# Corellation: Statistics

Fox, Levin, & Forde, Elementary Statistics in Criminal Justice Research (4th ed.)

• Chapter 10: Correlation

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• Chapter 15: Cousins or Just Good Friends? Testing Relationships Using the Correlation Coefficient

·  Module notes

Correlation

When we use hypothesis tests, we ask the question, “Are these groups different?” The answer we get is not very precise. We can tell if the groups are different; and, depending on how we set up the null and research hypotheses, we may be able to tell the direction of the difference. But beyond that, we have very little information about how the groups differ.

For example, using hypothesis tests, we may be able to tell if younger males (less than 25 years of age) have higher arrest rates than older males (men 25 years and older). However, we cannot tell how much the arrest rate changes with each additional year of age. In order to make policies, it is frequently necessary to have a more precise measurement of how variables are associated. Correlation coefficients allow us to not only measure whether two variables are related, but, if they are, to determine the nature of the relationship.

A word of caution about this correlation: Correlation is not causation. Just because two variables are related, it does not mean that one causes the other. Many new statisticians make this assumption, which can be very problematic. In order to tease out causal relationships, studies have to be designed to do so if a study, and the theoretical foundation underlying the study, is not geared towards finding causality, statistics cannot help you do so.

Correlation

Correlations are widely used in research papers, institutional reports, and media articles. Understanding what correlation means in the context of the study, what it can tell you, and how it can help you interpret the data is an important skill.

Review one of the following articles:

Respond to the questions below:

• What are the variables in the study? Identify the independent and the dependent variables. How are the variables measured?
• Is the sample appropriate for the study? What is the data collection method?
• What are the variables of interest in the correlation?
• What is the correlation coefficient? Is it a strong correlation?
• Based on theory, do you expect a relationship between the variables? Explain. Does the correlation match your expectation?
• What other variables may have an effect on the dependent variable? Are any of those variables related to the independent variable?
• Could the correlation be coincidental? Explain.