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Please start portfolios

Please start portfolios. MGMT 276: Statistical Inference in Management McClelland Hall, Room 132 8:30 – 10:45 Monday - Thursday Summer II , 2012. Welcome. Experiment. http://www.youtube.com/watch?v=Ahg6qcgoay4&watch_response. Schedule of readings. Before next exam:

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Please start portfolios

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  1. Please start portfolios

  2. MGMT 276: Statistical Inference in ManagementMcClelland Hall, Room 1328:30 – 10:45 Monday - ThursdaySummer II, 2012. Welcome Experiment http://www.youtube.com/watch?v=Ahg6qcgoay4&watch_response

  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. Use this as your study guide By the end of lecture today7/17/12 Five objectives in conducting business research Characteristics of a distribution: Central Tendency, Dispersion, Shape Measures of central tendency: Mean, Median, Mode Measures of variability: Range, Standard deviation and Variance Definitional formula for standard deviation and variance for both samples and populations Counting ‘standard deviationses’ – z scores Connecting raw scores, z scores and probabilityConnecting probability, proportion and area of curve Percentiles

  5. Why do we concern ourselves about research in business? – 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

  6. 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 • cluster similar characteristics into related constructs . - Business strategies e.g. business socks – how might you market this? - Types of management style - Strategies for quality control

  7. 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

  8. 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

  9. 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

  10. These would be helpful to memorize these Standard Deviation Variance 2 sd above and below mean 95% 1 sd above and below mean 68% 3 sd above and below mean 99.7%

  11. 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

  12. 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

  13. z = -1 z = 1 Normal distribution Raw scores z-scores -3 -2 -1 0 +1 +2 +3 z scores -3 -2 -1 0 +1 +2 +3 z scores raw scores In z-score distribution mean = 0 standard deviation = 1 In a normal distribution mean = µstandard deviation = σ

  14. 50 60 68% Mean = 50sd = 10 We’re going to want to talk probabilities (area under the curve) for pairs of scores 34% 34% Find the area under the curve that falls between 50 and 60 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) Draw the picture 2) Find z score z score = raw score - mean standard deviation 3) Go to z table - find area under correct column 4) Report the area Hint always draw a picture!

  15. 50 60 1) Draw the picture 2) Find z score .3413 3) Go to z table - find area under correct column 4) Report the area Page 514 Find the area under the curve that falls between 50 and 60 60 - 50 10 +1.0 = z score of 1 = area of .3413 Are we done? Yes

  16. 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%

  17. Mean = 50 sd = 10 40 50 50 60 68% We’re going to want to talk probabilities (area under the curve) for pairs of scores 34% 34% Find the area under the curve that falls between 40 and 60 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) Draw the picture 2) Find two z scores z score = raw score - mean standard deviation 60 - 50 10 40 - 50 10 +1.0 -1.0 = = 3) Go to z table - find area under correct column 4) Report the area Hint always draw a picture!

  18. 40 50 50 60 1) Draw the picture .6826 2) Find z score 3) Go to z table - find area under correct column .3413 .3413 4) Report the area Page 514 Find the area under the curve that falls between 40 and 60 40 - 50 10 -1.0 = z score of -1 = area of .3413 60 - 50 10 +1.0 = z score of 1 = area of .3413 Not Yet Now, we’re done Are we done? .3413 +.3413 = .6826

  19. 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%

  20. Mean = 50 sd = 10 We’re going to want to talk probabilities (area under the curve) for pairs of scores 30 40 50 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) 1) Draw the picture Raw Scores (actual data) Proportion of curve (area from mean) 30 40 50 2) Find z score z score = raw score - mean standard deviation 30 - 50 10 - 2.0 = 3) Go to z table - find area under correct column 4) Report the area Hint always draw a picture!

  21. Mean = 50 sd = 10 1) Draw the picture 2) Find z score .4772 3) Go to z table - find area under correct column 4) Report the area 30 40 50 Page 514 Find the area under the curve that falls between 30 and 50 30 - 50 10 -2.0 = z score of -2 = area of .4772 Are we done? Yes

  22. 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!

  23. 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!

  24. 50 75 50 75 We’re going to want to talk probabilities (area under the curve) for pairs of scores ? Find the area under the curve that falls between 50 and 75 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) Draw the picture 2) Find z score z score = raw score - mean standard deviation 75 - 50 10 +2.5 = 3) Go to z table - find area under correct column 4) Report the area Hint always draw a picture!

  25. 50 75 1) Draw the picture 2) Find z score .4938 3) Go to z table - find area under correct column 4) Report the area Page 514 Find the area under the curve that falls between 50 and 75 75 - 50 10 +2.5 = z score of 2.5 = area of .4938 Are we done? Yes

  26. 50 75 50 75 Mean = 50 sd = 10 We’re going to want to talk probabilities (area under the curve) for pairs of scores ? Find the area under the curve that falls below a score of 75 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) Draw the picture 2) Find z score z score = raw score - mean standard deviation 75 - 50 10 +2.5 = 3) Go to z table - find area under correct column 4) Report the area Hint always draw a picture!

  27. 50 75 Mean = 50 sd = 10 .4938 1) Draw the picture 2) Find z score .9938 3) Go to z table - find area under correct column 4) Report the area Page 514 Find the area under the curve that falls below a score of 75 75 - 50 10 +2.5 = z score of 2.5 = area of .4938 This is the same thing as “Please find the percentile for a score of 75”. Are we done? No Now, we’re done .4938 +.5000 = .9938

  28. 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!

  29. 45 45 Mean = 50 sd = 10 ? We’re going to want to talk probabilities (area under the curve) for pairs of scores Please find the percentile rank for a 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) Draw the picture 2) Find z score z score = raw score - mean standard deviation 45 - 50 10 -0.5 = 3) Go to z table - find area under correct column 4) Report the area Hint always draw a picture!

  30. .1915 45 45 Mean = 50 sd = 10 1) Draw the picture ? .3085 2) Find z score 3) Go to z table - find area under correct column 4) Report the area Please find the percentile rank for a score of 45 .1915 45 - 50 10 -0.5 = ? .3085 z score of -0.5 = area of .1915 Are we done? No Look at your picture - need to subtract Now, we’re done .5000 - .1915 = .3085

  31. 50 55 50 55 Mean = 50 sd = 10 We’re going to want to talk probabilities (area under the curve) for pairs of scores ? Please find the percentile rank for a score of 55 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) Draw the picture 2) Find z score z score = raw score - mean standard deviation 55 - 50 10 +0.5 = 3) Go to z table - find area under correct column 4) Report the area Hint always draw a picture!

  32. 50 55 Mean = 50 sd = 10 .1915 1) Draw the picture 2) Find z score .6915 3) Go to z table - find area under correct column 4) Report the area Page 514 Please find the percentile rank for a score of 55 55 - 50 10 +0.5 = z score of 0.5 = area of .1915 Are we done? No Now, we’re done .1915 +.5000 = .6915

  33. Let’s do some problems ? 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

  34. ? .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

  35. ? .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

  36. ? .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

  37. ? .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

  38. Hint: Always draw a picture! Homework worksheet

  39. Review for Exam 1

  40. Thank you! See you next time!!

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