Statistical Methods for Psychology

weight for females. These values are shown in Table 10.1, along with the correlation coef-

ficient. The slope of the line is negative because we have set “female” 5 1 and therefore

plotted females to the right of males. If we had reversed the scoring the slope would have

been positive. The fact that the regression line passes through the two Ymeans assumes

particular relevance when we later consider eta squared (^2 ) in Chapter 11, where the re-

gression line is deliberately drawn to pass through several array means.

From Table 10.1 you can see that the correlation between weight and sex is 2 .565. As

noted, we can ignore the sign of this correlation, since the decision about coding sex is ar-

bitrary. A negative coefficient indicates that the mean of the group coded 1 is less than the

mean of the group coded 0, whereas a positive correlation indicates the reverse. We can still

interpret as usual, however, and say that of the variability in weight can

be accounted for by sex. We are not speaking here of cause and effect. One of the more im-

mediate causes of weight is the additional height of males, which is certainly related to sex,

but there are a lot of other sex-linked characteristics that enter the picture.

Another interesting fact illustrated in Figure 10.1 concerns the equation for the regres-

sion line. Recall that the intercept is the value of when X 5 0. In this case, X 5 0 for

males and 5 151.25. In other words, the mean weight of the group coded 0 is the inter-

cept. Moreover, the slope of the regression line is defined as the change in for a one-unit

change in X. Since a one-unit change in Xcorresponds to a change from male to female,

and the predicted value ( ) changes from the mean weight of males to the mean weight of

females, the slope (–19.85) will represent the difference in the two means. We will return

to this idea in Chapter 16, but it is important to notice it here in a simple context.

The Relationship Between and t

The relationship between and t is very important. It can be shown, although the proof

will not be given here, that

where t is obtained from the t test of the difference of means (for example, between the

mean weights of males and females) and df 5 the degrees of freedom for t, namely

. For example, if we were to run a ttest on the difference in mean weight be-
tween male and female subjects, using a t for two independent groups with unequal sample
sizes,

=

19.85

5.799

=3.42

=

151.25 2 131.4

B

224.159

12

1

224.159

15

t=

X 12 X 2

B

s^2 p

N 1

1

s^2 p

N 2

=

11(18.869^2 ) 1 14(10.979^2 )

1211522

=224.159

s^2 p=

(N 12 1)s^211 (N 22 1)s^22

N 11 N 222

N 11 N 222

r^2 pb=

t^2

t^21 df

rpb

rpb

YN

YN

YN

YN

r^2 - .565^2 =32%

h

Section 10.1 Point-Biserial Correlation and Phi: Pearson Correlations by Another Name 297