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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 today7/16/12 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. Create example of each type Identify IV (one or two) Identify DV (one or two) Draw possible graph for each Writing Assignment Study Type 1: Confidence Intervals Study Type 2: t-test Study Type 3: One-way Analysis of Variance (ANOVA) Study Type 4: Two-way Analysis of Variance (ANOVA) Study Type 5: Correlation Study Type 6: Simple and Multiple regression Study Type 7: Chi Square

  6. Overview Frequency distributions The normal curve 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 Mean, Median, Mode, Trimmed Mean Standard deviation, Variance, Range Mean Absolute Deviation Skewed right, skewed left unimodal, bimodal, symmetric

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

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

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

  10. 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

  11. Remember… Frequency 10 20 30 40 50 60 70 80 90 100 Score on Exam Note: Label and Numbers Note: Always “frequency”

  12. Examples of data that would produce three of these shapes

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

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

  15. Dispersion: Variability Fun fact: Mean is 72 Wildcats Baseball team: Tallest player = 76” (same as 6’4”) Shortest player = 68” (same as 5’8”) Range: The difference between the largest and smallest scores 76” – 68” = 8” Range is 8” (76” – 68”) xmax - xmin = Range Please note: No reference is made to numbers between the min and max

  16. Fun fact: Mean is 78 Wildcats Basketball team: Tallest player = 83” (same as 6’11”) Shortest player = 70” (same as 5’10”) Range is 13” (83” – 70”) Range: The difference between the largest and smallest scores 83” – 70” = 13” xmax - xmin = Range

  17. 5’ 7’ 6’ 6’6” 5’6” 5’ 7’ 6’ 6’6” 5’6” 5’ 7’ 6’ 6’6” 5’6” Variability 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 But what is a “deviation score”?

  18. 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”

  19. 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 0” Remember, it’s relative to the mean Generally, (on average) how far away is each score from the mean? Based on difference from the mean Mean Diallo Please memorize these Preston Shea Mike

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

  21. 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!

  22. 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

  23. 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

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

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

  26. Deviation scores • Writing Assignment: • 1. What is a “deviation score” • 2. Preston has a deviation score of 2: What does that tell us about Preston? • Is he taller or shorter than the mean? And by how much? • Are most people in the group taller or shorter than Preston • Mike has a deviation score of -4: What does that tell us about Mike? • Is he taller or shorter than the mean? And by how much? • Are most people in the group taller or shorter than Mike • Diallo has a deviation score of 0: What does that tell us about Diallo? • Is he taller or shorter than the mean? And by how much? • Are most people in the group taller or shorter than Diallo? • 5. Please write the formula for the standard deviation of a population Diallo is 0” Preston is 2” Mike is -4” Hunter is -2 Shea is 4 David 0” How far away is each score from the mean? Mean Diallo Preston Shea Mike

  27. 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

  28. 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 What is the most common “deviation score”? Shea is 4 David is 0” Remember, We are thinking in terms of “deviations” 5’8” 5’10” 6’0” 6’2” 6’4”

  29. 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)

  30. Raw scores, z scores & probabilities Please note spatially where 1 standard deviation falls on the curve

  31. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) 12 10 Frequency 8 6 4 2 0 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package What’s the ‘typical’ or standard deviation? Mean = $37 Range = $27 - $47 Standard Deviation = 3.5

  32. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 0,0,0,0,0,0,0,0,0 What is the most common score? What is the most common “deviation score”? Deviation = 0 12 10 Frequency What is the least common “deviation scores”? 8 6 4 2 0 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package $27 – $37 = -$10 $47 – $37 = $10 What’s the largest possible deviation? Mean = $37 Range = $27 - $47

  33. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 What is the deviation score for $38? 12 Deviation = 1 10 Frequency 8 6 4 2 0 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

  34. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 What is the deviation score for $39? 12 10 Deviation = 2 Frequency 8 6 4 2 0 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

  35. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 What is the deviation score for $40? 12 10 Frequency Deviation = 3 8 6 4 2 0 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

  36. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 What is the deviation score for $41? 12 10 Frequency 8 Deviation = 4 6 4 2 0 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

  37. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 What is the deviation score for $42? 12 10 Frequency 8 Deviation = 5 6 4 2 0 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

  38. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 What is the deviation score for $43? 12 10 Frequency 8 6 Deviation = 6 4 2 0 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

  39. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 What is the deviation score for $44? 12 10 Frequency 8 6 Deviation = 7 4 2 0 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package Mean = $37 Range = $27 - $47

  40. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 8,8,8 12 10 Frequency 8 6 Deviation = 8 4 2 0 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package What is the deviation score for $45? Mean = $37 Range = $27 - $47

  41. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 8,8,8 9,9 12 10 Frequency 8 6 Deviation = 9 4 2 0 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package What is the deviation score for $46? Mean = $37 Range = $27 - $47

  42. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 8,8,8 9,9 10 12 10 Frequency 8 6 4 Deviation = 10 2 0 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package What is the deviation score for $46? Mean = $37 Range = $27 - $47

  43. Movie Packages We sampled 100 movie theaters(Two tickets, large popcorn and 2 drinks) Deviation scores 0,0,0,0,0,0,0,0,0,0 1,1,1,1,1,1,1,1,1 2,2,2,2,2,2,2 3,3,3,3,3,3 4,4,4,4,4 5,5,5,5 6,6,6,6 7,7,7 8,8,8 9,9 10 Estimate Average Deviation Score 12 10 Frequency 8 6 4 2 0 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Price per Movie Package What’s the ‘typical’ or standard deviation? Mean = $37 Range = $27 - $47 Standard Deviation = 3.5

  44. Pounds of pressure to break casing on an insulator(We applied pressure until the insulator casing broke) What’s the largest possible deviation? 2100– 1700 = 400 1200 – 1700 = -500 Mean = 1700 pounds Range = 1200 – 2100 What’s the ‘typical’ or standard deviation? Standard Deviation = 200

  45. Amount of Bonuses (based on commission)We sampled 100 retail workers $75 – $50= $25 What’s the largest possible deviation? $25 – $50= -$25 Mean = $50 Range = $25 - $75 What’s the ‘typical’ or standard deviation? Standard Deviation = 10

  46. Waiting time for service at bankWe sampled 100 banks(From time entering line to time reaching teller) 3.8 – 3.0= .8 What’s the largest possible deviation? 2.2 – 3.0= -.8 Mean = 3 minutes Range = 2.2- 3.8 What’s the ‘typical’ or standard deviation? Standard Deviation = 0.30

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

  48. Number of kids in familyWe sampled 100 families(counted number of kids) 8 – 3= 5 What’s the largest possible deviation? 1 - 3= -2 Mean = 3 kids Range = 1 - 8 What’s the ‘typical’ or standard deviation? Standard Deviation = 1.7

  49. 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

  50. 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

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