: Σ = add up x or X = scores n or N = number of scores Σx / n = mean = x Measures of “location” Where on the number line the scores tend to cluster

20. Measures of Central Tendency (Measures of location) The mean, median and mode Mean: The balance point of a distribution. Found by adding up all observations and then dividing by the number of observations Mean for a sample: Note: Σ = add up x or X = scores n or N = number of scores Σx / n = mean = x Number of kids in family 14 32 18 42 214 41/ 10 = mean = 4.1

21. How many kids are in your family? What is the most common family size? Number of kids in family 13 14 24 28 214 Median: The middle value when observations are ordered from least to most (or most to least)

22. How many kids are in your family? What is the most common family size? Median: The middle value when observations are ordered from least to most (or most to least) 1, 3, 1, 4, 2, 4, 2, 8, 2, 14 1, 2, 3, 4, 8, 14 Number of kids in family 14 32 18 42 214

23. Number of kids in family 14 32 18 42 214 14 8, 4, 2, 1, How many kids are in your family? What is the most common family size? Number of kids in family 13 14 24 28 214 Median: The middle value when observations are ordered from least to most (or most to least) 1, 3, 1, 4, 2, 4, 2, 8, 2, 14 2.5 2, 3, 1, 2, 4, 2, 4,8, 1, 14 2, 3, 1, Median always has a percentile rank of 50% regardless of shape of distribution 2 + 3 µ = 2.5 If there appears to be two medians, take the mean of the two

24. Mode: The value of the most frequent observation Number of kids in family 13 14 24 28 214 Score f. 12 23 31 42 50 60 70 81 90 100 110 120 130 141 Please note: The mode is “2” because it is the most frequently occurring score. It occurs “3” times. “3” is not the mode, it is just the frequency for the value that is the mode Bimodal distribution: If there are two most frequent observations

25. What about central tendency for qualitative data? Mode is good for nominal or ordinal data Median can be used with ordinal data Mean can be used with interval or ratio data

26. 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

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

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

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

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

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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

39. Range: The difference between the largest and smallest scores 84” – 71” = 13” Tallest player = 84” (same as 7’0”) (Kaleb Tarczewski and Dusan Ristic) Shortest player = 71” (same as 5’11”) (Parker Jackson-Cartwritght) Wildcats Basketball team: Range is 13” Fun fact: Mean is 78 x max - x min = Range

40. Range: The difference between the largest and smallest score 77” – 70” = 7” Tallest player = 77” (same as 6’5”) (Austin Schnabel) Shortest player = 70” (same as 5’10”) (Five players are 5’10”) Wildcats Baseball team: Range is 7” (77” – 70” ) Fun fact: Mean is 72 x max - x min = Range Please note: No reference is made to numbers between the min and max Baseball

41. Frequency distributions The normal curve

42. 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?

43. 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

44. 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?

45. 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

46. 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

47. 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

48. 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

49. 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

50. 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

51. 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

52. 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

53. 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

54. 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 Mike Hunter Preston 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 Σ(x - µ ) = 0 = average height N ΣxΣx = average deviation Σ(x - µ ) N How do we find the average spread?

55. 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 - x = ? 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 Σ(x - µ ) = 0 Big problem Σ(x - x) 2 Square the deviations Σ(x - µ ) 2 N ΣxΣx N Big problem 2

56. Mean: The average value in the data Standard deviation: The average amount scores deviate on either side of their mean Standard deviation is typical “spread” (typical size of deviations or distance from mean) – can never be negative Mean is a measure of typical “value” (where the typical scores are positioned on the number line)

57. 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

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

59. Standard deviation: The average amount by which observations deviate on either side of their mean What do these two formula have in common? n-1 is “Degrees of Freedom” More, next lecture

60. 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

61. 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

62. 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”

63. 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”

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

65. 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?

66. Review notation 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?

67. Review notations 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

68. Review notations 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

69. Review Notations 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

70. 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 Variance population sample Sigma squared S squared Deviation scores population sample Sum of squares population sample Degrees of freedom sample Review Notations

71. Review notations 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 Variance population sample Standard Deviation population sample

72. 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” Review Remember, We are thinking in terms of “deviations”