Describing and Testing Aptitude-Treatment Interaction Effects with Structural Equation Models ...

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TM 008 391
ED 169 082
Jan-Eric; Lindstropc, Berner
GustafsAg,
AUTHOR
Describing and Testing'Alptitude-Treatment Interaction
TITLE
Effects with Structural Equation Models: Reanalysis
of a Study by M. J. 4hr.- No. 73.
(Sweden) . Inst. of Education.
Gothenburg Univ.
INSTITUTION
National Swedish'Board of Education, Stockholm.;
SPONS AGENCY
Swedish Council for Social -Science Research,
Stockholm.
Dec 78
PUB DATE
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; Parts may
50p.; For Behr's Study, see EJ 039 647
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Academic Aptitude; *Aptitude; *Computer Programs;
DESCRIPTORS
*Data AnalySis; Elementary School Teachers; *Factor
Analysis; *Learning; *Mathematical Models;
Mathematics Instruction; Multiple Regression
Analysis; Predictor Variables
Interaction; *LISREL Computer
* *Aptitude Treatment
IDENTIFIERS
Program
'ABSTRACT
The Joreskog and Sorbom LISREL (linear structural
regression
relations) method is investigated as an alternative to
(ATI), to
analygis,',in studies of aptitude-treatment interactions
liroblems caused by_ unreliability of measurements and by large
is reanalyzed. This
sets of 42ariakles. A study reported. by M.J. Behr
figural, aptitude
study investigated relations between verbal and
and one figural
variables And outcome variablgs within one verbal
prospective
treatment, teaching modulus seven arithmetic to
variables
elem'entrn tealphers- The 'relations between latent aptitude
four LURK. models with
and Ala tent outdome.variables are studied in
(interpretable as a
or .two latent aptitude variables
either on
ability, respectively), and
geneFal factor and verbal and "_figural
(interpretable as
with two sets of latent outcome variables
/understanding)'. No
learning/retention' and computation speed
interactipn
significant interaction is found, but tendencies towards
has several advantages in the
are noted. It is concluded that LISREL
.
the test of ATI
analysis of ATI studies, but also that the power of
correlation between
effects is low, particularly when there is a high
(Author/GDC)
the latent aptitude variables.
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r
ta
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_
De-scribing and testing aptitude-treatment interactioR
Reanalysis of
'.1,
effec*r with structural equation models.:
a.
a 'study by M.J. pehr.
j
Jan-Eric Gusttfsson
Berner Lindstrom
University of GotebOrg
(
supported
The research presented in thiS report,has been
financially by the Swedish Council for Research in the
HUmanistic_ and Social Sciences and by the National Board
of Education in Sweden. We want to express our gratitude
to Dag Sorbom and :engt Mgthen for iving much instruction
assume, however,
of LISREL;
'and advice in the u
r an
is se..
complete responsibilit
ABSTRACT
The Joreskog -and SorboM LISREL method is. investigated as
an alternative to regression4analysis in studies of
i s
aptitude-treatment interactions (ATI), to solve problems
caused by unr eliability of measurements and by large
sets of variables. A stud
reported by M.J. Behr is
reanalyzed. The study in estigated relations between
verbal and figural aptitu e variables and outcome
variables within one verbal and one figural treatment
teaching modulus 'seven arithmetic. The, relations
between latent aptitude variables and latent outcome
variables are studied in 4 LISREL models with either
1 or 2 latent aptitude variables, interpretable as a
general factor and verbal and figural ability, respecti-
vely, and with 2, sets'of latent outcome variables,
.
interpretable-as learning/retention and computational
'speed /understanding. No significant interaction is
found, but tendencies towards interaction are noted.
It is concluded that LISREL has several advantages in
the analysis'of ATI studies, but also that the power
of the testbof ATI effects is low, particularly when
there is\a high correlation betwen the latent aptitude
variables.
a
`INTRODUCTION
In research, on aptitude-treatment interactions (ATI) the
interest is focussed on joint effects of instructional
treatment and individual differences. The standard procedure-'
for ana,lyzing,data from ATI studies is to regress outcome
on one or, more aptitude variables
one at a time
variables
within treatment groups and to test'for homogeneity/of
the within treatment regression slopes (Cronbach & Snow,
'1977, ch. 3).
However, the 4rdinary regression analysis of ATI data is
not freecfrom problems. The regression on an observed
from thefgression,on
aptitude Variable is differen
the true aptitude variable-when it is not perfectly
reliable; errors of measurement in the aptitude variables
thus bias the tests and descriptions of ATI effects.
Cronbach and. Snow (1977) stated that "Ideally, every ATI
.
udy would rxamine the regression of outcome onto the
true aptitude score... This... regression will have a
different slope than the observed-score regression, and
under some circumstances the apparent interaction may
be radically altered. Important as this matter is, it
has been ignored in ATI research to date..." (p.34).
The problem,, is seve e enough when only one aptitude
\rani(
able is, considered(but it is aggravated in multiple
regression (Cronbach & Snow, 1977, p. 36). Furthermore,
n the regression based
an additional complication arises
approach to the analysis of ATI data when there are many
variales. Then a great many regression coefficients are
estimated and tested, which makes for chance significan-
give rise to complex patterns of results
cies and tends to
%
which are' hard to interpret.
In this paper an alternative approacp to the analysis of
ATI data will be illustrated 7-7 the.LISREL method of
/ts
2
and Sorbom (see JOreskog, 1970, 1973, 104;
(joreskog
JOreskog 8,'SOrbom, 1976, 1977, 1978): LISREL (LInear
Structural RELations) is a method, and a ,computer pro-
gram, for analysis of linear structural relations between
variables, which may be either observed or latent. When
latent variables are studied a factorial structure is
imposed.on the observed variables; which structure serves
to identify the latent v riables and allows estimation
.of the error variances
n the observed variables. In
this'way Several observed variables may be rediced to.c.
fewer latent variables and relations between true
%
variables rather -ehan observed variables can be studied.
_It cannot'be taken for granted, however, that LISREL only
has advantages when.. applied to analysis oPATI studies:
The method is built on st,rong assumptions concerning the
nature of the daea;,not only consistency of thy, estimates
is of importance but also their variance, just to mention'
two possible sources of problems.jbere seems)thus to be a
need for empirical studies of the
applicability
of this
alternative method in the analysis of ATI.ata.
One purpose of the present study
s to make such an
appraisal Of the problems (and virtues of L CSREL. The
e
-Study is a reanalysis of 6 study present
by Behr (1967),
which was chosen because it included several aptitude
and outcome variables and because.thepr Sent authors
f'
Are familiar with the substantive
problem
studied by
,,
Behr.
A
(-
'Behr investigated the hypothesis that tests of verbal
1.
a
ability aria'more highly correlated with achievement in
) a verbal treatment than in a figural treatment and that
-tests of figural ability are more highly correlated with
1 ach evement in a figural treatm
t than in a verbal
tratment (cf. GuStafon, 1976/. This was.bne.'of the
first ATI.pypotheses to be 'suggested and several of the
4
of which the Behr stddlys one,jnvesti-
early ATI-st
.
les
gated this,hypothes'S.
3
Behr used 14 aptitdde variabels; about, half of them were
verbal and half of them were figural. One group of subjects
studied a verbal-symbolic (VS) programmed teaching material
and another group of subjectsstudied a figural-symbolic
'(FS) teaching material. The study included 7 outcome
Behr'
variablesfor a more detailed' desCription of the
study, see below) %
rf
Behr investigated interactions by comparing the within-
treatment regressions Of,,each of the dependent variables
dozen signi-
on each of the aptitude variables. About a
ficant interactions were found, and alnAost.all interactions
in the
were due to a steeper regression on verbal tests
4
VS treatment than inthe ES.treatment.
Vs\
(1977,
In their review of ATI research Cronb ch and Snow
.
ligure.q pr'esented
p. 286) made a simple reanalysis usi
?egression
by Behr. For one outcome they's
.gAA6rarately fOr
dil>the,figural
coefficients of
e
for the
.wasp
the two tr,eatments.
Of'teSts Was higher
verbal tests. The sum for both 5i,c1.4ps
differOOd.fwA
in the VS- treatment, even thOughi the
bronpach !alikSnOw. drew
smaller for theficlqal tests.
associated ,.
the concitision that a general:' factor was
_
.
VS 4.thanin the FS treatent:
with achievement in th
Gustafsson (1974, pp, 15-16;-cf: Gustafsson, 1976, p.56)
presented another simple reanalysis of the Behr study.,:.
The most reliable tests were seletted and one verbal
separate
were entered into
and one figural test at a
.tiMe
treatmentsiIt
multiple regression equations for the two
/
zero7
was found thatOne figural test that
had .a highe
treatment, in
order regression coefficient in the FS
the multipl,aualysis came out:with a much higher ?partial
iA the
regression coefficient in the FS treatment than
VS treatment. This result was interpreted as a very
wi*figural ability
weaktendency towards interaction
!!"
4
seemed
and since the interaction with verbal ability
the
relatively well' established it was concluded that
verbal/figural ATI
Behr study gave sofie support to the
been
hypothesis. Three different conclusions have thus
dravin from the Behr study: Behr himself stressed the
result's obtained with each particular aptitude variable;
being
Cronbach and Snow interpreted the effects found as
accountable for by general ability; and Gustafsson,
verbAl
finally, saw some value in the distinction between
and figural abilities. In addition to the,methodological
of LISREL, another
purpose of studying the applicability
of these conclusions
purpose will be tosee which, if any,
'receives support.
METHOD
The Behr study
$
in the Behr study was modulus seven
The subject matter taught
treatments algebraic symbols
arithmetic. In both the VS and FS
supple-
VS treatment this information was
were used but in the
In the FS treatment figural
mented with verbal information.
figUral
symbolic presentation. The
information was added to the
consisting for example of a
material was .of low complexity,
operations were illustrated
circle with whiCh the arithmetic
the circle.
as movements along.
cells
The aptitude varibles were seledted to correspond to
"Structure-of-Intellect (SI)" model.
in the Guilford-(1967)
,
figural content (-F-), 5 had a semantic
Of the tests, 6 had a
(-S-)
(numeric)
(verbal) content (-M-) and 2 had a symbolic
called Integration,
content. In addition there was a test,
structre. This test
which was not classifiable in the SI
instructions concerning directions.
gave verbally-formulated
figural
It can be hypothesized that this test measures
which Brooks
ability; it comes quite close to the task
be of a spatial/
(1967) in experimental studies has shown to
cognition (C--) and
figural kind. Two kinds of operations,