1. APPLIED DATA ANALYSIS IN CRIMINAL JUSTICE CJ 525 MONMOUTH UNIVERSITY Juan P. Rodriguez

2. Lecture 5 Assessing Associations Bivariate Analysis

3. Juan P. Rodriguez - Fall 2007 3 Perspective Research Techniques Accessing, Examining and Saving Data Univariate Analysis – Descriptive Statistics Constructing (Manipulating) Variables Association – Bivariate Analysis Association – Multivariate Analysis Comparing Group Means – Bivariate Multivariate Analysis - Regression

4. Juan P. Rodriguez - Fall 2007 4 Assessing Association – Bivariate Analysis Why do we need significance tests? Analyzing Bivariate Relationships Categorical Variables: Cross Tabulations Bar Charts Numerical Variables Correlations Scatter Plots

5. Juan P. Rodriguez - Fall 2007 5 Variable Relationships Questions addressed by SS examine relationships between variables: Is death penalty associated with lower crimes? Is school funding related to educational success? Are religious people more conservative? We need to understand if the observed relationships are true or the result of chance: significance tests

6. Juan P. Rodriguez - Fall 2007 6 Significance Tests Patterns in data are due to: Random Chance: the Null Hypothesis Real Relationships: the Alternate Hypothesis Significance Tests rely on Significance Levels, estimates of the probability degree to which chance is a likely explanation for the observed pattern: Probability: A mathematical measurement of the likelihood that an event has occurred or will occur. Ranges from 0 to 1

7. Juan P. Rodriguez - Fall 2007 7 Significance Tests A high SL indicates a strong possibility that the observed pattern is due to chance A low SL indicates that chance alone is unlikely to explain the observed pattern and thus the AH is to be considered SL give an exact estimate of the probability that chance produced a pattern in the data

8. Juan P. Rodriguez - Fall 2007 8 Significance Tests Statistically Significant: relationship is low enough Usually 0.05 or 0.01

9. Juan P. Rodriguez - Fall 2007 9 Significance Tests Based on: Strength of Association Sample size Strong Association for small samples Not as strong for large samples They do not indicate that: The relationship is important That relationship is causal

10. Juan P. Rodriguez - Fall 2007 10 Bivariate Relationships Categorical Variables Cross Tabulations: Grids of all possible combinations of the values of 2 categorical variables Example: Full and part-time work preferences by gender Load Dataset GSS98

11. Juan P. Rodriguez - Fall 2007 11 Bivariate Relationships Categorical Variables

12. Juan P. Rodriguez - Fall 2007 12 Bivariate Relationships Categorical Variables

13. Juan P. Rodriguez - Fall 2007 13 Bivariate Relationships Categorical Variables

14. Juan P. Rodriguez - Fall 2007 14 Bivariate Relationships Categorical Variables

15. Juan P. Rodriguez - Fall 2007 15 Bivariate Relationships Categorical Variables

16. Juan P. Rodriguez - Fall 2007 16 Bivariate Relationships Categorical Variables

17. Juan P. Rodriguez - Fall 2007 17 Bivariate Relationships Categorical Variables

18. Juan P. Rodriguez - Fall 2007 18 Bivariate Relationships Categorical Variables Null Hypothesis: No association between gender and job preference, i.e., women and men do not vary in their preferences for full and part time work

19. Juan P. Rodriguez - Fall 2007 19 Bivariate Relationships Categorical Variables

20. Juan P. Rodriguez - Fall 2007 20 Bivariate Relationships Categorical Variables Group sample sizes are not equal (they rarely are) A solution is to convert the counts to percentages:

21. Juan P. Rodriguez - Fall 2007 21 Bivariate Relationships Categorical Variables

22. Juan P. Rodriguez - Fall 2007 22 Bivariate Relationships Categorical Variables

23. Juan P. Rodriguez - Fall 2007 23 Bivariate Relationships Categorical Variables

24. Juan P. Rodriguez - Fall 2007 24 Bivariate Relationships Categorical Variables

25. Juan P. Rodriguez - Fall 2007 25 Bivariate Relationships Categorical Variables

26. Juan P. Rodriguez - Fall 2007 26 Bivariate Relationships Categorical Variables There seems to be a relationship between sex and work preferences: Men (71%) are more willing than women (46.6%) to say they prefer full time work Women are more willing than men to say they prefer to work part time It would appear the the Null Hypothesis is false. Before making that conclusion, we need a Test of Significance

27. Juan P. Rodriguez - Fall 2007 27 Bivariate Relationships Categorical Variables SPSS offers several tests of significance We’ll use Chi Square

28. Juan P. Rodriguez - Fall 2007 28 Bivariate Relationships Categorical Variables

29. Juan P. Rodriguez - Fall 2007 29 Bivariate Relationships Categorical Variables

30. Juan P. Rodriguez - Fall 2007 30 Bivariate Relationships Categorical Variables

31. Juan P. Rodriguez - Fall 2007 31 Bivariate Relationships Categorical Variables

32. Juan P. Rodriguez - Fall 2007 32 Bivariate Relationships Categorical Variables

33. Juan P. Rodriguez - Fall 2007 33 Bivariate Relationships Categorical Variables

34. Juan P. Rodriguez - Fall 2007 34 Bivariate Relationships Categorical Variables

35. Juan P. Rodriguez - Fall 2007 35 Bivariate Relationships Categorical Variables Results of Significance Test: Relationship is statistically significant because the significance level is 0.000 The probability that the observed relationship between sex and work preference is random is less than 1/1000

36. Juan P. Rodriguez - Fall 2007 36 Bivariate Relationships Bar Charts Display Bivariate relationships between 2 categorical variables We’ll graph the relationship in previous example

37. Juan P. Rodriguez - Fall 2007 37 Bivariate Relationships Bar Charts

38. Juan P. Rodriguez - Fall 2007 38 Bivariate Relationships Bar Charts

39. Juan P. Rodriguez - Fall 2007 39 Bivariate Relationships Bar Charts

40. Juan P. Rodriguez - Fall 2007 40 Bivariate Relationships Bar Charts

41. Juan P. Rodriguez - Fall 2007 41 Bivariate Relationships Bar Charts

42. Juan P. Rodriguez - Fall 2007 42 Bivariate Relationships Bar Charts

43. Juan P. Rodriguez - Fall 2007 43 Bivariate Relationships Bar Charts

44. Juan P. Rodriguez - Fall 2007 44 Bivariate Relationships Bar Charts

45. Juan P. Rodriguez - Fall 2007 45 Bivariate Relationships Bar Charts

46. Juan P. Rodriguez - Fall 2007 46 Bivariate Relationships Bar Charts The Bar Chart shows quite clearly how women outnumber men in their preference for part time jobs

47. Juan P. Rodriguez - Fall 2007 47 Bivariate Relationships Numerical Variables Numerical Variables display a range of values: Age, Income, miles driven to work Analysis: Recode them into categorical variables and do cross tabulation Correlation analysis on numerical values

48. Juan P. Rodriguez - Fall 2007 48 Bivariate Analysis - Numerical Variables Correlations Correlation is a measure of the degree to which the values in 2 variables correspond to each other Pearson’s Correlation coefficient measures the strength of the Linear relationship between 2 variables Other types of relationships: curvilinear, U shaped, inverted U

49. Juan P. Rodriguez - Fall 2007 49 Bivariate Analysis - Numerical Variables Correlations

50. Juan P. Rodriguez - Fall 2007 50 Bivariate Analysis - Numerical Variables Correlations Linear Relationships A change in one variable is associated with a consistent change in another variable Correlation coefficients: -1 to 1

51. Juan P. Rodriguez - Fall 2007 51 Bivariate Analysis - Numerical Variables Correlations We’ll examine relationship between “social disorganization” and suicide Social disorganization indicators: crime, divorce, substance abuse Null Hypothesis: There is no real linear relationship between suicide rates and divorce rates Alternate Hypothesis: There is a positive linear relationship

52. Juan P. Rodriguez - Fall 2007 52 Bivariate Analysis - Numerical Variables Correlations Use States dataset

53. Juan P. Rodriguez - Fall 2007 53 Bivariate Analysis - Numerical Variables Correlations

54. Juan P. Rodriguez - Fall 2007 54 Bivariate Analysis - Numerical Variables Correlations

55. Juan P. Rodriguez - Fall 2007 55 Bivariate Analysis - Numerical Variables Correlations

56. Juan P. Rodriguez - Fall 2007 56 Bivariate Analysis - Numerical Variables Correlations

57. Juan P. Rodriguez - Fall 2007 57 Bivariate Analysis - Numerical Variables Correlations

58. Juan P. Rodriguez - Fall 2007 58 Bivariate Analysis - Numerical Variables Correlations There is a positive relationship between divorce and suicide rates (0.683). This relationship is statistically significant (P<0.001)

59. Juan P. Rodriguez - Fall 2007 59 Bivariate Analysis - Numerical Variables Scatterplots Graph relationships between 2 numerical variables The “independent” variable is placed on the X axis and the dependent on the Y axis

60. Juan P. Rodriguez - Fall 2007 60 Bivariate Analysis - Numerical Variables Scatter plots

61. Juan P. Rodriguez - Fall 2007 61 Bivariate Analysis - Numerical Variables Scatter plots

62. Juan P. Rodriguez - Fall 2007 62 Bivariate Analysis - Numerical Variables Scatter plots

63. Juan P. Rodriguez - Fall 2007 63 Bivariate Analysis - Numerical Variables Scatter plots

64. Juan P. Rodriguez - Fall 2007 64 Bivariate Analysis - Numerical Variables Scatter plots

65. Juan P. Rodriguez - Fall 2007 65 Bivariate Analysis - Numerical Variables Scatter plots