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Which of the following is the most appropriate interpretation of a product-moment correlation coefficient of 0.8?
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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?
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We know that Pearson’s product-moment correlation coefficient takes values between negative one and positive one.
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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.
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We’re asked which of the given options is the most appropriate interpretation of a product-moment correlation coefficient of positive 0.8.
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And the correlation coefficient of positive 0.8 means that we have direct or positive correlation.
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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.
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This means we can eliminate option (A) and option (B) since these both specify negative linear correlation.
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We can also eliminate option (E) since this specifies no correlation and we do not have zero correlation.
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This leaves us with option (C) and option (D), a moderate positive linear correlation or a strong positive linear correlation.
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If we consider the magnitude of correlation coefficients — the stronger the correlation, the closer the magnitude to positive or negative one.
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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.
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Since the given coefficient is 0.8, which is close to positive one, we can say this represents strong positive linear correlation.
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We can therefore eliminate option (C), which refers to a moderate positive linear correlation.
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And so the most appropriate interpretation of a product-moment correlation coefficient of 0.8 is option (D) a strong positive linear correlation.