In statistics, what does correlation measure?

Correlation measures the strength and direction of the relationship between two variables. It quantifies how closely related the changes in one variable are to changes in another. A positive correlation indicates that as one variable increases, the other also tends to increase, while a negative correlation suggests that as one variable increases, the other tends to decrease. This relationship is often depicted using a correlation coefficient, which ranges from -1 to +1. A coefficient close to 1 implies a strong positive correlation, while one close to -1 indicates a strong negative correlation. A coefficient around 0 suggests little to no linear relationship between the two variables.

The other choices focus on different statistical concepts. The first option pertains to comparisons between group means, often associated with t-tests or ANOVA rather than correlation. The third option relates to probability and the chances of specific outcomes occurring, which falls under a different branch of statistics. The fourth option deals with categorical data, typically analyzed using frequencies and distributions, rather than the numerical relationships that correlation focuses on. Thus, the answer about the strength and direction of the relationship between two variables accurately captures the essence of what correlation measures in statistics.