RIANCE

are pro-
isformed

A recip-
reaction

4

—-— zr

': n

ve for X'
z given in
s. Bartlett

1
dl-zi

servations

n may be
stribution
r of trials
yries from

r transfor-
iproach to
jances are
he correct
je relation-
determined
espectively,
remove the
isformation
butions for

is to apply
n the treat-
rmined and

RN z šča Še 2 ANE NA MOON Ev ič me tija

perg

KRE jn ANE NI TA a ŽA En kam ea Mona re

PERJE vz

ZEENNN Im iana MEREI ba m AN

SECTION 2.7 TRANSFORMATIONS 67
a NI IIIIAIIO—<———

the ratio of the largest to the smallest range is computed. The transformation
that produces the smallest ratio is selected as the most appropriate one.
This procedure is illustrated in Table 2.7-2 for the data in Table 2.7-l.
On the basis of this procedure, a sguare-root formation would be selected
for these data.

Once an appropriate transformation is selected and the data
analyzed on the new scale, all inferences regarding treatment effects
must be made with respect to the new scale. In most behavioral research
situations, inferences based on log X's or VX "s, for example, are just as
meaningful as inferences based on untransformed scores.

If additivity of treatment effects is the principal concern of an experi-
menter, the appropriateness of a particular transformation can be deter-
mined by a test of nonadditivity that is described in Section 5.3. This test
provides a means of determining if treatment effects are additive for the
untransformed scores and for any transformations that may be tried.
A mathematically sophisticated exposition of general issues involved in the
use of transformations is given by Box and Cox (1964).

TABLE 2.7-2 Transformations Applied to Largest
and Smallest Scores in Table 2.7-1

Treatment Levels
b, b, b;

Range,,rgesi
RANE, nantest

Largest score (L) 4 7 12
Smallest score (S) 0 2 6
5 6 6/4 < 1.50

Range <—

141/99 — 1.42

; 1.1139
0000 4711 .8451
.4260 .2688

log (S -£ 1)

Range — .6990 .6990/.2688 < 2.60

t(L 4 b) š ; J
14S - 1) 00 33 14
Range < 80 21 06

.80/.06 < 13.33