Statistical Methods for Psychology

Notice that both this formula for t and the one we have just been using involve dividing

the difference between the sample means by an estimate of the standard error of the differ-

ence between means. The only change concerns the way in which this standard error is es-

timated. When the sample sizes are equal, it makes absolutely no difference whether or not

you pool variances; the answer will be the same. When the sample sizes are unequal, how-

ever, pooling can make quite a difference.

Degrees of Freedom

Two sample variances ( and ) have gone into calculating t. Each of these variances is

based on squared deviations about their corresponding sample means, and therefore each

sample variance has 2 1 df. Across the two samples, therefore, we will have ( 2 1) 1

( 2 1) 5 ( 1 2 2) df. Thus, the t for two independent samples will be based on

degrees of freedom.

Homophobia and Sexual Arousal

Adams, Wright, and Lohr (1996) were interested in some basic psychoanalytic theories

that homophobia may be unconsciously related to the anxiety of being or becoming homo-

sexual. They administered the Index of Homophobia to 64 heterosexual males, and classed

them as homophobic or nonhomophobic on the basis of their score. They then exposed ho-

mophobic and nonhomophobic heterosexual men to videotapes of sexually explicit erotic

stimuli portraying heterosexual and homosexual behavior, and recorded their level of sex-

ual arousal. Adams et al. reasoned that if homophobia were unconsciously related to anxi-

ety about one’s own sexuality, homophobic individuals would show greater arousal to the

homosexual videos than would nonhomophobic individuals.

In this example, we will examine only the data from the homosexual video. (There

were no group differences for the heterosexual and lesbian videos.) The data in Table 7.5

were created to have the same means and pooled variance as the data that Adams collected,

n 11 n 222

n 2 n 1 n 2

ni n 1

s^21 s^22

t=

(X 12 X 2 )

sX 12 X 2

=

(X 12 X 2 )

D

s^2 p

n 1

1

s^2 p

n 2

=

(X 12 X 2 )

B

s^2 pa

1

n 1

1

1

n 2

b

Section 7.5 Hypothesis Tests Applied to Means—Two Independent Samples 207

Table 7.5 Data from Adams et al. on level of sexual arousal in homophobic and

nonhomophobic heterosexual males

Homophobic Nonhomophobic

39.1 38.0 14.9 20.7 19.5 32.2 24.0 17.0 35.8 18.0 2 1.7 11.1

11.0 20.7 26.4 35.7 26.4 28.8 10.1 16.1 2 0.7 14.1 25.9 23.0

33.4 13.7 46.1 13.7 23.0 20.7 20.0 14.1 2 1.7 19.0 20.0 30.9

19.5 11.4 24.1 17.2 38.0 10.3 30.9 22.0 6.2 27.9 14.1 33.8

35.7 41.5 18.4 36.8 54.1 11.4 26.9 5.2 13.1 19.0 2 15.5

8.7 23.0 14.3 5.3 6.3

Mean 24.00 Mean 16.50

Variance 148.87 Variance 139.16

n 35 n 29