SOC 4930 & SOC 5050 - Week 10

Lecture slides for Week 10 of the Saint Louis University Course Quantitative Analysis: Applied Inferential Statistics. These slides cover the topics related to correlation analyses. Handouts created in RMarkdown are also discussed.

Transcript

1. Make sure you clone the lecture-10 repo using GitHub Desktop so that we can get right in to today’s lecture! WELCOME! GETTING STARTED
2. CORRELATION 
 (PART 1) QUANTITATIVE ANALYSIS CHRISTOPHER PRENER, PH.D. FALL 2018 WEEK 10 LECTURE 10
3. AGENDA QUANTITATIVE ANALYSIS / WEEK 10 / LECTURE 10 1. Front Matter 2. Public Polling 3. Handouts 4. Covariance 5. Scatterplots 6. Pearson’s R 7. Back Matter
4. 1 FRONT 
 MATTER
5. 1. FRONT MATTER ANNOUNCEMENTS How have the ITS related issues been? Final project presentation and handout drafts due next Monday! Lab 09 due next Monday! We will not have any additional lecture preps after today. Midterm grades were very strong. Well done!
6. PUBLIC POLLING 2
7. 2. PUBLIC POLLING INTERPRETING A GIVEN POLL
8. 2. PUBLIC POLLING MARGIN OF ERROR AND N
9. 2. PUBLIC POLLING INTERPRETING A GIVEN POLL
13. 2. PUBLIC POLLING SOURCES OF ERROR: INTENTION VS. TURNOUT
14. 2. PUBLIC POLLING SOURCES OF ERROR: LIKELY VOTER SCREENS
15. 2. PUBLIC POLLING SOURCES OF ERROR: LIKELY VOTER SCREENS
16. 2. PUBLIC POLLING SOURCES OF ERROR: LIKELY VOTER SCREENS
17. 2. PUBLIC POLLING SOURCES OF ERROR: LIKELY VOTER SCREENS
18. 2. PUBLIC POLLING SOURCES OF ERROR: SURVEY MECHANISM
19. 2. PUBLIC POLLING SOURCES OF ERROR: SURVEY MECHANISM
20. 2. PUBLIC POLLING SOURCES OF ERROR: SOCIAL DESIRABILITY
21. 2. PUBLIC POLLING SOURCES OF ERROR: NON-RESPONSE
22. 2. PUBLIC POLLING SOURCES OF ERROR: NON-RESPONSE
23. 2. PUBLIC POLLING SOURCES OF ERROR: SURVEY MECHANISM
24. SOURCES OF ERROR: SURVEY MECHANISM
25. 2. PUBLIC POLLING SOURCES OF ERROR: DEMOGRAPHIC WEIGHTS
26. 2. PUBLIC POLLING SOURCES OF ERROR: DEMOGRAPHIC WEIGHTS
27. 2. PUBLIC POLLING HOUSE EFFECTS
28. 2. PUBLIC POLLING HOUSE EFFECTS
29. 2. PUBLIC POLLING POLLING ERROR = UNCERTAINTY
30. 2. PUBLIC POLLING POLLING ERROR = UNCERTAINTY
31. 2. PUBLIC POLLING POLLING ERROR = UNCERTAINTY
32. 2. PUBLIC POLLING POLLING ERROR = UNCERTAINTY
33. 2. PUBLIC POLLING MANAGING UNCERTAINTY: AVERAGES
34. 2. PUBLIC POLLING MANAGING UNCERTAINTY: HERDING
35. 2. PUBLIC POLLING MANAGING UNCERTAINTY: RATING http://projects.fivethirtyeight.com/pollster-ratings/
36. 2. PUBLIC POLLING MANAGING UNCERTAINTY: RATING http://flowingdata.com/2016/07/28/what-that- election-probability-means/
37. 2. PUBLIC POLLING WHAT HAPPENED IN 2016?
38. WHAT HAPPENED IN 2016?
39. 2. PUBLIC POLLING WHAT HAPPENED IN 2016?
40. WHAT HAPPENED IN 2016?
41. HANDOUTS 3
42. This section supersedes final project instructions - this is the method you should use for creating your handout!
43. COVARIANCE 4
44. ▸ s2 = variance ▸ x = value of observation ▸ x = mean of x ▸ n = sample size 4. COVARIANCE Let: VARIANCE Second Moment
45. 4. COVARIANCE VARIANCE RE-STATED
46. 4. COVARIANCE COVARIANCE ▸ s2 = variance ▸ x = value of observation ▸ x = mean of x ▸ y = value of observation ▸ y = mean of y ▸ n = sample size Let:
47. SCATTERPLOTS 5
48. SCATTER PLOT
49. SCATTER PLOT WITH GROUPS
50. SCATTER PLOT WITH FACETS
51. SCATTER PLOT WITH LINE
52. SCATTER PLOT WITH GROUP LINES
53. SCATTER PLOT WITH FACETS & GROUP LINES
54. SCATTER PLOT WITH LOESS
55. PEARSON’S R 6
56. ▸ English mathematician ▸ Student of Sir Francis Galton (and, like Galton, he was a eugenicist and social Darwinist) ▸ Developed the “product-moment correlation coefficient” based on work Galton had done in 19th century. ▸ Also introduced “moments”, histograms, and core concepts related to statistical significance (including the “p-value”)! 6. PEARSON’S R KARL PEARSON
57. 6. PEARSON’S R COVARIANCE
58. 6. PEARSON’S R CORRELATION Product of first moments Product-Moment Correlation Coefficient
59. 6. PEARSON’S R CORRELATION ▸ x = value of observation ▸ x = mean of x ▸ y = value of observation ▸ y = mean of y ▸ sx = std. deviation of x ▸ sy = std. deviation of y ▸ n = sample size Let:
60. 6. PEARSON’S R PEARSON’S R 
 Assumptions: 1. Both x and y should be continuous, normally distributed variables 2. There should be a linear relationship between x and y 3. Sufficiently large sample size (n >= 30) 4. There should be no extreme outliers
61. 5. DEPENDENT SAMPLES SAMPLE MEAN z = [ 1, 3, 4, 16, 18, 19, 22, 36, 52, 64, 81 ] a = [ 2, 2, 4, 10, 16, 21, 28, 36, 52, 64, 81 ] b = [ 2, 3, 3, 5, 6, 10, 14, 15, 17, 22, 219 ]
66. 6. PEARSON’S R PEARSON’S R 
 Interpretation: 1. Range: -1 <= r <= 1 2. Direction: negative or positive?
69. 6. PEARSON’S R PEARSON’S R 
 Interpretation: 1. Range: -1 <= r <= 1 2. Direction: negative or positive? 3. Effect size (absolute value): •Weak: 0 <= r < .3 •Moderate: .3 <= r < .6 •Strong: .6 <= r < 1
70. 6. PEARSON’S R PEARSON’S R 
 Interpretation: http://istics.net/Correlations/
71. ▸ Squaring r will give us a value of 
 0 <= r2 <= 1 ▸ r2 value corresponds to the amount of variation that x accounts for in y (or vice versa) • This is not casual ▸ A r2 value of .8 suggests that x accounts for 80% of the variance in y 6. PEARSON’S R PERCENT OF VARIANCE
72. ▸ t = t value ▸ r = correlation coefficient ▸ r2 = variance accounted for ▸ v = degrees of freedom (n-2) 6. PEARSON’S R Let: STATISTICAL SIGNIFICANCE Use function from Week-07 to find the p value associated with t.
73. 6. PEARSON’S R PEARSON’S R 
 Report: 1. The value of r and the associated p value 2. The direction of the relationship (positive or negative) 3. The strength of the relationship (weak, moderate, or strong) 4. The r2 value - how much of the variation does x account for in y? 5. A plain English interpretation of the observed relationship.
74. COMMON PITFALLS ▸ Correlation != causation, but we should not dismiss strong correlations as not being suggestions of causality either ▸ r ≈ 0 does not imply independence (check for non-linearity) ▸ Ecological fallacy - correlations between groups are stronger than correlations within groups ▸ Simpson’s Paradox - correlations within groups may have different directions than correlation overall 6. PEARSON’S R
80. 7 BACK 
 MATTER
81. AGENDA REVIEW 7. BACK MATTER 2. Public Polling 3. Handouts 4. Covariance 5. Scatterplots 6. Pearson’s R
82. We will not have any additional lecture preps after today. Midterm grades were very strong. Well done! REMINDERS 7. BACK MATTER Final project presentation and handout drafts due next Monday! Lab 09 due next Monday!