What does a correlation coefficient measure?

The correlation coefficient specifically measures the strength and direction of the relationship between two variables. This statistical measure quantifies how closely related two variables are. A correlation coefficient can range from -1 to +1, where values close to +1 indicate a strong positive relationship (as one variable increases, the other also increases), values close to -1 indicate a strong negative relationship (as one variable increases, the other decreases), and values near 0 suggest no relationship. This makes the correlation coefficient an essential tool for researchers looking to understand associations between variables in criminal justice studies, as it can highlight patterns and potential causal relationships that may warrant further investigation.

In contrast, the mean of a data set focuses on the average value of a single variable, failing to capture relational dynamics between pairs of variables. The distribution of a single variable deals with how data points are spread across different values, which does not provide insight into relationships. Lastly, the effectiveness of statistical tests evaluates how well a particular test performs in detecting relationships or differences, rather than describing the nature of a relationship between two variables.