What does a correlation coefficient measure?

A correlation coefficient quantifies the relationship between two variables by measuring both the strength and direction of that relationship. A positive correlation indicates that as one variable increases, the other variable tends to also increase, while a negative correlation suggests that as one variable increases, the other tends to decrease. The value of the correlation coefficient ranges from -1 to 1, with values closer to 1 or -1 representing a stronger relationship and values near 0 indicating little to no relationship. This measure is essential in research as it helps to understand how two variables are associated, without implying causation.

In contrast, the central tendency of a dataset refers to measures like the mean, median, or mode, which summarize the dataset with a single value. The frequency of a specific outcome pertains to how often certain outcomes occur, which is not the focus of correlation coefficients. Lastly, the amount of variance explained by a model relates to the effectiveness of a statistical model in accounting for variability in the data, commonly assessed through other statistical measures such as R-squared, rather than correlation coefficients. Thus, the correct selection highlights the specific purpose of a correlation coefficient in research methodologies.