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For the relationship between X and Y you have obtained a correlation coefficent of .67. When...

For the relationship between X and Y you have obtained a correlation coefficent of .67. When you computed the partial correlation coefficient between X and Y controlling for the effects of Z, you obtained a partial r of .55. What can you say about the relationship of X and Y when you have this information?

a) the relationship between X and Z is stronger than the relationship between X and Y

b) the relationship between X and Y is less strong when the effects of Z are held constant

c) Z is likely to be the cause of both X and Y

d) the partial correlation is an artifact of the orginial correlation between X, Y, Z and some unknown fourth variable.

Math   Statistics-And-Probability   
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Answer #1

Correct answer: b) the relationship between X and Y is less strong when the effects of Z are held constant

Explanation: The correlation coefficient between X and Y when not controlling for the effects of Z is 0.67. The partial correlation coefficient between X and Y controlling for the effects of Z is 0.55. The value of correlation coefficient is reduced due to effect of z in partial correlation as compared to simple correlation. Hence we can say that the relationship between X and Y is less strong when the effects of Z are held constant.

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