Part A. A student is analyzing how two variables are correlated: size of committ

Question

Part A. A student is analyzing how two variables are correlated: size of committee and “efficiency” of committee. He reports to his friends that he had a correlation coefficient (r) of -.85.   What does the negative sign on the “r” tell us?

Part B. Consider again the -.85. How strong does this appear to be, based on the textbook's description of how to qualitatively interpret the size of “r”?

Part C. Challenge question: Think about the two variables and the “r” of .85.
Why might his friends or colleagues think this researcher is lying about the correlation between group size and efficiency?

Explanation / Answer

Part A) A negative sign on the correlation coefficient 'r' tells us that there is a negative linear relationship between the 2 variables aalyzed that is an increase in the value of 1 variable decreases the value of the other and vice versa. Therefore here a negative value of correlation coefficient means that as the size of committee increases, the efficiency of the committee decreases and as the size of the committee decreases the efficiency of the committee increases.

Part B) Now here we have to analyze the strength of the negative relationship between the 2 variables. Generally any value between -1 and -0.7 is said to have a strong negative linear relationship. As the value here is -0.85, there is a strong negative relationship between the 2 variables.

Part C) r= 0.85 suggest the opposite that is a strong positive correlation between the 2 variables. This might not be true after a particular point because then more number of people will be doing the same amount of work and thus the efficiency should decrease after a certain point of size of committee. Therefore His friends or colleagues might think that his researcher is lying about the positive correlation between the group and the efficiency.

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