bivariate analysis to real-world criminal justice problems.

Module 5: Bivariate Analysis of Qualitative Variables
When statistically describing a variable, we engage in univariate analysis. Statistics for such an analysis are called descriptive statistics. They are qualitative in nature, describing or categorizing certain characteristics or attributes of a research subject/participant. Examples of descriptive statistics include age, race, gender, ethnicity, and education level. In criminal justice, measurements that categorize occupational status, rank or career label (e.g., probation officer, juvenile parole officer, police captain, defense attorney, forensic psychologist/therapist, victim advocate) are also considered descriptive statistics. Measurements or categorizations of offender types (e.g., burglar, arsonist, robber, child molester, rapist, violent, non-violent, juvenile, adult) are considered descriptive statistics generated via univariate analysis in SPSS.

When statistically exploring a relationship between two variables, we engage in bivariate analysis and use inferential statistics in such analyses. Example of bivariate analyses are:

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Measuring the strength of correlation between the variable of psychopathy and the variable of recidivism;
Determining the degree of association between the variable of police training and the variable of police shootings;
Analyzing the relationship between the variable of political party affiliation and the variable of prosecution decisions; and
Evaluating the association between the variable of victim advocacy engagement and the variable of victim attendance/participation as a witness in court.
Bivariate analysis not only involves an analysis to determine whether there is a statistically significant association/correlation between two variables, but also involves a determination of the strength and direction of any statistically significant relationship between the variables.

In Module 5, we explore these topics in detail and attempt to apply bivariate analysis to real-world criminal justice problems.

Learning Outcomes

Evaluate the properties of a bivariate relationship.
Construct and read contingency (crosstab) tables.
Test a hypothesis with Chi-square.
Differentiate between Lambda and Gamma.
For Your Success & Readings
Bivariate analysis refers to statistical techniques designed to observe and describe the relationship between two variables (as illustrated above in the Module Overview).

Understanding levels of measurement (i.e., nominal, ordinal and ratio/scale), which may be coded dichotomously or categorically (1=yes, the offender recidivated; 0=no, the offender did not recidivate) or coded to reflect ordinal levels (-1=disagree with gun control efforts; 0=feel neutral about gun control efforts; +1=agree with gun control efforts; or 1=1st place in a race; 2=2nd place and 3=3rd place) and/or kept numerically uncoded on numeric continuous scale in accordance with actual measurements (such as age in years; time in hours, months or years; or temperature in degrees centigrade) is crucial in this course. Feel free to reach out to your instructor if you have any questions relative to levels of measurement. There is also plenty of information contained in our textbook(s) and via OnlineStatBook .

This module addresses bivariate analysis of the relationship between two categorical variables measured at the nominal and ordinal levels of measurement. Future modules will address bivariate analysis of continuous/ratio/scale/interval variables.

Make sure you participate in this week’s Discussion.

You are encouraged to skim the two research articles in recommended readings to get a sense of how bivariate analyses are completed and applied to criminal justice practice.


Chapters 9 & 10 in Social Statistics for a Diverse Society
Chapter 17 in Online Statistics Education: A Multimedia Course of Study

Konopasek, J. E. (2015). Expeditious disclosure of sexual history via polygraph testing: Treatment outcome and sex offense recidivism. Journal of Offender Rehabilitation, 54(3), 194-211.
Taub, S., Feingold, D., Rehm, J., & Lev-Ran, S. (2018). Patterns of cannabis use and clinical correlates among individuals with major depressive disorder and bipolar disorder. Comprehensive Psychiatry, 80, 89-96.
Tredoux, C., & Durrheim, K. (2004). Numbers, hypotheses & conclusions: A course in statistics for the social sciences. Cape Town: University of Cape Town Press.

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