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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