CHAPTER 15 Introducing Correlation and Regression 205

3.

Calculate the lower and upper 95 percent confidence limits for r:

r

e

e

r

e

Lower

Upper

/

(

) (

)

.

(

(

.

)

(

.

)

.

2

2

2

0 104

0 104

1

1

1

0 104

203

1 203

1

1

0 835

2

) (

)

.

.

/ e

Notice that the 95 percent confidence interval goes from – .0 104 to 0 835

.

, a range

that includes the value zero. This means that the true r value could indeed be zero,

which is consistent with the non-significant p value of 0.098 that you obtained

from the significance test of r in the preceding section.

Determining whether two r values are

statistically significantly different

Suppose that you have two correlation coefficients and you want to test whether

they are statistically significantly different. It doesn’t matter whether the two r

values are based on the same variables or are from the same group of participants.

Imagine that a significance test for comparing two correlation coefficient values

(which we will call r1 and r2) that were obtained from N1 and N 2 participants,

respectively. You can utilize the Fisher z transformation to get z1 and z2. The dif-

ference (z

z

1

2^{) has a standard error (SE) of SE}

N

N

z

z

2

1

1

3

1

3

1

2

/

/

.

You obtain the test statistic for the comparison by dividing the difference by its

SE. You can convert this to a p value by referring to a table (or web page) of the

normal distribution.

For example, if you want to compare an r1 value of 0.4 based on an N1 of 100 par-

ticipants with an r2 value of 0.6 based on an N2 of 150 participants, you perform the

following steps:

1.

Calculate the Fisher z transformation of each observed r value:

z

z

1

2

1

2

1

0 4

1

0 4

0 424

1

2

1

0 6

1

0 6

0

log

.

.

.

log

.

.

/

/

..693

2.

Calculate the (z

z

2

1^{) difference:}

0 693

0 424

0 269

.

.

.

3.

Calculate the SE of the (z

z

2

1^{) difference:}

SE z

z

2

1

1

100

3

1

150

3

0 131

/

/

.