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Statistics Workshop B ivariate Descriptive Statistics J-Term 2009 Bert Kritzer

Statistics Workshop B ivariate Descriptive Statistics J-Term 2009 Bert Kritzer. Describing Relationships Between Two Variables. Variables X Predictor (“independent”) X i as the value for the i th observation Y Response (“dependent”) variables

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Statistics Workshop B ivariate Descriptive Statistics J-Term 2009 Bert Kritzer

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  1. Statistics WorkshopBivariate Descriptive StatisticsJ-Term 2009Bert Kritzer

  2. Describing Relationships Between Two Variables • Variables • X Predictor (“independent”) • Xi as the value for the ith observation • Y Response (“dependent”) variables • Yias the value for the ith observation • Depends on nature of two variables (e.g., two nominal, two interval, etc.) • Simple table • Percentages: the right and the wrong way • Difference of means or medians • Multiple boxplots • Regression: fitting a line through a “scatterplot” of points (Xis and Yis) • Correlation: Measuring the strength of the relationship

  3. Data Spreadsheet Paired Values

  4. Salary Example from Cope

  5. Variable Combinations

  6. Simple “Crosstabulation”Trust in the Police Question: How much of the time do you think you can trust the local police?

  7. Percentage TableTrust in the Police

  8. Percentage TableTrust in the Police

  9. How Not To Do Percentages Source: Sarver, Kaheny, & Szmer, The Attorney Gender Gap in U.S. Supreme Court Litigation, 91 Judicature 238, 248 (2008).

  10. More Informative Percentages

  11. Graphics for CrosstabulationsMultiple Pie Charts Trust in the Police by Race

  12. Graphics for CrosstabulationsStacked Bar Chart

  13. Feeling Thermometer Source: http://www.laits.utexas.edu/txp_media/html/poll/features/feeling/slide1.html (visited September 4, 2008)

  14. Table of MeansFT-SCOTUS by Ideology

  15. Bar Chart of Means

  16. FT-SCOTUSMeans with Standard Deviation Bars Note: Red dots represent mean; lines go one standard deviation above and below the mean.

  17. FT-SCOTUS by Ideology

  18. Litigation Rates as a Dot Plot

  19. Simple Scatter PlotStarchway Example from Cope

  20. Simple Scatter PlotTort Reform by Citizen Liberalism

  21. Scatter Plot with LineTort Reform by Citizen Liberalism

  22. The Regression Line The Line: An Observation: A Prediction: eiis the difference between the actual observed value, Yi, and the value of Y on the line that corresponds with Xi

  23. Fitting the Line • Eyeball • Split medians • Minimize sum of errors • Minimize sum of absolute errors • Minimize sum of squared errors (“Least Squares”)

  24. The Fitted Regression Line For every ten point increase in citizen liberalism, one less tort reform was adopted Y = 12.89 – 0.10X

  25. Salary Example from Cope

  26. Salary Example without Outlier

  27. Correlation • Measure of association; strength of relationship • Range: 0 to 1 or -1 to 0 to +1 • Proportional reduction in error (“PRE”) • Determining a prediction method • Setting a baseline • Non-PRE correlation coefficients

  28. (Goodman-Kruskal) LambdaTrust in Police by Race

  29. (Goodman-Kruskal) TauTrust in Police by Race

  30. R2 (or r2)Tort Reform by Citizen Liberalism

  31. Computing R2Tort Reform by Citizen Liberalism

  32. Correlation Coefficients

  33. Product Moment Correlation Traditional formula for r:

  34. Other Ways of Computing r Cope’s Method Traditional Method Sum values of X and sum the values of Y to get ΣX and ΣY Compute the square of X and Y Sum the values of X2 and sum the values of Y2 to get ΣX2 and ΣY2 Multiple together each pair of values for X and Y to get the product XY Sum the values of the product XY to get ΣXY Use the values in the formula below to get r

  35. Salary Example from Cope

  36. Time Plots: Showing Change Over TimeWomen Law Graduates & Women SC Clerks

  37. Predicting Clerk Gender

  38. eta2FT-SCOTUS by Ideology Baseline = 332462.11 Alternative = 316208.24 eta2= (332462.11 – 316208.24)/332462.11=.049 eta = .221

  39. Moving Beyond Two Variables Tort Reform by Citizen Liberalism & Elite Liberalism

  40. Multiple Regression ONE PREDICTOR: TWO PREDICTORS: or k PREDICTORS: or

  41. Multiple Regression: Tort Reform by Citizen and Elite Liberalism TortReformIndex = 13.032 – 0.062∙Citizen – 0.040∙Elite R2 = 0.264

  42. With Illustrations by the Author, A SQUARE(Edwin A. Abbott 1838-1926) 1884

  43. Lineland

  44. A Visitor from Spaceland(A Land of three Dimensions)

  45. Flatland(seen from above)

  46. Descriptive Statistics: Summary • Summarize and describe data • Univariate • Central tendency & dispersion • Distribution • Bivariate • Describe the relationship • Degree of relationship • Multivariate

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