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Chapter 28: Problem 10

When a correlation coefficient is statistically significant, what do you conclude about the two variables? What do the results mean with regard to cause and effect?

Short Answer

Expert verified
A statistically significant correlation coefficient shows there is a strong statistical relationship between two variables, but it doesn't determine a cause and effect relationship. Further research is needed to infer potential causal relationships.

Step by step solution

01

Implication of A Significant Correlation Coefficient

A statistically significant correlation coefficient suggests a strong statistical relationship between the two variables being observed. It indicates that the probability of observing such a strong relationship by chance alone would be very slim. Following statistical conventions, a high correlation coefficient (close to 1 or -1) would provide more confidence that there is a real, meaningful relationship between the variables.
02

Cause and Effect from Correlation Results

While a significant correlation coefficient suggests a strong association between variables, it does not imply causation. Therefore, it does not prove that changes in one variable cause changes in the other. It simply suggests that the two variables move together based on observed data. Further experimental or longitudinal research would be needed to infer potential causal relationships.

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