Test-taking speed, grade, and the Spearman correlation coefficient: Does speed in completing a test correlate with one’s grade? Here are test scores for eight students in one of our statistics classes. They are arranged in order from the student who turned in the test first to the student who turned in the test last. 98 74 87 92 88 93 62 67 

a. What are the two variables of interest? For each variable, state whether it’s scale or ordinal.

 b. Calculate the Spearman correlation coefficient for these two variables. Remember to convert any scale variables to ranks. 

c. What does the coefficient tell us about the relation between these two variables? 

d. Why couldn’t we calculate a Pearson correlation coefficient for these data? 

e. Does this Spearman correlation coefficient suggest that students should take their tests as quickly as possible? That is, does it indicate that taking the test quickly causes a good grade? Explain your answer. 

f. What third variables might be responsible for this correlation? That is, what third variables might cause both speedy test taking and a good test grade? 

g. Imagine that each of the following numbers represents the Spearman correlation coefficient that quantifies the relation between test grade and speed in taking the test: 1.00, −0.001, 0.52, −0.27, −0.98, 0.09 Specify which of these coefficients suggests the strongest relation between the two variables as well as which coefficient suggests the weakest relation between the two variables.