1 / 68

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

Please click in. Set your clicker to channel 03. My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z . MGMT 276: Statistical Inference in Management. Welcome.

sirvat
Télécharger la présentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Please click in Set your clicker to channel 03 My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z

  2. MGMT 276: Statistical Inference in Management Welcome Please double check – All cell phones other electronic devices are turned off and stowed away http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man

  3. It went really well! Exam 1 – This past Tuesday Thanks for your patience and cooperation We should have the grades up by Tuesday

  4. Please read: Chapters 5 - 9 in Lind book & Chapters 10, 11, 12 & 14 in Plous book: Lind Chapter 5: Survey of Probability Concepts Chapter 6: Discrete Probability Distributions Chapter 7: Continuous Probability Distributions Chapter 8: Sampling Methods and CLT Chapter 9: Estimation and Confidence Interval Plous Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability and Risk Chapter 14: The Perception of Randomness We’ll be jumping around some…we will start with chapter 7

  5. Use this as your study guide By the end of lecture today9/22/11 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

  6. Please click in Homework due next class - (Due September 27th) My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z Complete z-score worksheet available on class website Please double check – All cell phones other electronic devices are turned off and stowed away Turn your clicker on

  7. Standard deviation: The average amount by which observations deviate on either side of their mean Deviation scores Diallo is 0” Preston is 2” Mike is -4” Hunter is -2 Shea is 4 David is 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

  8. 2 sd above and below mean 95% 1 sd above and below mean 68% 3 sd above and below mean 99.7% This will be so helpful now that we know these by heart

  9. Raw scores, z scores & probabilities 1 sd above and below mean 68% z = +1 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

  10. Raw scores, z scores & probabilities 2 sd above and below mean 95% 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

  11. Raw scores, z scores & probabilities 3 sd above and below mean 99.7% 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

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

  13. 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”

  14. 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.

  15. 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.

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

  17. 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

  18. 1 sd above and below mean 68% Raw scores, z scores & probabilities z = +1 z-table (from z to area) Distance from the mean ( from raw to z scores) If we go up to score of 60 we are going up 1.0 standard deviation z = -1 Then, z score = +1.0 Raw Scores (actual data) Proportion of curve (area from mean) z score = 60 – 50 10 10 10 = 1 = Mean = 50 Standard deviation = 10 If we go down to score of 40 we are going down 1.0 standard deviation Then, z score = - 1.0 z score = 40 – 50 10 -10 10 = -1 = z score = raw score – mean standard deviation

  19. 2 sd above and below mean 95% Raw scores, z scores & probabilities z = +2 z-table (from z to area) Distance from the mean ( from raw to z scores) z = -2 If we go up to score of 70 we are going up 2.0 standard deviations Then, z score = +2.0 Raw Scores (actual data) Proportion of curve (area from mean) z score = 70 – 50 10 20 10 = 2 = Mean = 50 Standard deviation = 10 If we go down to score of 30 we are going down 2.0 standard deviations Then, z score = - 2.0 z score = 30 – 50 10 -20 10 = -2 = z score = raw score – mean standard deviation

  20. 3 sd above and below mean 99.7% Raw scores, z scores & probabilities z = +3 z = -3 z-table (from z to area) Distance from the mean ( from raw to z scores) If we go up to score of 80 we are going up 3.0 standard deviations Then, z score = +3.0 Raw Scores (actual data) Proportion of curve (area from mean) z score = 80 – 50 10 30 10 = 3 = Mean = 50 Standard deviation = 10 If we go down to score of 20 we are going down 3.0 standard deviations Then, z score = - 3.0 z score = 20 – 50 10 -30 10 = -3 = z score = raw score – mean standard deviation

  21. Mean = 50 sd = 10 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 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 60 - 50 10 +1.0 = 3) Go to z table - find area under correct column 4) Report the area Hint always draw a picture!

  22. 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

  23. 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!

  24. 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

  25. Ties together z score with Draw picture of what you are looking for... Find z score (using formula)... Look up proportions on table...(Appendix B – page 514) • probability • proportion • percent • area under the curve 68% 34% 34%

  26. 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!

  27. 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

  28. 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!

  29. 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

  30. 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!

  31. 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

  32. 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!

  33. 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

  34. 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!

  35. .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 Page 514 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

  36. 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

  37. ? .5500 ? Mean = 50Standard deviation = 10 Find the score for percentile rank of 55(55th percentile - 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

  38. ? .5500 ? Mean = 50Standard deviation = 10 .05 Find the score for percentile rank of 55(55th percentile - 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

  39. ? .5500 ? Mean = 50Standard deviation = 10 .05 Find the score for percentile rank of 55(55th percentile - 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

  40. ? .5500 ? Mean = 50Standard deviation = 10 .05 Find the score for percentile rank of 55(55th percentile - 55%ile) .5 x = 51.3 .5 .05 1) Go to z table - find z score for for area .0500 (.5500 - .5000) = .05 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

  41. Hint: Always draw a picture! Homework worksheet

  42. z = -1 z = 1 Normal distribution -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

  43. Characteristics of Normal Distribution We’re talking about distribution of raw scores Normal Distribution How would you describe the shape? Symmetric and bell-shaped Shape

  44. Characteristics of Normal Distribution Normal Distribution What is the standard deviation? σ Standard Deviation Shape Symmetric and bell-shaped

  45. Characteristics of Normal Distribution Normal Distribution What is the mean? µ Mean Standard Deviationσ Shape Symmetric and bell-shaped

  46. Characteristics of Normal Distribution Normal Distribution What is the theoretical range? -∞< X < +∞ Domain Mean µ Standard Deviationσ Shape Symmetric and bell-shaped

  47. Characteristics of Normal Distribution What is the ‘practical’ range(covers 99.7% of curve) Normal Distribution µ - 3σ< X < µ + 3σ -∞< X < +∞ Domain Mean µ Standard Deviationσ Shape Symmetric and bell-shaped

  48. Characteristics of Normal Distribution Once we know the mean (anchor point) and standard deviation (spread) we can define any normal curve Normal Distribution Parameters µ = population σ= population standard deviation -∞< X < +∞ Domain Mean µ Standard Deviationσ Shape Symmetric and bell-shaped

  49. Characteristics of Normal Distribution Normal Distribution Parameters µ = population σ= population standard deviation -∞< X < +∞ Domain Mean µ Standard Deviationσ Shape Symmetric and bell-shaped

  50. Characteristics of Standard Normal Distribution (distribution of z-scores) Normal Distribution How would you describe the shape? Shape Symmetric and bell-shaped

More Related