Statistical Methods for Psychology

The important statistics from the two regressions are shown in Table 15.4. Because

SPSS does not report the standard error of Beta, we need to calculate it. The tstatistic

given in these tables is either the unstandardized regression coefficient (b) divided by its

standard error, or the standardized regression coefficient divided by its standard error.

Thus we can solve

Similarly for the path from Self-esteem to Self-efficacy, partialling Maternal care, we have

These results yield the following table.

Then the regression coefficient for the path from Maternal care Self-esteem Self-

efficacy is equal to ba3 bb 5 .403 3 .323 5 .130, where aand brefer to the relevant

paths. (Path cis the direct path from Maternal care to Self-efficacy.) In addition, we know

that the standard error of this two-part path is given by

where baand bbare the paths, and and are the corresponding standard errors of the

standardized regression coefficients for those paths.^12 We can calculate the standard error

of the combined path as:

We now know the path coefficient (.403 3 .323 5 .130) and its standard error (.052),

and we can form a tratio as

Sobel (1982) stated that this ratio is asymptotically normally distributed, which, for large

samples, would lead to rejection of the null hypothesis at a5.05 when the ratio exceeds

1.96. It would presumably have a t distribution on N– 3 dffor small samples. In our case

the path is clearly significant, as we would expect from the previous results. Therefore we

6

t=

babb

sbabb

=

.130

.052

=2.50

=0.052

= 1 0.0027

sbabb= 3 b^2 as^2 b1b^2 bs^2 a 2 s^2 as^2 b= 3 .403^2 (.106^2 ) 1 .323^2 (.096^2 ) 2 (.106^2 )(.098^2 )

s^2 a s^2 b

sbabb= 3 b^2 as^2 b1b^2 bs^2 a 2 s^2 as^2 b

: :

t=

b

sb

; sb=

b

t

=

0.323

3.041

=0.106

t=

b

sb

; sb=

b

t

=

0.403

4.178

=0.096

556 Chapter 15 Multiple Regression

Table 15.4 Regression coefficients and standard errors

for two parts of mediating path

Path a Path b

Maternal Self- Self- Self-

Care Esteem Esteem Efficacy

b 0.403 b .323

sa 0.096 sb .106

t 4.18* t 3.041*

(^12) There is some disagreement over the exact form of these equations, but the one given here is recommended by
Baron and Kenny. The differences among the various equations turn out to be very minor in practice.