2. Lecturer’s desk Physics- atmospheric Sciences (PAS) - Room 201 s c r e e n Row A Row B Row C Row D Row E Row F Row G Row H 131211109 87 Row A 14131211109 87 Row B 1514131211109 87 Row C 1514131211109 87 Row D 16 1514131211109 87 Row E 17 16 1514131211109 87 Row F 1716 1514131211109 87 Row G 1716 1514131211109 87 Row H 16 18 table Row A Row B Row C Row D Row E Row F Row G Row H 15141716 1819 16 15 18171920 17161918 2021 18172019 2122 19182120 2223 20192221 2324 18172019 2122 19182120 2223 2143 56 2143 56 2143 56 2143 56 2143 56 2143 56 2143 56 2143 56 Row J Row K Row L Row M Row N Row P 2143 5 2143 5 2143 5 2143 5 2143 5 1 5 Row J Row K Row L Row M Row N Row P 27262928 30 25242726 28 24232625 27 23222524 26 25242726 28 27262928 30 6 14 131211109 87 16151817 19 202122 614131211109 87 16 15 18 17 19 20212223 614131211109 87 16 15 18171920 2122 23 6 14 131211109 87 1624181719 20 2122 231525 6 14 131211109 87 1624181719 20 2122 231525 Row Q 2143 5 27262928 30 6 14 131211109 87 242223 21 - 15 25 37363938 40 34 3132 3335 69 87 13 table 14 18 192021 Hand in (Optional) Revised Memo

3. MGMT 276: Statistical Inference in Management Fall 2015

4. We’ll be starting this today

5. Just for Fun Assignments Go to D2L - Click on “Content” Click on “Interactive Online Just-for-fun Assignments” Complete Assignments 1 – 7 Please note: These are not worth any class points and are different from the required homeworks

6. Schedule of readings Before next exam: September 24 th Please read chapters 1 - 4 & Appendix D & E 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

7. By the end of lecture today 9/15/15 Questionnaire design and evaluation Surveys and questionnaire design Correlational methodology Positive, Negative and Zero correlation Strength and direction Writing Summaries of results

8. Homework Assignment Assignment 4 Describing Data Visually using MS Excel Due: Thursday, September 17 th

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

10. 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 Range between -1 and +1 The closer to zero the weaker the relationship The closer to zero the weaker the relationship and the worse the prediction Positive or negative Positive or negative

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

12. Height of Mothers by Height of Daughters Positive Correlation Height of Daughters Height of Mothers 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

13. Brushing teeth by number cavities Negative Correlation Number Cavities Brushing Teeth 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

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

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

16. Correlation

17. Is it possible that they are causally related? Correlation does not imply causation 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 Birthday Cakes Number of Birthdays

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

19. 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

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

21. r = +0.97 This shows a strong positive relationship (r = 0.97) between the price of the house and its eventual sales price Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

22. r = +0.97r = -0.48 This shows a moderate negative relationship (r = -0.48) between the amount of pectin in orange juice and its sweetness Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

23. r = -0.91 This shows a strong negative relationship (r = -0.91) between the distance that a golf ball is hit and the accuracy of the drive Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

24. r = -0.91 r = 0.61 This shows a moderate positive relationship (r = 0.61) between the price of the length of stay in a hospital and the number of services provided Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

25. r = +0.97r = -0.48 r = -0.91 r = 0.61

26. Height of Daughters (inches) Height of Mothers (in) 48 52 56 60 64 68 72 76 48 52 5660 64 68 72 This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Both axes and values are labeled Both axes have real numbers listed Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

27. Height of Daughters (inches) Height of Mothers (in) 48 52 56 60 64 68 72 76 48 52 5660 64 68 72 This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Both axes and values are labeled Both axes have real numbers listed Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

28. Height of Daughters (inches) Height of Mothers (in) 48 52 56 60 64 68 72 76 48 52 5660 64 68 72 This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Both axes and values are labeled Both axes have real numbers listed Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

29. Height of Daughters (inches) Height of Mothers (in) 48 52 56 60 64 68 72 76 48 52 5660 64 68 72 This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Both axes and values are labeled Both axes have real numbers listed Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

30. Height of Daughters (inches) Height of Mothers (in) 48 52 56 60 64 68 72 76 48 52 5660 64 68 72 This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Both axes and values are labeled Both axes have real numbers listed Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number)

31. 1. Describe one positive correlation Draw a scatterplot (label axes) 2. Describe one negative correlation Draw a scatterplot (label axes) 3. Describe one zero correlation Draw a scatterplot (label axes) Break into groups of 2 or 3 Each person hand in own worksheet. Be sure to list your name and names of all others in your group Use examples that are different from those is lecture 4. Describe one perfect correlation (positive or negative) Draw a scatterplot (label axes) 5. Describe curvilinear relationship Draw a scatterplot (label axes) You have 12 minutes (approximately 2 minutes per example)

32. Height of Daughters (inches) Height of Mothers (in) 48 52 56 60 64 68 72 76 48 52 5660 64 68 72 This shows the strong positive (r = +0.8) relationship between the heights of daughters (in inches) with heights of their mothers (in inches). Both axes and values are labeled Both axes have real numbers listed 1. Describe one positive correlation Draw a scatterplot (label axes) 2. Describe one negative correlation Draw a scatterplot (label axes) 3. Describe one zero correlation Draw a scatterplot (label axes) 4. Describe one perfect correlation (positive or negative) Draw a scatterplot (label axes) 5. Describe curvilinear relationship Draw a scatterplot (label axes) Variable name is listed clearly Description includes: Both variables Strength (weak,moderate,strong) Direction (positive, negative) Estimated value (actual number) Hand in Correlation worksheet

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

34. Another example: How many kids in your family? 3 4 8 2 2 1 4 1 14 2 Number of kids in family 1414 3232 1818 4242 214

35. Measures of Central Tendency (Measures of location) The mean, median and mode Mean: The balance point of a distribution. Found by adding up all observations and then dividing by the number of observations Mean for a sample: Mean for a population: ΣX / N = mean = µ (mu) Note: Σ = add up x or X = scores n or N = number of scores Σx / n = mean = x Measures of “location” Where on the number line the scores tend to cluster

36. Measures of Central Tendency (Measures of location) The mean, median and mode Mean: The balance point of a distribution. Found by adding up all observations and then dividing by the number of observations Mean for a sample: Note: Σ = add up x or X = scores n or N = number of scores Σx / n = mean = x Number of kids in family 14 32 18 42 214 41/ 10 = mean = 4.1

37. How many kids are in your family? What is the most common family size? Number of kids in family 13 14 24 28 214 Median: The middle value when observations are ordered from least to most (or most to least)

38. How many kids are in your family? What is the most common family size? Median: The middle value when observations are ordered from least to most (or most to least) 1, 3, 1, 4, 2, 4, 2, 8, 2, 14 1, 2, 3, 4, 8, 14 Number of kids in family 14 32 18 42 214

39. Number of kids in family 14 32 18 42 214 14 8, 4, 2, 1, How many kids are in your family? What is the most common family size? Number of kids in family 13 14 24 28 214 Median: The middle value when observations are ordered from least to most (or most to least) 1, 3, 1, 4, 2, 4, 2, 8, 2, 14 2.5 2, 3, 1, 2, 4, 2, 4,8, 1, 14 2, 3, 1, Median always has a percentile rank of 50% regardless of shape of distribution 2 + 3 µ = 2.5 If there appears to be two medians, take the mean of the two Median also called the 2 nd Quartile

40. 4, Number of kids in family 14 32 18 42 214 14 8, 4, 2, 1, How many kids are in your family? What is the most common family size? Number of kids in family 13 14 24 28 214 2, 1, 2, 4, 2, 4, 8, 1, 14 2, 1, 14 8, 4, 2, 1, 2, 3, 1, 2, 3, Median: The middle value when observations are ordered from least to most (or most to least) 1 st Quartile Middle number of lower half of scores Lower half Upper half 3 rd Quartile Middle number of upper half of scores 3, 2.5 2 nd Quartile Middle number of all scores (Median)

41. Mode: The value of the most frequent observation Number of kids in family 13 14 24 28 214 Score f. 12 23 31 42 50 60 70 81 90 100 110 120 130 141 Please note: The mode is “2” because it is the most frequently occurring score. It occurs “3” times. “3” is not the mode, it is just the frequency for the value that is the mode Bimodal distribution: If there are two most frequent observations

42. What about central tendency for qualitative data? Mode is good for nominal or ordinal data Median can be used with ordinal data Mean can be used with interval or ratio data

43. Overview Frequency distributions The normal curve Mean, Median, Mode, Trimmed Mean 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 Skewed right, skewed left unimodal, bimodal, symmetric