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MGMT 276: Statistical Inference in Management.

MGMT 276: Statistical Inference in Management. Welcome. http://www.youtube.com/watch?v=tKH2oLjQIAA. Please click in. Homework due Thursday - (Feb 3 rd ). On class website: please print and complete homework worksheet #4. My last name starts with a letter somewhere between A. A – D

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MGMT 276: Statistical Inference in Management.

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  1. MGMT 276: Statistical Inference in Management. Welcome http://www.youtube.com/watch?v=tKH2oLjQIAA

  2. Please click in Homework due Thursday - (Feb 3rd) On class website: please print and complete homework worksheet #4 My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z Please read Chapters 1, 5, 6 and 13 from Plous: (selected chapters are on our class website) Chapter 1: Selective Perception Chapter 5: Plasticity Chapter 6: Effects of Question Wording and Framing Chapter 13: Anchoring and Adjustment Turn your clicker on

  3. Exam 1 – This Tuesday (2/8/11) Study guide will be online soon Bring 2 calculators (remember only simple calculators,we can’t use calculators with programming functions) Bring 2 pencils (with good erasers) Bring ID

  4. Use this as your study guide By the end of lecture today2/1/11 Surveys and questionnaire design Correlational methodology Dot Plots Frequency Distributions - Frequency Histograms Frequency, cumulative frequency Relative frequency, cumulative relative frequency Guidelines for constructing frequency distributions

  5. Must be complete and must be stapled Review of Homework Worksheet

  6. Peer review Please exchange questionnaires with someone (who has same TA as you) and complete the peer review handed out in class You have 10 minutes Peer review is an important skill in nearly all areas of business and science. Please strive to provide productive, useful and kind feedback as you complete your peer review

  7. Review of Homework Worksheet Hand in the peer review with the questionnaire *Hand them in together*

  8. Designed our study / observation / questionnaire Collected our data Organize and present our results

  9. Scatterplot displays relationships between two continuous variables Correlation: Measure of how two variables co-occur and also can be used for prediction Range between -1 and +1 The closer to zero the weaker the relationship and the worse the prediction Positive or negative

  10. Correlation Range between -1 and +1 +1.00 perfect relationship = perfect predictor +0.80 strong relationship = good predictor +0.20 weak relationship = poor predictor 0 no relationship = very poor predictor -0.20 weak relationship = poor predictor -0.80 strong relationship = good predictor -1.00 perfect relationship = perfect predictor

  11. Positive correlation: as values on one variable go up, so do values for the other variable Negative correlation: as values on one variable go up, the values for the other variable go down Height of Mothers by Height of Daughters Height ofMothers Positive Correlation Height of Daughters

  12. Positive correlation: as values on one variable go up, so do values for the other variable Negative correlation: as values on one variable go up, the values for the other variable go down Brushing teeth by number cavities BrushingTeeth Negative Correlation NumberCavities

  13. Perfect correlation = +1.00 or -1.00 One variable perfectly predicts the other Height in inches and height in feet Speed (mph) and time to finish race Positive correlation Negative correlation

  14. Correlation The more closely the dots approximate a straight line,(the less spread out they are) the stronger the relationship is. Perfect correlation = +1.00 or -1.00 One variable perfectly predicts the other No variability in the scatterplot The dots approximate a straight line

  15. Correlation

  16. Correlation does not imply causation Is it possible that they are causally related? Yes, but the correlational analysis does not answer that question What if it’s a perfect correlation – isn’t that causal? No, it feels more compelling, but is neutral about causality Number of Birthdays Number of Birthday Cakes

  17. Positive correlation: as values on one variable go up, so do values for other variable Negative correlation: as values on one variable go up, the values for other variable go down Number of bathrooms in a city and number of crimes committed Positive correlation Positive correlation

  18. Linear vs curvilinear relationship Linear relationship is a relationship that can be described best with a straight line Curvilinear relationship is a relationship that can be described best with a curved line

  19. Correlation - How do numerical values change? http://neyman.stat.uiuc.edu/~stat100/cuwu/Games.html http://argyll.epsb.ca/jreed/math9/strand4/scatterPlot.htm Let’s estimate the correlation coefficient for each of the following r = +.80 r = +1.0 r = -1.0 r = -.50 r = 0.0

  20. Describing Data Visually Lists of numbers too hard to see patterns 14 17 20 25 21 29 16 25 27 18 16 13 11 21 19 24 20 11 20 28 16 13 17 14 14 16 8 17 17 11 11 14 17 19 24 8 16 12 25 9 20 17 11 14 16 18 22 14 18 23 12 15 10 13 15 11 11 8 11 14 17 19 24 8 12 14 17 20 25 9 12 15 17 20 25 10 13 15 17 20 25 11 13 16 17 20 27 11 13 16 17 21 28 11 14 16 18 21 29 11 14 16 18 22 11 14 16 18 23 11 14 16 19 24 Organizing numbers helps Graphical representation even more clear This is a dot plot

  21. Describing Data Visually 8 12 14 17 19 24 8 12 14 17 20 25 9 13 15 17 20 25 10 13 15 17 20 25 11 13 16 17 20 27 11 13 16 17 21 28 11 14 16 18 21 29 11 14 16 18 22 11 14 16 18 23 11 14 16 19 24 Measuring the “frequency of occurrence” Then figure “frequency of occurrence” for the bins We’ve got to put these data into groups (“bins”)

  22. Frequency distributions Frequency distributions an organized list of observations and their frequency of occurrence How many kids are in your family? What is the most common family size?

  23. Another example: How many kids in your family? Number of kids in family 1 3 1 4 2 4 2 8 2 14 14 4 2 1 4 2 3 2 1 8

  24. Frequency distributions Number of kids in family 1 3 1 4 2 4 2 8 2 14 How many kids are in your family? What is the most common family size? Crucial guidelines for constructing frequency distributions: 1. Classes should be mutually exclusive: Each observation should be represented only once (no overlap between classes) Wrong 0 - 5 5 - 10 10 - 15 Correct 0 - 4 5 - 9 10 - 14 Correct 0 - under 5 5 - under 10 10 - under 15 2. Set of classes should be exhaustive: Should include all possible data values (no data points should fall outside range) Correct 0 - 3 4 - 7 8 - 11 12 - 15 Wrong 0 - 3 4 - 7 8 - 11 No place for our family of 14!

  25. Frequency distributions Number of kids in family 1 3 1 4 2 4 2 8 2 14 How many kids are in your family? What is the most common family size? Crucial guidelines for constructing frequency distributions: 3. All classes should have equal intervals (even if the frequency for that class is zero) Correct 0 - 4 5 - 9 10 - 14 Wrong 0 - 4 8 - 12 14 - 19 Correct 0 - under 5 5 - under 10 10 - under 15 missing space for families of 5, 6, or 7

  26. 8 12 14 17 19 24 8 12 14 17 20 25 9 13 15 17 20 25 10 13 15 17 20 25 11 13 16 17 20 27 11 13 16 17 21 28 11 14 16 18 21 29 11 14 16 18 22 11 14 16 18 23 11 14 16 19 24 4. Selecting number of classes is subjective Generally 5 -15 will often work How about 6 classes? (“bins”) How about 16 classes? (“bins”) How about 8 classes? (“bins”)

  27. 8 12 14 17 19 24 8 12 14 17 20 25 9 13 15 17 20 25 10 13 15 17 20 25 11 13 16 17 20 27 11 13 16 17 21 28 11 14 16 18 21 29 11 14 16 18 22 11 14 16 18 23 11 14 16 19 24 5. Class width should be round (easy) numbers Lower boundary can be multiple of interval size Remember: This is all about helping readers understand quickly and clearly. Clear & Easy 8 - 11 12 - 15 16 - 19 20 - 23 24 - 27 28 - 31 Round numbers: 5, 10, 15, 20 etc or 3, 6, 9, 12 etc • 6. Try to avoid open ended classes • For example • 10 and above • Greater than 100 • Less than 50

  28. Let’s do one Scores on an exam 82 58 64 80 75 72 87 73 88 94 84 78 93 69 70 60 53 84 76 87 84 61 89 95 87 91 75 99 53 58 60 61 64 69 70 72 73 75 75 76 78 80 82 84 84 84 87 87 87 88 89 91 93 94 95 99 Step 1: List scores Step 2: List scores in order Step 3: Decide whether grouped or ungrouped If less than 10 groups, “ungrouped” is fine If more than 10 groups, “grouped” might be better How to figure how many values Largest number - smallest number + 1 99 - 53 + 1 = 47 Step 4: Generate number and size of intervals (or size of bins) If we have 6 bins – we’d have intervals of 8 Sample size (n) 10 – 16 17 – 32 33 – 64 65 – 128 129 - 255 256 – 511 512 – 1,024 Number of classes 5 6 7 8 9 10 11 Let’s just try it and see which we prefer… Whaddya think? Would intervals of 5 be easier to read?

  29. Scores on an exam 82 58 64 80 75 72 87 73 88 94 84 78 93 69 70 60 53 84 76 87 84 61 89 95 87 91 75 99 Scores on an exam Score Frequency 93 - 100 4 85 - 92 6 77- 84 6 69 - 76 7 61- 68 2 53 - 60 3 Scores on an exam Score Frequency 95 - 99 2 90 - 94 3 85 - 89 5 80 – 84 5 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 53 58 60 61 64 69 70 72 73 75 75 76 78 80 82 84 84 84 87 87 87 88 89 91 93 94 95 99 Let’s just try it and see which we prefer… 6 bins Interval of 8 10 bins Interval of 5 Scores on an exam Score Frequency 95 - 99 2 90 - 94 3 85 - 89 5 80 – 84 5 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 Remember: This is all about helping readers understand quickly and clearly.

  30. Scores on an exam 82 58 64 80 75 72 87 73 88 94 84 78 93 69 70 60 53 84 76 87 84 61 89 95 87 91 75 99 Scores on an exam Score Frequency 95 - 99 2 90 - 94 3 85 - 89 5 80 – 84 5 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 Let’s make a frequency histogram using 10 bins and bin width of 5!!

  31. Scores on an exam 82 58 64 80 75 72 87 73 88 94 84 78 93 69 70 60 53 84 76 87 84 61 89 95 87 91 75 99 Step 6: Complete the Frequency Table Scores on an exam Score Frequency 95 - 99 2 90 - 94 3 85 - 89 5 80 – 84 5 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 RelativeCumulative Frequency 1.0000 .9285 .8214 .6428 .4642 .3213 .2142 .1785 .0714 .0357 Relative Frequency .0715 .1071 .1786 .1786 .1429 .1071 .0357 .1071 .0357 .0357 Cumulative Frequency 28 26 23 18 13 9 6 5 2 1 Just adding up the relative frequency data from the smallest to largest numbers Please note: Also just dividing cumulative frequency by total number 1/28 = .0357 2/28 = .0714 5/28 = .1786 6 bins Interval of 8 Just adding up the frequency data from the smallest to largest numbers Just dividing each frequency by total number to get a ratio (like a percent) Please note: 1 /28 = .0357 3/ 28 = .1071 4/28 = .1429

  32. Scores on an exam 82 58 64 80 75 72 87 73 88 94 84 78 93 69 70 60 53 84 76 87 84 61 89 95 87 91 75 99 Where are we? Scores on an exam Score Frequency 95 - 99 2 90 - 94 3 85 - 89 5 80 – 84 5 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 Relative Frequency .0715 .1071 .1786 .1786 .1429 .1071 .0357 .1071 .0357 .0357 Cumulative Rel. Freq. 1.0000 .9285 .8214 .6428 .4642 .3213 .2142 .1785 .0714 .0357 Cumulative Frequency 28 26 23 18 13 9 6 5 2 1 Cumulative Frequency Data Cumulative Frequency Histogram

  33. 55 - 59 75 - 79 50 - 54 60 - 64 80 - 84 95 - 99 70 - 74 85 - 89 65 - 69 90 - 94 Score on exam Scores on an exam 82 58 64 80 75 72 87 73 88 94 84 78 93 69 70 60 53 84 76 87 84 61 89 95 87 91 75 99 Step 1: List scores Step 2: List scores in order Step 3: Decide grouped Step 4: Decide 10 for # bins (classes) 5 for bin width (interval size) Step 5: Generate frequency histogram Scores on an exam Score Frequency 95 - 99 2 90 - 94 3 85 - 89 5 80 – 84 5 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 6 5 4 3 2 1

  34. 55 - 59 75 - 79 50 - 54 60 - 64 80 - 84 95 - 99 70 - 74 85 - 89 65 - 69 90 - 94 Score on exam Scores on an exam 82 58 64 80 75 72 87 73 88 94 84 78 93 69 70 60 53 84 76 87 84 61 89 95 87 91 75 99 Generate frequency polygon Plot midpoint of histogram intervals Connect the midpoints Scores on an exam Score Frequency 95 - 99 2 90 - 94 3 85 - 89 5 80 – 84 5 75 - 79 4 70 - 74 3 65 - 69 1 60 - 64 3 55 - 59 1 50 - 54 1 6 5 4 3 2 1

  35. 55 - 59 75 - 79 50 - 54 60 - 64 80 - 84 95 - 99 70 - 74 85 - 89 65 - 69 90 - 94 Score on exam Scores on an exam 82 58 64 80 75 72 87 73 88 94 84 78 93 69 70 60 53 84 76 87 84 61 89 95 87 91 75 99 Generate frequency ogive (“oh-jive”) Frequency ogive is used for cumulative data Plot midpoint of histogram intervals Connect the midpoints Scores on an exam Score 95 – 99 90 - 94 85 - 89 80 – 84 75 - 79 70 - 74 65 - 69 60 - 64 55 - 59 50 - 54 30 Cumulative Frequency 28 26 23 18 13 9 6 5 2 1 25 20 15 10 5

  36. Pareto Chart: Categories are displayed in descending order of frequency

  37. Stacked Bar Chart: Bar Height is the sum of several subtotals

  38. Simple Line Charts: Often used for time series data (continuous data)(the space between data points implies a continuous flow) Note: For multiple variables lines can be better than bar graph Note: Fewer grid lines can be more effective Note: Can use a two-scale chart with caution

  39. Pie Charts: General idea of data that must sum to a total(these are problematic and overly used – use with much caution) Exploded 3-D pie charts look cool but a simple 2-D chart may be more clear Exploded 3-D pie charts look cool but a simple 2-D chart may be more clear Bar Charts can often be more effective

  40. Thank you! See you next time!!

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