Microsoft Office Tutorials and References
In Depth Information
6.1.1 Understanding the Formula for Computing a Correlation
Objective: To understand the formula for computing the correlation r
The formula for computing the correlation r is as follows:
n 1 P X X
Þ Y Y
1
ð
ð
Þ
r ¼
ð 6 : 1 Þ
S x S y
This formula looks daunting at first glance, but let’s ‘‘break it down into its
steps’’ to understand how to compute the correlation r.
6.1.2 Understanding the Nine Steps for Computing a Correlation, r
Objective: To understand the nine steps of computing a correlation r
The nine steps are as follows:
Step
Computation
Result
1
Find the sample size n by noting the number of students
8
2
Divide the number 1 by the sample size minus 1 (i.e., 1/7)
0.14286
3
For each student, take the HSGPA and subtract the mean HSGPA for the 8
students and call this X X (For example, for student # 6, this would be 2.6 -
2.86)
-0.26
Note: With your calculator, this difference is -0.26, but when Excel uses 16
decimal places for every computation, this result could be slightly different
for each student
4
For each student, take the FRGPA and subtract the mean FRGPA for the 8
students and call this Y Y (For example, for student # 6, this would be: 2.3 -
2.74)
-0.44
X X
Y Y
5
+0.1144
Then, for each student, multiply
ð
Þ times
ð
Þ (For example, for student
# 6 this would be: (-0.26) 9 (-0.44)
X X
Y Y
6
Add the results of
ð
Þ times
ð
Þ for the 8 students
+1.09
Steps 1–6 would produce the Excel table given in Fig. 6.8 .
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