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:

X

Y

n
1
S
ð

1

X

Þð

Y

Þ

r

¼

(6.1)

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 subt
ract the mean

FRGPA for the 8 students and call this
Y

Y
(For example,

for student # 6, this would be: 2.3 – 2.
)

0.44

─

5.

Then
,
for each student
, multiply (
X

X
) times

(
Y

Y
) (For example, for student # 6 this would

be: (

0.26) x (

0.44)

þ

0.1144

─

─

6.

Add the results of (
X

X
) times (Y –
Y
) for the 8 students

þ

1.09

Steps 1-6 would produce the Excel table given in Fig.
6.8
.

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