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Fig. 6.7 Worksheet Data for High School GPA and Frosh GPA (Practical Example)
that we will ask you to use your pocket calculator to ﬁnd a correlation, but knowing
how the correlation is computed step-by-step will give you the opportunity to
understand how the formula works in practice.
To do that, let’s create a situation in which you need to ﬁnd the correlation
between two variables.
Suppose that you wanted to ﬁnd out if there was a relationship between high
school grade-point average (HSGPA) and freshman GPA (FRGPA) for Biology
majors at a College of Science and Technology. You have decided to call HSGPA
the x-variable (i.e., the predictor variable) and FRGPA as the y-variable (i.e., the
criterion variable) in your analysis. To test your Excel skills, you take a random
sample of freshmen Biology majors at the end of their freshman year and record
their GPA. The hypothetical data for eight students appear in Fig. 6.7 . (Note: We
are using only one decimal place for these GPAs in this example to simplify the
mathematical computations.)
Notice also that we have used Excel to ﬁnd the sample size for both variables, X
and Y, and the MEAN and STDEV of both variables. (You can practice your Excel
skills by seeing if you get this same results when you create an Excel spreadsheet
for these data.)
Now, let’s use the above table to compute the correlation r between HSGPA and