Given the following sets of paired sample scores:
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a. Use the equation
to compute the value of Pearson r for each set. Note that in set B, where the correlation is lowest, some of the X Y values are positive and some are negative. These tend to cancel each other, causing r to have a low magnitude. However, in both sets A and C, all the products have the same sign, causing r to be large in magnitude. When the paired scores occupy the same or opposite positions within their own distributions, theX Y products have the same sign, resulting in high magnitudes for r.
b. Compute r for set B, using the raw score equation. Which do you prefer: using the raw score or the ÃÂ score equation?
c. Add the constant 5 to t he X scores i n set A and compute r again, using t he r aw score equation. Has the value changed?
d. Multiply the X scores in set A by 5 and compute r again. Has the value changed?
e. Generalize the results obtained in parts c and d to subtracting and dividing the scores by a constant. What does this tell you about r?