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MGMT 276: Statistical Inference in Management Summer Session I Harvill, Room 101 8:30 – 10:45 Monday - Thursday June 9 – July 10, 2014. Welcome. Green sheet Seating Chart. Please start portfolios. Schedule of readings. Before next exam:

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  1. MGMT 276: Statistical Inference in ManagementSummer Session IHarvill, Room 1018:30 – 10:45 Monday - ThursdayJune 9 – July 10, 2014 Welcome Green sheet Seating Chart

  2. Please start portfolios

  3. Schedule of readings • Before next exam: • Please read:• Supplemental reading (Appendix D) • • Supplemental reading (Appendix E) • • Supplemental reading (Appendix F) • 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

  4. Please click in My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z

  5. Use this as your study guide By the end of lecture today6/16/14 • Measures of variability • Range, Standard deviation and Variance • Memorizing the four definitional formulae • Objectives of research in business • Counting ‘standard deviationses’ – z scores • Connecting raw scores, z scores and probabilityConnecting probability, proportion and area of curve • Percentiles

  6. Why do we concern ourselves about research? – Five objectives 1. To explore potential phenomena • explore whether phenomenon is present • explore a phenomenon with a fresh take • generate new ideas and discover relationships

  7. Why do we concern ourselves about research? – Five objectives 1. To explore potential phenomena • explore whether phenomenon is present • explore a phenomenon with a fresh take • generate new ideas and discover relationships Yo, you wanna meet up, have a seizure whilst listening to the noise of a wampwampwampwamp wampwampwampwampwampuntil your ears bleed?"

  8. Why do we concern ourselves about research in business? – Five objectives 2. To describe phenomena • build a vocabulary of constructs and make distinctions between similar constructs • (how is dubstep different from techno or house?) • cluster similar characteristics into related constructs . - Types of management style - Strategies for quality control

  9. Why do we concern ourselves about research in business? – Five objectives 3. To explain and model phenomena • explanation: find cause and effect relationships • propose mechanisms that determine outcomes • show how and why a phenomenon operates as it does

  10. Why do we concern ourselves about research in business? – Five objectives 4. To predict future behavior • what characteristics are likely to result in workerproductivity, consumer behavior, etc... • explanations can help with predictions, but being able to predict an outcome doesn’t necessarily provide a good explanation

  11. Why do we concern ourselves about research in business? – Five objectives 5. To influence behavior • how can we use what we know about human behavior to affect how people around us react and behave (and do what we want) • increasing probability of sales • supervisors increasing probability of happy employees • parent increasing probability of child taking out the trash • to advance better practices

  12. Raw scores, z scores & probabilities The normal curve is defined mostly by its mean, and standard deviation. Once we know that we can figure out a lot z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) Given any of these values (score, probability of occurrence, or distance from the mean) and you can figure out the other two.

  13. Mean = 100 Standard deviation = 5 If we go up one standard deviation z score = +1.0 and raw score = 105 If we go down one standard deviation z score = -1.0 and raw score = 95 85 90 95 100 105 110 115 If we go up two standard deviations z score = +2.0 and raw score = 110 If we go down two standard deviations z score = -2.0 and raw score = 90 85 90 95 100 105 110 115 If we go up three standard deviations z score = +3.0 and raw score = 115 If we go down three standard deviations z score = -3.0 and raw score = 85 85 90 95 100 105 110 115 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 Review

  14. Raw scores, z scores & probabilities • Notice: • 3 types of numbers • raw scores • z scores • probabilities Mean = 50 Standard deviation = 10 z = -2 z = +2 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

  15. Raw scores, z scores & probabilities Distance from the mean (z scores) convert convert Proportion of curve (area from mean) Raw Scores (actual data) We care about this! What is the actual number on this scale?“height” vs “weight” “pounds” vs “test score” We care about this! “percentiles” “percent of people” “proportion of curve” “relative position” Proportion of curve (area from mean) Raw Scores (actual data) Distance from the mean (z scores) convert convert

  16. Normal distribution Raw scores z-scores probabilities Z Scores Have z Find raw score Have z Find area z table Formula Have area Find z Area & Probability Raw Scores Have raw score Find z

  17. Scores, standard deviations, and probabilities What is total percent under curve? What proportion of curve is above the mean? .50 100% Given any of these values (score, probability of occurrence, or distance from the mean) and you can figure out the other two.

  18. Scores, standard deviations, and probabilities What score is associated with 50th percentile? What percent of curve is below a score of 50? 50% mean Mean = 50 S = 10 (Note S = standard deviation)

  19. Find z score for raw score of 60 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 z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) 50 60 z = 1 10 Mean = 50 Standard deviation = 10 Review

  20. Find z score for raw score of 30 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 z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) 50 30 z = - 2 10 Mean = 50 Standard deviation = 10 Review

  21. Find z score for raw score of 70 Raw scores, z scores & probabilities z-table (from z to area) Distance from the mean ( from raw to z scores) If we go up to score of 70 we are going up 2.0 standard deviations Raw Scores (actual data) Proportion of curve (area from mean) Then, z score = +2.0 z score = raw score - mean standard deviation z score = 70 – 50 . 10 = 20. 10 = 2 Mean = 50 Standard deviation = 10 Review

  22. Find z score for raw score of 80 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 z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) 50 80 z = 3 10 Mean = 50 Standard deviation = 10 Review

  23. Find z score for raw score of 20 Raw scores, z scores & probabilities z-table (from z to area) Distance from the mean ( from raw to z scores) If we go down to score of 20 we are going down 3.0 standard deviations Raw Scores (actual data) Proportion of curve (area from mean) Then, z score = -3.0 z score = raw score - mean standard deviation z score = 20 – 50 10 = - 30 . 10 = - 3 Mean = 50 Standard deviation = 10 Review

  24. Raw scores, z scores & probabilities Have z Find area Z Scores Have z Find raw score z table Formula Have area Find z Area & Probability Raw Scores Have raw score Find z

  25. Ties together z score with Draw picture of what you are looking for... Find z score (using formula)... Look up proportions on table • probability • proportion • percent • area under the curve 68% 34% 34%

  26. 50 60 Find the area under the curve that falls between 50 and 60 34.13% 1) Draw the picture 2) Find z score 3) Go to z table - find area under correct column 4) Report the area z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) z = 1 50 60 10

  27. Ties together z score with Draw picture of what you are looking for... Find z score (using formula)... Look up proportions on table... • probability • proportion • percent • area under the curve 68% 34% 34%

  28. z table z table Mean = 50 Standard deviation = 10 68.26% Find the area under the curve that falls between 40 and 60 34.13% 34.13% z score = raw score - mean standard deviation Hint always draw a picture! z score = 60 - 50 10 z score = 40 - 50 10 z score = 10 = 1.0 10 z score = 10 = -1.0 10 z score of 1 = area of .3413 z score of 1 = area of .3413 .3413 + .3413 = .6826

  29. Mean = 50 Standard deviation = 10 1) Draw the picture 2) Find z score 3) Go to z table - find area under correct column 4) Report the area Find the area under the curve that falls between 30 and 50 z-table (from z to area) Distance from the mean ( from raw to z scores) z score = raw score - mean standard deviation Raw Scores (actual data) Proportion of curve (area from mean) z score = 30 - 50 10 z score = - 20 = - 2.0 10 Hint always draw a picture!

  30. z table Mean = 50 Standard deviation = 10 1) Draw the picture 2) Find z score 3) Go to z table - find area under correct column 4) Report the area 47.72% Find the area under the curve that falls between 30 and 50 z score = raw score - mean standard deviation z score = 30 - 50 10 z score = - 20 = - 2.0 10 z score of - 2 = area of .4772 Hint always draw a picture! Hint always draw a picture!

  31. Let’s do some problems z table Mean = 50 Standard deviation = 10 47.72% Find the area under the curve that falls between 70 and 50 z score = raw score - mean standard deviation z score = 70 - 50 10 z score = 20 = +2.0 10 z score of 2 = area of .4772 Hint always draw a picture!

  32. Let’s do some problems Mean = 50 Standard deviation = 10 .4772 .4772 95.44% z score of 2 = area of .4772 z-table (from z to area) Distance from the mean ( from raw to z scores) Find the area under the curve that falls between 30 and 70 Raw Scores (actual data) Proportion of curve (area from mean) .4772 + .4772 = .9544 Hint always draw a picture!

  33. Scores, standard deviations, and probabilities Actually 68.26 Actually 95.44 To be exactly 95% we will use z = 1.96

  34. Writing AssignmentLet’s do some problems Mean = 50Standard deviation = 10

  35. Let’s do some problems ? Mean = 50Standard deviation = 10 60 Find the area under the curve that falls below 60 means the same thing as Find the percentile rank for score of 60

  36. Let’s do some problems ? 60 Mean = 50Standard deviation = 10 Find the percentile rank for score of 60 z-table (from z to area) Distance from the mean ( from raw to z scores) .3413 .5000 Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 60 - 50 10 = 1 2) Go to z table - find area under correct column (.3413) 3) Look at your picture - add .5000 to .3413 = .8413 4) Percentile rank or score of 60 = 84.13% Hint always draw a picture!

  37. ? 75 Mean = 50Standard deviation = 10 Find the percentile rank for score of 75 .4938 1) Find z score z score = 75 - 50 10 z score = 25 10 = 2.5 2) Go to z table Hint always draw a picture!

  38. ? 75 Mean = 50Standard deviation = 10 Find the percentile rank for score of 75 .4938 .5000 1) Find z score z score = 75 - 50 10 z score = 25 10 = 2.5 2) Go to z table 3) Look at your picture - add .5000 to .4938 = .9938 4) Percentile rank or score of 75 = 99.38% Hint always draw a picture!

  39. ? 45 Mean = 50Standard deviation = 10 Find the percentile rank for score of 45 z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 45 - 50 10 z score = - 5 10 = -0.5 2) Go to z table

  40. ? 45 Mean = 50Standard deviation = 10 Find the percentile rank for score of 45 .1915 ? 1) Find z score z score = 45 - 50 10 z score = - 5 10 = -0.5 2) Go to z table

  41. ? 45 Mean = 50Standard deviation = 10 Find the percentile rank for score of 45 .1915 z-table (from z to area) Distance from the mean ( from raw to z scores) .3085 Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 45 - 50 10 z score = - 5 10 = -0.5 2) Go to z table 3) Look at your picture - subtract .5000 -.1915 = .3085 4) Percentile rank or score of 45 = 30.85%

  42. ? Mean = 50Standard deviation = 10 Find the percentile rank for score of 55 z-table (from z to area) Distance from the mean ( from raw to z scores) 55 Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 55 - 50 10 z score = 5 10 = 0.5 2) Go to z table

  43. ? Mean = 50Standard deviation = 10 Find the percentile rank for score of 55 .1915 55 1) Find z score z score = 55 - 50 10 z score = 5 10 = 0.5 2) Go to z table

  44. ? Mean = 50Standard deviation = 10 Find the percentile rank for score of 55 .1915 z-table (from z to area) Distance from the mean ( from raw to z scores) .5 55 Raw Scores (actual data) Proportion of curve (area from mean) 1) Find z score z score = 55 - 50 10 z score = 5 10 = 0.5 2) Go to z table 3) Look at your picture - add .5000 +.1915 = .6915 4) Percentile rank or score of 55 = 69.15%

  45. Find the score for z = -2 ? Mean = 50Standard deviation = 10 30 Hint always draw a picture! Find the score that is associated with a z score of -2 z-table (from z to area) Distance from the mean ( from raw to z scores) raw score = mean + (z score)(standard deviation) Raw Scores (actual data) Proportion of curve (area from mean) Raw score = 50 + (-2)(10) Raw score = 50 + (-20) = 30 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion

  46. ? .5500 ? Mean = 50Standard deviation = 10 Find the score for percentile rank of 55%ile z-table (from z to area) Distance from the mean ( from raw to z scores) Raw Scores (actual data) Proportion of curve (area from mean) Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion

  47. ? .5500 ? Mean = 50Standard deviation = 10 .05 Find the score for percentile rank of 55%ile .5 .5 .05 1) Go to z table - find z score for for area .0500 (.5500 - .5000) = .05 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion area = .0517 (closest I could find to .0500) z = 0.13

  48. ? .5500 ? Mean = 50Standard deviation = 10 .05 Find the score for percentile rank of 55%ile .5 .5 .05 1) Go to z table - find z score for for area .0500 (.5500 - .5000) = .05 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion area = .0517 (closest I could find to .0500) z = 0.13

  49. ? .5500 ? Mean = 50Standard deviation = 10 .05 Find the score for percentile rank of 55%ile .5 x = 51.3 .5 .05 1) Go to z table - find z score for for area .0500 (.5500 - .5000) = .0500 area = .0517 (closest I could find to .0500) z = 0.13 2) x = mean + (z)(standard deviation) x = 50 + (0.13)(10) x = 51.3 Please note: When we are looking for the score from proportion we use the z-table ‘backwards’. We find the closest z to match our proportion x = 51.3

  50. Raw scores, z scores & probabilities Have z Find area Z Scores Have z Find raw score z table Formula Have area Find z Area & Probability Raw Scores Have raw score Find z

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