APPLIED DATA ANALYSIS IN CRIMINAL JUSTICE

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APPLIED DATA ANALYSIS IN CRIMINAL JUSTICE

• CJ 525
• MONMOUTH UNIVERSITY
• Juan P. Rodriguez

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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

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Lecture 6

• Comparing Group Means
• Bivariate Analysis

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

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One Way ANOVA

• How much the Mean Values of a Numerical Variable
  differ among the categories of a categorical
  variable

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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

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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

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Analysis Of Variance
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Analysis Of Variance
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Analysis Of Variance
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Analysis Of Variance
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Analysis Of Variance
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Analysis Of Variance
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Analysis Of Variance
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Analysis Of Variance
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Analysis Of Variance
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Analysis Of Variance
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Analysis Of Variance
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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

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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

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Bar Chart
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Bar Chart
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Bar Chart
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Bar Chart
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Bar Chart
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Bar Chart
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Bar Charts- Results

• Separated and widowed people watch more TV, on
  the average, than the other categories of people

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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

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Box Plots
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Box Plots
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Box Plots
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Box Plots
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Box Plots
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Box Plots
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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

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Post-hoc Tests
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Post-hoc Tests
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Post-hoc Tests
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Post-hoc Tests
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Post-hoc Tests
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Post-hoc Tests
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Post-hoc Tests
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Post-hoc Tests
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Post-hoc Tests
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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.

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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.

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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.)

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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.

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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.

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Assumptions - Normality
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Assumptions - Normality
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Assumptions - Normality
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Variance Homogeneity
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Variance Homogeneity
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Variance Homogeneity
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Variance Homogeneity
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t Tests

• Compares the means of 2 groups
• Independent samples
• Paired Samples

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t Test - Independent
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t Test - Independent
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t Test - Independent
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t Test - Independent
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t Test - Independent
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t Test - Paired

• Categories are related
• Are rates of incarceration the same for black
  (PRC61) and whites (PRC58) in the states dataset?
• Assumption is that states with high incarceration
  rates will tend to have high rates for blacks and
  whites

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t Test - Paired
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t Test - Paired
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t Test - Paired
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t Test - Paired
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t Test - Paired
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t Test - Paired