Criminal Justice agencies often gather large quantities of variables to be used in descriptive analyses. That is, to help describe situations, populations, and so on. For instance, the Department of Corrections collects data on inmates. Variables often include crime type, race, gender, originating jurisdiction (where they were convicted), education level, and many others.
These data are often captured categorically rather than numerically. For instance, education level might be captured by simply identifying the name of the highest grade an offender achieved, such as high school diploma or GED, Bachelor’s degree, Associates degree, and so forth. Similarly, race data are most often captured by recording the label of the race the offender belongs to, such as Caucasian, African American, Asian, Native American, Pacific Islander, and so on. These labels have no inherent numerical value because they are simply categories. Thus, they are categorical variables.
You cannot use traditional statistical analysis to investigate relationships between categorical variables because they are not numbers. Instead, you would use nonparametric tests, such as the chi-square test of independence. You will use this test to investigate the data below.
This assignment has 2 steps.
Step 1: Watch both of the following videos regarding chi-square analysis:
Filling Out Frequency Table for Independent Events
Contingency Table Chi-Square Test
Step 2: Calculate chi-square using the data in the table below, this Chi Square Example Handout, and the Distribution Values Chart that go with this IP.
Using the Chi-Square Example Handout and the Chi-Square Distribution Values Chart as guides to figure the calculations, calculate chi-square for the following data:
Originating Jurisdiction Caucasian African American
Denver County 16 3
El Paso County 4 6
Pueblo County 6 15
Then, answer the following questions about your results:
What is the column total for Caucasian?
What is the column total for African American?
What is the row total for Denver County?
What is the row total for El Paso County?
What is the row total for Pueblo County?
Are race and originating jurisdiction significantly dependent? How do you know?
What is the final chi-square value?
How many degrees of freedom are there for this chi-square table?
What is the value for the 0.05 significance level and 2 degrees of freedom on the Chi-Square Distribution Values Chart?
Do you reject or accept the null hypothesis that states, “Originating Jurisdiction and Race are not significantly dependent (they are independent)”?
For assistance with your assignment, please use your text, Web resources, and all course materials.
Khan Academy. (2017a). Contingency table chi-square test [Video file]. Retrieved from https://www.khanacademy.org/math/statistics-probability/inference-categorical-data-chi-square-tests/chi-square-tests-for-homogeneity-and-association-independence/v/contingency-table-chi-square-test
Khan Academy. (2017b). Filling out frequency table for independent events [Video file]. Retrieved from https://www.khanacademy.org/math/statistics-probability/inference-categorical-data-chi-square-tests/chi-square-tests-for-homogeneity-and-association-independence/v/frequency-table-independent-events