Please start portfolios

1. Please start portfolios

2. MGMT 276: Statistical Inference in ManagementRoom McClelland Hall, Room 129Summer II, 2011 Welcome

3. 4 1 0 1 0 9 9 1 1 1 3 – 5 = -2 6 – 5 = 1 8 – 5 = 3 4 – 5 = -1 5 – 5 = 0 8 – 5 = 3 2 – 5 = -3 4 – 5 = -1 6 – 5 = 1 4 – 5 = -1 Homework Worksheet 50 0 36 36 2 = 2 9 4 5 4.5 2 6 8 1 4 1 1 9 0 1 9 1 25 5 – 6 = -1 8 – 6 = 2 5 – 6 = -1 5 – 6 = -1 9 – 6 = 3 6 – 6 = 0 5 – 6 = -1 9 – 6 = 3 7 – 6 = 1 1 – 6 = -5 60 0 52 52 2.4037 = 2.4 9 5.5 5 6 1 9 8

5. Use this as your study guide By the end of lecture today7/18/11 Measures of variability Standard deviation and Variance Counting ‘standard deviationses’ – z scores Connecting raw scores, z scores and probabilityConnecting probability, proportion and area of curve Percentiles Central Limit Theorem

6. Schedule of readings • Before next exam (Wednesday): • Please read chapters 1 - 4 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

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

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

9. Variability Standard deviation: The average amount by which observations deviate on either side of their mean Based on difference from the mean Generally, (on average) how far away is each score from the mean? Remember, it’s relative to the mean Mean is 6’

10. Variability Standard deviation: The average amount by which observations deviate on either side of their mean Based on difference from the mean Generally, (on average) how far away is each score from the mean? Remember, it’s relative to the mean Mean is 6’ Doug Chuck Irwin Raoul

11. Deviation scores Standard deviation: The average amount by which observations deviate on either side of their mean Diallo is 0” Preston is 2” Mike is -4” Hunter is -2 Shea is 4 David is 0” Remember, We are thinking in terms of “deviations” 5’8” 5’10” 6’0” 6’2” 6’4”

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

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

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

15. Standard deviation: The average amount by which observations deviate on either side of their mean Would you be ready today to show you know these formula?

16. Standard deviation: The average amount scores deviate on either side of their mean Standard deviation = Mean is a measure of “position” (it lives on one location of the curve) Standard deviation is a ‘spread’ score a ‘typical distance’ score – can never be negative

17. Let’s estimate some standard deviation values Standard deviation is a ‘spread’ score We’re estimating the typical distance score (distance of each score from the mean)

18. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) $47 – $37 = $10 What’s the largest possible deviation? $27 – $37 = -$10 Mean = $37 Range = $27 - $47 What’s the ‘typical’ or standard deviation? Standard Deviation = 4.3

19. Waiting time for service at bankWe sampled 100 banks(From time entering line to time reaching teller) 3.6 – 3.0= .6 What’s the largest possible deviation? 2.2 – 3.0= -.8 Mean = 3 minutes Range = 2.2- 3.6 What’s the ‘typical’ or standard deviation? Standard Deviation = 0.31

20. Pounds of pressure to break casing on an insulatorWe sampled 100 insulators(applied pressure until the insulator broke) What’s the largest possible deviation? 2110 – 1700 = 410 1240 – 1700 = -460 Mean = 1700 pounds Range = 1240 – 2110 What’s the ‘typical’ or standard deviation? Standard Deviation = 200

21. Number of kids in familyWe sampled 100 families(counted number of kids) 8 – 2.5= 5.5 What’s the largest possible deviation? 1 - 2.5= -1.5 Mean = 2.5 kids Range = 1 - 8 What’s the ‘typical’ or standard deviation? Standard Deviation = 1.7

22. Number correct on examWe tested 100 students(counted number of correct on 100 point test) 55 - 80= -25 What’s the largest possible deviation? 100 - 80 = 20 Mean = 80 Range = 55 - 100 What’s the ‘typical’ or standard deviation? Standard Deviation = 10

23. Monthly electric bills for 50 apartments(amount of dollars charged for the month) Let’s try one What’s the largest possible deviation? Mean = $150 Range = 97 - 213 150 – 97 = 53 150 – 213 = - 63 The best estimate of the population standard deviation is a. $150 b. $27 c. $53 d. $63 Standard Deviation = 27

24. Amount of soda in 2-liter containers(measured amount of soda in 2-liter bottles) Let’s try one What’s the largest possible deviation? 2 – 1.894 = 0.106 2 – 2.109 = -0.109 Mean = 2.0 Range = 1.894 – 2.109 The best estimate of the population standard deviation is a. 0.106 b. 0.109 c. 0.044 d. 2.0 Standard Deviation = 0.044

25. Scores on an Art History exam(measured number correct out of 100) Let’s try one What’s the largest possible deviation? 25 - 50= - 25 Mean = 50 Range = 25 - 70 70 - 80 = 20 The best estimate of the population standard deviation is a. 50 b. 25 c. 10 d. .5 Standard Deviation = 10

26. Amount of soda in 2-liter containers(measured amount of soda in 2-liter bottles) Let’s try one One way to estimate standard deviation* σ≈ range / 5 45 / 5 = 9 Mean = 50 Range = 25 - 70 The best estimate of the population standard deviation is a. 50 b. 25 c. 10 d. .5 Standard Deviation = 10

27. Number correct on examWe tested 100 students(counted number of correct on 100 point test) Mean = 50 Range = 25 - 70 Standard Deviation = 10

28. Number correct on examWe tested 100 students(counted number of correct on 100 point test) Mean = 50 Range = 25 - 70 Standard Deviation = 10

29. Scores, standard deviations, and probabilities Mean = 50 S = 10 (Note S = standard deviation)

30. Scores, standard deviations, and probabilities Mean = 50 S = 10 (Note S = standard deviation)

31. Scores, standard deviations, and probabilities Mean = 50 S = 10 (Note S = standard deviation)

32. Scores, standard deviations, and probabilities Mean = 50 S = 10 (Note S = standard deviation)

33. Scores, standard deviations, and probabilities Mean = 50 S = 10 (Note S = standard deviation) 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

34. Scores, standard deviations, and probabilities Mean = 50 S = 10 (Note S = standard deviation) 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

35. Scores, standard deviations, and probabilities Mean = 50 S = 10 (Note S = standard deviation) 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

36. Scores, standard deviations, and probabilities What if we go up 2.0 standard deviations? Then, z score = +2.0

37. Scores, standard deviations, and probabilities What if we go up 2.5 standard deviations? Then, z score = +2.5

38. Scores, standard deviations, and probabilities What if we go down 1.26 standard deviations? Then, z score = -1.26

39. z scores 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 What’s the biggest possible z score? How are standard deviations (or z scores) related to probability (also known as area under the curve or proportion of curve or percent of curve)

40. The Empirical Rule for “normal curve” Probability / proportion / percent / area under the curve Mean = 50 S = 10 (Note S = standard deviation)

41. Scores, standard deviations, and probabilities 68% 34% 34% Mean = 50 S = 10 (Note S = standard deviation) 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

42. The Empirical Rule for “normal curve” Probability / proportion / percent / area under the curve Mean = 50 S = 10 (Note S = standard deviation)

43. Scores Probability (also percent Distance from mean or proportion (z scores) or area) Scores, standard deviations, and probabilities 95% 47.5% 47.5% Mean = 50 S = 10 (Note S = standard deviation) 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

44. The Empirical Rule for “normal curve” Probability / proportion / percent / area under the curve Mean = 50 S = 10 (Note S = standard deviation)

45. Scores Probability (also percent Distance from mean or proportion (z scores) or area) Scores, standard deviations, and probabilities 99.7% 49.85 49.85 Mean = 50 S = 10 (Note S = standard deviation) 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

46. 2 sd above and below mean 95% 1 sd above and below mean 68% 3 sd above and below mean 99.7% These would be helpful to know by heart – please memorize areas

47. Raw scores, z scores & probabilities 1 sd above and below mean 68% z = +1 • Notice: • 3 types of numbers • raw scores • z scores • probabilities z = -1 Mean = 50 S = 10 (Note S = standard deviation) 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

48. Raw scores, z scores & probabilities 2 sd above and below mean 95% • Notice: • 3 types of numbers • raw scores • z scores • probabilities z = -2 z = +2 Mean = 50 S = 10 (Note S = standard deviation) 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

49. Raw scores, z scores & probabilities 3 sd above and below mean 99.7% • Notice: • 3 types of numbers • raw scores • z scores • probabilities z = +3 z = -3 Mean = 50 S = 10 (Note S = standard deviation) 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

50. If score is within 2 standard deviations (z < 2) “not unusual score” If score is beyond 2 standard deviations (z = 2 or up to 3) “is unusual score” If score is beyond 3 standard deviations (z = 3 or up to 4) “is an outlier” If score is beyond 4 standard deviations (z = 4 or beyond) “is an extreme outlier”