APPLIED DATA ANALYSIS IN CRIMINAL JUSTICE

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

2. 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

3. Lecture 6 Comparing Group Means Bivariate Analysis

4. Relationships between categorical and numerical variables • ANOVA: • Compares group means • Test for significance • Bar Charts and Box Plots • Tests for Differences in means

5. One Way ANOVA • How much the Mean Values of a Numerical Variable differ among the categories of a categorical variable

6. One Way ANOVA • Example: Relationship between television viewing and marital status in GSS98 dataset • TVHOURS: numerical variable – number of hours spent watching TV per day • MARITAL: categorical variable – married, widowed, divorced, separated and never married

7. One Way ANOVA • Null Hypothesis: • No relationship - People in all groups watch, on average, the same amount of television • Alternate Hypothesis: • There is a relationship – At least 2 of the categories differ in the number of hours of television watched

8. Analysis Of Variance

9. Analysis Of Variance

10. Analysis Of Variance

11. Analysis Of Variance

12. Analysis Of Variance

13. Analysis Of Variance

14. Analysis Of Variance

15. Analysis Of Variance

16. Analysis Of Variance

17. Analysis Of Variance

18. Analysis Of Variance

19. Analysis Of Variance • The differences in the Mean values for these groups are so large that are not likely due to chance: • There is a significant relationship between marital status and television viewing

20. Graphing ANOVA Results • Bar charts • Used to present data to general people or to people not well versed in statistics • Box Plots • Show both the central tendencies and the distributions of each category

21. Bar Chart

22. Bar Chart

23. Bar Chart

24. Bar Chart

25. Bar Chart

26. Bar Chart

27. Bar Charts- Results • Separated and widowed people watch more TV, on the average, than the other categories of people

28. Box Plots • Depict differences in both the spread and center among groups of means. • By placing box plots side by side, it is easy to compare distributions

29. Box Plots

30. Box Plots

31. Box Plots

32. Box Plots

33. Box Plots

34. Box Plots

35. Post-hoc Tests • ANOVA found significant differences among means with respect to TV viewing • Are only 2 means significantly different? • Are all of them are significantly different? • Or anything in between?. • Post-hoc tests tell us this

36. Post-hoc Tests

37. Post-hoc Tests

38. Post-hoc Tests

39. Post-hoc Tests

40. Post-hoc Tests

41. Post-hoc Tests

42. Post-hoc Tests

43. Post-hoc Tests

44. Post-hoc Tests

45. Assumptions in ANOVA • Within each sample, the values are independent, and identically normally distributed (same mean and variance). • The samples are independent of each other. • The different samples are all assumed to come from populations with the same variance, allowing for a pooled estimate of the variance. • For a multiple comparisons test of the sample means to be meaningful, the populations are viewed as fixed, so that the populations in the experiment include all those of interest.

46. Assumptions of ANOVA • Distributions are normal: • The one-way ANOVA's F test is not affected much if the population distributions are skewed unless the sample sizes are seriously unbalanced. • If the sample sizes are balanced, the F test will not be seriously affected by light-tailedness or heavy-tailedness, unless the sample sizes are small (less than 5), or the departure from normality is extreme (kurtosis less than -1 or greater than 2). • In cases of nonnormality, a nonparametric test or employing a transformation may result in a more powerful test.

47. Assumptions of ANOVA • Samples are Independent • A lack of independence within a sample is often caused by the existence of an implicit factor in the data. • Values collected over time may be serially correlated (here time is the implicit factor). • If the data are in a particular order, consider the possibility of dependence. (If the row order of the data reflect the order in which the data were collected, an index plot of the data [data value plotted against row number] can reveal patterns in the plot that could suggest possible time effects.)

48. Assumptions of ANOVA • Variances are homogeneous: • Assessed by examination of the relative size of the sample variances, either informally (including graphically), or by a robust variance test such as Levene's test. • The risk of having unequal sample variances is incorrectly reporting a significant difference in the means when none exists. The risk is higher with greater differences between variances, particularly if there is one sample variance very much larger than the others.

49. Assumptions of ANOVA • Variances are homogeneous (continued) • The F test is fairly robust against inequality of variances if the sample sizes are equal • If both nonnormality and unequal variances are present, use a transformation • A nonparametric test like the Kruskal-Wallis test still assumes that the population variances are comparable.

50. Assumptions - Normality