Which statement is true about correlation and causation?

• A. Correlation measures association between variables, but it does not by itself establish a cause-and-effect relationship.
• B. A strong correlation between two variables implies that changes in one variable cause changes in the other.
• C. If two variables have zero correlation, then they are independent in all cases.
• D. Correlation can only be computed for categorical variables.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the concept of correlation. Correlation is a statistical measure that describes the strength and direction of a linear relationship between two quantitative variables. It is usually represented by the correlation coefficient, denoted as \(r\), which ranges from \(-1\) to \$1$.
2. Step 2: Recognize that correlation measures association, not causation. This means that even if two variables have a strong correlation (positive or negative), it does not necessarily mean that one variable causes the other to change. There could be other factors or confounding variables involved.
3. Step 3: Clarify the difference between correlation and independence. Zero correlation means no linear relationship between variables, but it does not guarantee that the variables are independent in all cases, because they might have a non-linear relationship.
4. Step 4: Understand the types of variables for which correlation can be computed. Correlation coefficients like Pearson's \(r\) are designed for continuous (quantitative) variables, not categorical variables. For categorical variables, other measures of association are used.
5. Step 5: Summarize the correct statement: Correlation measures association between variables, but it does not by itself establish a cause-and-effect relationship.