Statistical Methods for Psychology

Boring is Attractive

A useful example of trend analysis comes from a study by Langlois and Roggman (1990),

which examined the question of what makes a human face attractive. They approached the

problem from both an evolutionary and a cognitive perspective. Modern evolutionary the-

ory would suggest that average values of some trait would be preferred to extreme ones,

and cognitive theory suggests that both adults and children respond to prototypes of ob-

jects more positively than to objects near the extremes on any dimension. A prototype, by

definition, possesses average values of the object along important dimensions. (A proto-

type of a cat is one that is not too tall or too short, not too fat or too thin, and doesn’t purr

too loudly or too quietly.)

Langlois and Roggman took facial photographs of 336 males and 214 females. They

then created five groups of composite photographs by computer-averaging the individual

faces. Thus, for one group the computer averaged 32 randomly selected same-gender faces,

producing a quite recognizable face with average width, height, eyes, nose length, and

so on. For the other groups the composite faces were averaged over either 2, 4, 8, or 16

individual faces. The label Composite will be used to represent the five different groups.

12.10 Trend Analysis 403

Figure 12.2 Typical linear and quadratic functions

30

20

10

0

–10

–20

–30

2*

X

–0.2*

(^2) X
15
Linear fit
0 5 10
(a) Linear trend Y= 2 X
–15 –10 –5
X
5
0
–15
–10
–5
–20
–25
10
0
–30
–20
–10
–40
–50
(c) Linear plus quadratic trendY= 2 X– 0.2X^2
X
Polynomial fit, degree = 2
Polynomial fit, degree = 2
(b) Quadratic trend Y= (–0.2) X^2
X
–15 –10 –5 0 5 10 15
2*
X

• 0.2*

X

2

–15 –10 –5 0 5 10 15