Video: Interpreting a Correlation Coefficient

Which of the following is the most appropriate interpretation of a product-moment correlation coefficient of 0.8? [A] a strong negative linear correlation [B] a moderate negative linear correlation [C] a moderate positive linear correlation [D] a strong positive linear correlation [E] no correlation

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Video Transcript

Which of the following is the most appropriate interpretation of a product-moment correlation coefficient of 0.8? Is it (A) a strong negative linear correlation, or (B) a moderate negative linear correlation, or (C) a moderate positive linear correlation, (D) a strong positive linear correlation, or (E) no correlation?

We know that Pearson’s product-moment correlation coefficient takes values between negative one and positive one. We also know that if 𝑟 is less than zero and greater than or equal to negative one, then we have inverse or negative correlation and that if 𝑟 is greater than zero and less than or equal to positive one, we have direct or positive correlation. We’re asked which of the given options is the most appropriate interpretation of a product-moment correlation coefficient of positive 0.8. And the correlation coefficient of positive 0.8 means that we have direct or positive correlation. And noting that the product-moment correlation coefficient applies to linear correlation, we can eliminate any of our options, which interpret the coefficient as a negative linear correlation.

This means we can eliminate option (A) and option (B) since these both specify negative linear correlation. We can also eliminate option (E) since this specifies no correlation and we do not have zero correlation. This leaves us with option (C) and option (D), a moderate positive linear correlation or a strong positive linear correlation. If we consider the magnitude of correlation coefficients — the stronger the correlation, the closer the magnitude to positive or negative one. The closer the magnitude is to zero, the weaker the correlation — then this means approximately midway between zero and positive or negative one, we have moderate correlation.

Since the given coefficient is 0.8, which is close to positive one, we can say this represents strong positive linear correlation. We can therefore eliminate option (C), which refers to a moderate positive linear correlation. And so the most appropriate interpretation of a product-moment correlation coefficient of 0.8 is option (D) a strong positive linear correlation.

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