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American
Educational Research
Journal
Fall
1983,
Vol.
20,
No.
3,
Pp.
359-373
Matthew Effects in Education
HERBERT J. WALBERG and SHIOW-LING TSAI
University
of
Illinois,
Chicago
To test the
hypothesized
cumulative
advantages of
educative
factors,
the science-achievement
scores on
a
69-item
test
of
science
knowledge
of
1,284
young
adults,
ages
26
to
35,
surveyed
by
the
National
Assessment
of
Educational
Progress
(NAEP)
in
1977,
were
regressed
on three
composite independent
variables: motivation and
prior
and
current educative
experiences.
The test scores were related
significantly
to
prior
experience-embodied
variables,
such as
parental
socioeco-
nomic
status,
respondent
education,
and
specific scientific training,
as
well
as to motivation to learn and current amount and
intensity of
information
acquisition,
such
as
news
media
exposure
and
reading.
Early
educative
experience
predicts
current educative activities and
motivation;
and all three
factors
contribute
significantly
and
indepen-
dently
to
the
prediction of
achievement.
For
unto
every
one that
hath
shall
be
given,
and
he shall have abundance:
but
from
him
that hath not
shall
be taken
away
even
that which he
hath.
(Gospel
according
to
Matthew,
XXV,
29)
It
is
often said that education is a
good
economic
investment;
and,
indeed,
Theodore W.
Schultz,
in
Nobel
prize winning
research,
showed that educa-
tion
generally
pays
excellent
monetary
returns
to
individuals and
nations,
even
considering
inflation
and
foregone
opportunities
to
work
during
the
school
and
college
years.
Investments in
people,
or
"human
capital,"
are
also
associated with
health,
longevity,
civic
participation,
self-rated
happi-
ness,
and
other
adult
outcomes
(see
Schultz,
1981,
for a
survey
of evidence
from
many periods
and
countries).
Such
benefits have
been demonstrated
repeatedly;
but
the variables that
intervene between educational
experiences
and
adult
outcomes,
such
as
knowledge
acquisition
and the
capacity
to
invest,
persevere,
and
profit
intellectually
from
experience,
are seldom
investigated,
even
though
they
may
be
considered valuable intermediate
products,
by-products,
or
consummatory
ends in
their own
right.
The
present
359
WALBERG
AND
TSAI
research
explores
these
intervening
variables.
Specifically,
it
investigates
a
hypothesized
enhancement of
knowledge acquisition
from
(a)
current
edu-
cative
activity,
(b)
motivation,
and
(c)
prior
formal
education and
informal
educative
experience.
The
enhancement,
cumulative-advantage
or
Matthew
hypothesis,
is
dis-
cussed
in
the
subsequent
sections. The
introductory
discussion is
somewhat
extended
and discursive for several
reasons. Research
in education
is
often
atheoretical or
guided by
implicit theory
and should be made
theoretically
explicit
if it is
to be made
falsifiable in
Popper's
(1972)
sense
(see
also
Cook
&
Campbell,
1979,
pp.
20-25).
Moreover,
several
versions of the
Matthew
hypothesis
and
related
concepts require
explication
and
empirical probing.
Lastly,
prior
evidence on
the
Matthew and related
effects
originates
in
mathematical
topics
and
disciplines
outside the
mainstream of
educational
research,
notably
the
microeconomics of
investment and
productivity;
this
scattered
evidence
deserves a brief
review.
MATTHEW AND
FAN-SPREAD
EFFECTS
A
close
reading
of
the
gospel
passage quoted
above and its
context
suggests
that the
Matthew
effect as
originally
set forth
was
absolute and
volitional:
absolute
in
that
those
who hid
and
thereby
merely
preserved
their
wealth,
whatever
its
initial
size,
rather
than
investing
and
multiplying
it,
would
lose
it
all rather
than
keeping
it or
gaining relatively
less
at a lower
rate;
and
volitional
or
motivational in
that
individuals
make
decisions
determining
their
fate. The
modem
"fan-spread"
hypothesis,
however,
holds that
rates of
gain
are
relative
and
proportional
to
initial
endowment.
A
comprehensive
review of
experimental
and
quasi-experimental
effects
describes a
"fan-spread"
of
beneficial
growth
during
educational or
other
experience
such
that
those who
score
higher
than
others on
pretests
or other
desirable
attributes
relevant
to a
treatment at
the
beginning
of an
experiment
gain
absolutely
and
relatively
more
than
others
from
the
same
experience
(Cook
&
Campbell,
1979,
pp.
184-185).
The
increasing
variation
during
the
course of
experience
leads to a
fan-spread
of
points
when
outcomes
are
plotted
against
time.
The
Equality
of
Educational
Opportunity
National
Survey,
for
example,
revealed
that
socioeconomic
and
ethnic
groups
that
scored
somewhat
higher
than
others in
the
early
grades
scored
much
higher
in
the
later
grades;
and
the
gap
or
cumulative
advantage
increased
steadily
with
grade
level
(Cole-
man
et
al.,
1966).
In
a
secondary
analysis
of
the
extensive
Sesame
Street
evaluation
data,
moreover,
Cook,
Appleton,
Conner,
and
Schaffer
(1975)
found
general
average
test
benefits to
the
children
who
watched
the
television
program
but
also,
contrary
to
the
program
goals,
an
increasing gap
over
time
between
poor
and
middle-class
children
as a
consequence
of
viewing.
The
cumulative
advantage
appeared
attributable
to
more
extensive and
reflective
discussions
of
the
program
encouraged
by
middle-class
parents.
360
MATTHEW EFFECTS
Even before
school,
children differ
greatly
in the amount
and
intensity
of
parental
care invested
in them.
By imputing
foregone wage
rates
of
mothers
and
obtaining
information
on
hours of care
spent
with their children
and
the
number of children
per
family
in
about
1,000
households,
Hill and
Stafford
(1974)
estimated
that the
maternal
care embodied in
preschool
children
of
higher
and lower socioeconomic status was
worth
respectively
$8,528
and
$1,702
in
1965,
a ratio of about five to one.
Thus it
might
be
expected
that
such
large
variation
may
account
for children's
widely varying capacities
to
profit
from
schooling
and other
subsequent
educative
experience.
ECONOMIC PRODUCTIVITY
Starting
in
the
19th
century,
economists noted that not
only
do the
rich
get
richer,
but such
acquisition may
be attributable to
multiple
factors
rather
than
simply
virtue, wealth,
or
motivated effort
alone.
Cobb
and
Douglas
first
empirically
demonstrated
such simultaneous
multiple
causes
in
1928.
The
19th-century
farm affords an instructive
example
of their
classical
economic
productivity theory.
Given
quantities
or
intensities
of the
multi-
plicative
factors of
land,
capital
equipment,
and
labor,
raising
any
factor will
increase
output.
Raising
a factor
that has a
high
ratio to the
others,
however,
will be less
productive
than
otherwise;
adding
additional
labor,
for
example,
to an
intensively
cultivated
farm
makes for less
allocative
efficiency
than
adding
more
land or better seed.
The
Cobb-Douglas
(1928)
production
function has
an excellent record for
parsimoniously
fitting
productivity
data for
many periods
and countries
(see,
e.g.,
Bosworth,
1976;
Jones,
1976).
It
postulates
that estimated
output
is an
explicit multiplicative
function
of
the
factors labor
and
capital,
O
=
aLbKc,
in which the
lower-case letters
are
fitted
constants,
that
is,
linear
multiple
regression
weights
for the
logged
variables. The
Cobb-Douglas
function
usually
subsumes land under
capital
in
economics, but,
to
reflect
more
closely
the
specific
technology,
the
factors
may
be
disaggregated,
for exam-
ple,
into
equipment,
land, seed,
fertilizer,
irrigation,
management,
tilling,
and
rotation,
and
the coefficients
may
be
simultaneously
estimated
separately
in
a
single
multiple regression.
Sets
of
exponents
that
sum to
one,
which
are
often
observed,
imply
constant
"return to
scale"
of the
technology;
for
example,
doubling
the
quantities
of both
labor and
capital
simultaneously
doubles
output.
Sums
greater
or
less
than
one
imply
respectively
increasing
or
decreasing
returns to
scale.
EDUCATIONAL
PRODUCTIVITY
Casting
school
learning
and its
major
correlates-motivation,
ability,
and
instruction-into a
Cobb-Douglas
formulation
suggests
several
hypotheses
(Walberg,
1981).
If
any
factor is
at a
zero
point
(setting
aside
the
difficult
problem
of
measurement),
no
learning
can
occur
because zero
multiplied by
361
WALBERG
AND
TSAI
zero
yields
zero;
thus,
for
example,
zero
motivation,
time,
or
ability
can
each
vitiate
learning.
With the other
factors
fixed, moreover,
adding
more of
a
factor will lead
to
diminishing
returns
to the factor
if
its
exponent
is
less
than
one,
as has
been
shown
in the
case of
instructional time
(see
Frederick
&
Walberg's,
1980,
review).
In
addition,
when
learning
is
regressed
on
the
factors,
each
can
be
hypothesized
to
carry
significant weight
and
make
a
unique
contribution to the
equation.
Because motivation
is
included as
an
independent
variable
in
Matthew,
in
the
Walberg theory,
and
many
for-
mulations
(see,
e.g.,
Willson's,
1981,
meta-analysis)
it
plays
a
similar
role
in
the
present
theoretical formulation.
Larger
investments
in
educative
conditions in
the
family,
in
years
of
general
education,
and in
specific learning
may provide
constructive
expe-
rience for later
learning.
Such
experience might
be
expected
to
make
current
learning
more
efficient;
that
is,
more
might
be
learned in
a
given
amount or
unit of
activity.
Thus the
three
factors
treated in the
present
Cobb-Douglas
formulation
are
motivation,
prior
educational
experience,
and
current
edu-
cative
activity.
It
is
also
possible,
however,
for
cumulative
advantages
to
occur
without
multiplicative
efficiencies
and
interactions in
that
early
environments
may
predict
later
environments that
add further
knowledge;
an
additive
linear
model
is
sufficient in
this
case
without
log
transformation.
In
either
case,
learning specific
bodies of
knowledge during
the life
span
may
be
analogous
to the
Matthew
effect
in
science
(Merton,
1968),
in
which
initial
advantages
of
university
study,
work
with
active
eminent
scientists,
early
publication
and
job
placement
confer
tastes,
skills,
rewards,
and
further
opportunities
that
cumulate
to
enable as
few as
the
top
fifth
of
natural
scientists in
various
fields
to
produce
or
acquire
four-fifths of
the
publications,
citations,
and
awards
(Merton,
1968).
PSYCHOLOGICAL
PRODUCTIVITY
In
both
science and
learning,
the
quantity,
association,
and
abstraction of
underlying
cognitive
elements
seem
essential
for
increasing
knowledge.
Simon
(1979)
and
other
cognitive
psychologists
showed
that a
greater
number
and
richness of
associations
of
permanent
memory
units
acquired
through
specific
prior
experience
allows
new
units
to be
acquired
more
rapidly
by
association
with
prior
units
and
other
learning-to-learn
processes.
Also
developed
in
prior
experience
with
specific
bodies of
knowledge
is
"chunking,"
or
abstracting
sets of
discrete
units and
treating
them
as
wholes,
which
allows
more
efficient
acquisition
and
processing
of new
knowledge.
As
Simon
(1979)
acknowledges,
however,
prior
and
current
acquisition
involve
more
than
exposure
and
cognitive
processes
since
both
causally
involve
motivation
(see
also
Willson,
1981).
362
MATTHEW EFFECTS
Research on
labor
economics and
mass
communication
effects
shows
similar
cumulative
cognitive
advantage
and
knowledge gaps.
Nelson
(1981)
concludes,
for
example,
that better
and
more
recently
educated farmers
and
doctors are
able to
better
assess new
technological
developments
in
their
fields and
adopt
promising
ones
early;
and
that,
in
general,
workers of
higher
educational
attainments
migrate
to
new,
rapidly
growing
industries
that
require
rapid
learning
by
doing.
Roberts
and
Bachen
(1982),
moreover,
conclude from a
review of
communications
research
that
groups
of
higher
socioeconomic status
(SES)
acquire
information
from
the mass
media
faster
than do
lower SES
groups
and thus
increase their
cumulative
advantage
in
knowledge.
These reviewers
suggest
the
possibility
that
efficiency
in
current
acquisition
of
knowedge
from
media
may
be
attributable to
motivation
to
acquire
it
rather than
earlier
cognitive
embodiments.
Willson
(1981)
also
points
to
the
possible
causal role
of
motivation in
science
achievement.
Because of
several
alternative
variables
explanations,
it
seems
most
construc-
tive to
investigate
these
rival,
or
possibly joint
or
interactive,
causes simul-
taneously
controlled for one
another in
multivariate
analysis,
and to
hypoth-
esize,
as in
the
present
research,
that
knowledge acquisition
is
determined
by
motivation
as well
as
amount and
intensity
of
past
and
current educative
activities.
METHOD
In
this
section,
the
sampling
and
instruments are
described. The
compos-
iting
of
the
variables and
the
translation of
specific
hypotheses
into
statistical
tests,
however,
are
presented
in
the
section on
results.
Sample
The
National
Assessment of
Educational
Progress
(NAEP)
provided
data
for
this
research. NAEP
employed
a
stratified,
multistage,
area-probability
sample
design
to
ascertain
the
performance
of
young
adults in
1977.
The
target
population
consisted of
those
born
between
January
1941
and
Decem-
ber
1950,
who
were
from 26
to
35
years
old at
the
time of
the
assessment.
Ninety-six
interviewers
attempted
to
administer
packages
to all
eligible
people
in
sample
households. In
the
first
stage
of
sampling,
the United
States
was
divided
into
58
primary
sampling
units
(PSUs),
comprised
of
Standard
Metropolitan-Statistical
Areas
(SMSAs)
and
counties or
groups
of
contig-
uous
counties
with a
population
of at
least
20,000.
The
PSUs
were then
stratified
by
region
of
the
country
and
SMSA/non-SMSA
status.
The next
stage
of
sampling
involved the
selection
of
2,265
housing
units
(SHUs),
of
which
2,213
were
eligible
and
occupied.
In
these
housing
units
were
1,379
age-eligible,
English-literate,
and
physically
and
mentally
undis-
abled adults
who
were
willing
to
participate
in
the
survey.
363
WALBERG
AND
TSAI
Instrument
The interviewers
asked
each
respondent
to
complete
a
background
ques-
tionnaire
and test
booklets,
for which an incentive
payment
of
$5
was
offered. The test booklet for
this
research consists
of 54
five-choice,
objective
achievement test items on science with an internal
consistency
of
.79 for the
sample employed
in
the
analysis.
The test covers three areas:
science
content,
including biology, physical
science,
and
integrated
topics;
science
processes,
including
inquiry
and
decisionmaking;
and science and
society,
including
social
problems,
science and the
self,
and
applied
science.
The science booklet also
contains 65
science motivation
items
concerning
the
respondent's opinions
about the extent to which scientists should
be
given
financial
support
for
studying
such
things
as nutrition and
continental
drift and about
the
degree
to which science can
help
solve
problems
such as
energy,
weather,
nutrition,
disease,
and
birth defects. The
internal
consis-
tency
of the total of
the
binary-scored
items is .68 for the
sample.
Procedure
Analyses
of variance were
computed
to
investigate
the association
of the
science-test
scores with motivation and
single
items
concerning past
and
current educative
experience.
As
explained
in
a
subsequent
section,
the item
responses
were used to form
weighted
composites.
The test scores
were
regressed
on linear and
logged
forms
of
the variables as well as
their
products
and
quadratic
forms. These
procedures
are illustrated and
explained
in
greater
detail
in
subsequent
sections.
RESULTS
AND DISCUSSION
The distribution of scores of the science-achievement test were
reasonably
well
spread
from the lowest to the
highest
class
intervals. Neither
inspection
nor
statistical
test,
moreover,
revealed
any departure
from
normality.
Ninety-
five
respondents,
or 6.9
percent,
of
those in the
sample,
however,
failed
to
complete
all items on the
test,
leaving
1,284,
or
93.1
percent,
of the
eligible
sample
with
complete
responses
for
analysis.
Each
person
in
the
sample
was
given
a
sample
weight
proportional
to
his or
her
representation
in
the
national
population
as a
whole,
reflecting
NAEP's
complex sampling
frame
and
weighting procedures
(see
Moore,
Chromy,
&
Rogers,
1974).
Bivariate and Partial
Correlations
Table
I
shows the
frequency
distribution of items
concerning
three
classes
of
variables:
prior
educative
background
and
activity;
current educative
activity, including exposure
to and reliance
on
mass
media
for information
about
health,
science,
and
technology;
and motivation. The
educational
background
items concern various
relatively predetermined
and stable traits
brought
about
by
educative
experiences
that are
empirically
associated
with
364
MATTHEW
EFFECTS
test achievement
as
revealed
by
past
research as
well
as in the
category
means, F-tests, correlations,
and
partial
correlations controlled
for current
activities
and motivation shown in
the
right-hand
columns of
the
table.
(The
last
category
of each item
was
omitted from
the correlations with achieve-
ment
so that the
regression equations
using binary-coded
variables would
not be
overdetermined;
but the achievement
trends across
the
items
can
easily
be seen in
patterns
of the
means.)
Although
all the educational
background
variables
are
significant,
the
respondent's
own education
and
ethnicity
are the
strongest
correlates of
science
achievement.
The
significant
correlations
involving ethnicity,
sex,
and socioeconomic status should
not
necessarily
be
interpreted
as
indicative
of inherent characteristics
but
as
indexes
of
educational
and other
environmental
experiences
that
vary widely
in
the
backgrounds
of
these
groups.
The
differences,
nonetheless,
are
large;
the
groups
within the
categories
of most
of
the items
vary
by
more than
a
full standard deviation
of
achievement
(9.78;
see Table
II).
Current
educative activities
are also
significant
correlates
of
achievement
but are
somewhat smaller
than
prior
educational
background
correlates.
They
are also reduced
considerably
when controlled for
prior
education
and
motivation.
It is
interesting
to
note
that moderate
amounts,
say,
about
I or
2 hours
per
day
of
pleasure
and
work
reading
and television
and radio
exposure
are
as
good
as
or
better
than
lesser or
greater
amounts
as far
as
science achievement
is concerned.
Those,
however,
who
rely
on
printed
material
or friends
for
information on
health,
science,
and
technology
scored
considerably
higher
than those
who
rely
on radio and
television.
The
motivation scale
is a
moderately strong
correlate of
achievement
controlled
and uncontrolled
for
education
and
current
activity,
as
shown
in
the last
part
of
Table
I.
(See
also Tables
1
and
III.)
Regression
A
nat,ysis
As
previously
mentioned,
the item alternatives
(save
one
for each item
to
serve as
the
contrast
and
prevent
indeterminacy)
were converted to
binary
or
dummy
variables. Achievement
was
regressed
on the set or
vector
of
educational variables
and
separately
on
the current
activity
variables.
The
two
predicted
achievement
variables from these
regressions
were taken
as
optimally weighted
composite
indicators
of
educational
background
and
current
information
acquisition activity; they
extract
maximum variance
from the
item
alternatives
including
linear
and,
as noted with
respect
to the
activity
variables,
nonlinear effects. Table III shows that. either
in raw or
logged
form,
they
are
strongly
correlated with
achievement,
motivation,
and
with
one
another.
These correlations reveal
colinear,
cumulative
advantage:
The
young
adults with
stronger
prior
educational
backgrounds
were more
strongly
motivated
and more
intensely
engaged
in
current activities
associ-
ated with science
achievement;
and
both
these
variables are correlated
with
achievement.
365
WALBERG
AND
TSAI
TABLE
I
Frequency Response
and
Achievement
Statisticsfor
Item
Alternative
Correlation
and
Achievement
partial
correlation
Achievement
Variable
Per-
of
alternatives
Variable
n
cent
with
achievement
M
SD
F
r
rp
Educative
background
(E)
SES
(parents'
education)
Less than
high
school
High
school
graduate
Post
high
school
College graduate
or
more
Own education
Less
than
high
school
Graduate from
high
school
Post
high
school
College
graduate
or
more
Ethnicity
White
Black
Hispanic
Others
Sex
Male
Female
Occupation
Blue collar
White
collar
Homemaker
Protective
Service
Student
Unemployed
Other
Head
of
household
occupa-
tion
Blue
collar
White
collar
Homemaker
Protective
Service
39.3
430,
29.8 326
19.0
208
27.23
9.14
33.22
8.31
35.92
7.93
83.07**
-.17**
.10**
.15**
11.9
130
38.18
8.51
20.5
262
21.76
7.25
248.39**
29.7
381
28.36 8.37
29.1
373
33.73 7.57
-.47**
-.29**
-.16**
-.10**
.19**
.10**
20.7
265
39.11
7.73
68.0
27.0
3.5
1.5
873
347
45
19
34.36
22.65
25.49
28.21
8.62
7.28
8.00
8.24
41.7
536
34.12
10.07
58.3
748
28.41
8.83
22.1
29.6
23.3
1.7
15.3
1.3
2.9
3.8
38.2
33.6
4.6
4.3
7.0
277
370
291
21
192
16
36
48
29.10
9.72
36.23
8.33
29.26
9.19
33.81
9.56
28.88
7.76
33.56
9.29
23.89
8.32
28.20
10.32
299
27.54
7.99
263
33.78
8.31
36
22.11
9.42
34
32.21
8.71
55
26.13
8.53
173.98**
115.75**
27.67**
.53**
-.51**
-.10**
-.29**
-.19**
-.09**
.35**
-.09**
.04
-.08**
.03
-.12**
23.94**
-.18**
.15**
-.15**
.02
-.10**
-.05
.18**
.03
.05
-.09**
-.02
-.08**
-.09**
.08**
-.09**
.04
-.07*
366
-.26**
.14**
.23**
MATTHEW
EFFECTS
TABLE I
Continued
Correlation and
Achievement
partial
correlation
Variabe
Per-
of
alternatives
Variable
n
cent
with
achievement
M
SD
F
r
r
Student
Unemployed
Other
Total household
income
Less than
$6,000
$6,000-11,999
$12,000-19,999
$20,000
or
more
Educational
training
in sci-
ence
or
technology
None
Less
than
2
years
2-4
years
4
years
or
more
Educational
training
in
medi-
cine
or
health
sciences
None
Less than
2
years
2-4
years
4
years
or
more
Work
experience
in
science or
technology
No
Yes
Work
experience
in
medicine
or
health
sciences
No
Yes
1.0
8
38.00
10.30
.06*
.05
2.8
22
19.68 6.21
-.15**
-.14**
8.3 65
27.69
9.53
16.7 202
24.59
8.87
27.1
327
29.28
9.16
34.9
422
32.79
8.63
21.3
257
36.18
8.54
60.8
772
27.52
8.67
25.0 318
34.62
8.61
7.3
93 34.89
9.81
6.9
87 42.01
8.03
81.3
1,025
30.28 9.65
12.1
152
33.20 9.11
4.2
53 32.55
10.69
2.5
31
37.23
9.01
82.6
1,033
29.42 9.19
17.4
218
37.83
9.30
81.7
1,001
30.31
9.62
18.3
224
33.48
9.31
75.13**
111.93**
9.25**
150.03**
20.09**
-.26**
.13**
.05
-.10**
.09**
.04
-.04
.02
.04
-.29** -.20**
-.09**
-.06
Current
activity
(A)
Reading
for
work
per
day
None
Less
than 1
hour
1-3
hours
More
than 3
hours
Reading
for
pleasure
per
day
None
Less
than
1
hour
1-2
hours
2
hours
or
more
Watching
television
per
day
None
38.4
27.1
24.6
9.8
480
28.17
9.47
339
32.57
9.46
308
33.51
9.46
123
31.33
9.69
6.7
84
23.61
10.41
45.9
574
31.48
9.37
34.5
431
31.71
9.38
12.9
162
31.50
10.07
4.1
51
31.14
13.34
24.53**
-.21**
.11**
.16**
18.23**
-.19**
.06**
.07*
27.01**
.01
-.01
.05
-.02
-.08**
-.02
.04
.02
367
WALBERG
AND TSAI
TABLE
I
Continued
Correlation
and
partial
correlation
Per-
Achevement
of
alternatives
Variable
cent
with achievement
M
SD
F
r
rp
Less than
1 hour
20.4 255 33.04
9.81
.11**
.02
1-_
hni,
r
328
409 33.32 9.05
.18** .09**
2 hours
or
more
Listening
to the
radio
per day
None
Less
than
1
hour
1-2 hours
2
hours
or
more
42.7
532
28.29 9.04
6.9
39.7
23.5
29.9
86
29.01
1.11 10.05**
496
32.33
.44
293
31.84 .57
373
29.08
.47
-.05*
.12**
.06*
.03
.06*
.01
What sources
did
you rely
on to
obtain
information
about
health
during
the last 12 months?
Broadcast
media
(TV, radio)
Never
Few
Some
Most
Printed
media
(newspapers,
magazines,
etc.)
Never
Few
Some
Most
Family
or friends
Never
Few
Some
Most
Other
sources
Never
Few
Some
Most
Didn't
get
any
information
Never
Few
Some
Most
44.4
39.5
13.7
2.4
19.4
31.2
34.1
15.3
74.5
23.4
1.6
.4
82.3
14.9
2.4
.4
70.4
22.2
6.1
1.3
570
32.25 9.75
507
30.47
9.34
176
27.90 10.18
31
25.84 9.50
249
26.71 10.45
400
30.50 9.73
438 31.85 9.08
197 34.24
8.67
957
30.73
9.71
301 31.00 9.85
21 29.52
11.62
5
37.60
9.56
1,057
30.55 9.76
191 32.16 9.88
31 30.74
9.52
5
32.20
7.85
904 31.08 9.74
285 31.18
9.74
78 28.04
8.89
17
21.89 10.48
12.50**
25.93**
.13**
-.03
.12**
-.21**
-.02
.08**
.06*
-.02
-.04
-.11**
.03
.02
.98 -.01
-.05
.01
.07*
-.02 -.06*
1.51 -.06*
.06*
-.00
-.02
.02
-.01
7.29**
.05*
.04
.02 -.02
-.07* -.04
What
sources
did
you
rely
on to
obtain information
about
science and
technology during
the
last 12
months?
Broadcast
media
Never
32.1
412 32.58 10.56 7.84**
368
.13** .07*
MATTHEW
EFFECTS
TABLE
I
Continued
Correlation and
partial
correlation
Achievement
Per-
of
alternatives
Vanable
cent
with
achievement
M
SD
F
r
rp
Few
17.4 223
30.94 9.45
.01
.02
Some
36.4 468
29.61 9.50
-.09**
-.04
Most
14.1 181 29.64
8.36
Variable
Percent
n
M
SD
F
r
r
Printed
media
Never
31.5
404
26.53
9.09 76.56** -.30**
-.13**
Few
20.0 257
28.92
9.67 -.10**
-.03
Some
29.2
375 32.70
8.80
.12**
.05
Most
19.3
248 36.83
8.48
Family
or
friends
Never
95.2
1,223
30.71
9.77 .87** -.04
-.03
Few
3.8
49
32.04 10.00
.03
.01
Some
.9
11
34.55
9.78 .04
.04
Most
.1
1
34.00
Other
sources
Never
95.9
1,231
30.74
9.81
1.26**
-.03
-.05
Few
3.3
42
31.14 8.95
.01
.04
Some
.7 9 37.00 8.60
.53**
.02
Most
.1
2
29.00 9.90
Didn't
get
any
information
Never
81.0
1,040
32.33
9.58
53.35**
.32**
.10
Few
9.7
125 25.55
7.49
-.18**
-.08**
Some
7.1
91 23.87 7.65 -.20**
-.003
Most
2.2 28 19.82
7.39
Variable
Percent
n
M
SD
F
r
rp
Motivation
(C)
Attitude score
Lower
25
percentile
23.5 301 23.26
8.14
178.45**
.56** .36**
26-50
percentile
26.5
340
28.72 8.28
51-75
percentile
26.4 338 33.17 8.50
76-100
percentile
23.6 303 38.00 7.87
Note. r, indicates
the correlation is
partial
out of all current
activity
and motivation
variables;
rb
indicates the correlation is
partial
out of
all educational
background
and motivation
variables;
rp
indicates the
correlation
is
partial
out of all
educational
background
and current
activity
variables.
*p<.05.
**p
<
.01.
369
WALBERG
AND TSAI
A
series of
planned
regressions containing
combinations
of the linear
and
quadratic
forms
of the variables as well
as their
products
showed
that
two
three-term
equations
(shown
in Table
III)
are most
parsimonious
and
best
fitting
by
the criterion
of
adjusted
accountable
variances
(Theil,
1971).
The
accountable
variances
of .67 and
.63,
respectively,
for the untransformed
and
logged
equations
are
highly significant. They
would be increased
12.5
percent
correction
for
attenuation for the achievement test
reliability
and reduced
by
3
percent
under
the conservative
assumption
that
100
binary
variables
rather
than
3 a
priori
composite
variables
entered the
regressions.
The
coefficients and
t-tests show that educational
background,
current
activity,
and motivation
make
unique
contributions to the
regression
when
controlled
for one another
and when the set of variables
including
achieve-
ment
is
in
either
raw or
logged
form.
The
t-tests
are
greatest
for educational
background among
the three
independent
variables
in both
equations,
although
all are
highly significant
(p
<
.001).
Perhaps
it should
be
mentioned
for
those familiar
with the "variance-added"
approach
of Coleman
et
al.
(1966)
that
the
Ts
provide
a
stringent
test of each variable
"going
in last."
Equations
with additional
product
and
square
terms that test for
interaction
and curvature
among
the
composite
variables add little
and
nonsignificantly
to the accountable
variance
adjusted
for the number of
independent
vari-
ables.
The accountable variances
of the two three-term
equations
cannot
be
compared
directly
because
they
are
in
different metrics.
To
compare
the
TABLE II
Univariate Statistics
and Correlations
M S
Ach
E
A
M
Achievement
(Ach)
30.80 9.78
-
.70 .56
.54
Educational
background
(E)
30.36 7.57
.77
-
.54 .32
Current
activity
(A)
30.78 5.59 .57 .55
-
.34
Motivation
(M)
42.44 8.23 .56
.45 .38
Note.
The
correlations
for
logged
variables are
above the
diagonal.
Correlation
of .05 and
.08
are
respectively significant
at the.05 and .01 levels.
TABLE III
Regression of
Untransformed
and
Logged
Variables
Constant
Education
Activity
Motivation
R2
Error
Untransformed -13.03
.73 .30
.29 .67
5.65
(T) (27.5)
(8.8)
(13.4)
Logged
-1.80
.71
.38
.39 .63
5.63
(T)
(24.7) (9.2) (17.1)
Note.
Both
R2
and all Ts are
significant
beyond
the
.01
level. The ratio
of the
variances of
the errors from the two
equations
is 1.006 and not
significant.
370
MATTHEW EFFECTS
overall
equations,
the
predicted
values
from the
logged equation
were
transformed
back
into
the
original
raw
metric and
subtracted from the
observed
values;
the
errors
or
standard
deviations of these residuals are
shown
in the
last
column of
Table
III. The
logged equation
produced
a
slightly
smaller error of
prediction;
but
the
ratio of the
variances,
1.006,
is
not
significant
at the
conventional .05
level.
Thus,
the
Cobb-Douglas logged
form
provides
a
slightly
better
but not
significantly
better fit than the
additive,
linear
model.
Figure
1
shows that
the curvature of the
logged
fit
is
slight
and
that,
reflecting
its
importance
and
larger weights
in
the
regression,
the
slope
for
prior
education is
higher
than
current educational
activity.
The
issues that these
data
do
not resolve are
theoretically
and
practically
important.
The
linear
equation
implies
that
adding
more of
any
one
of the
three factors would
keep
increasing
achievement
indefinitely
and
indepen-
dently
of the
other
factors;
more
and more
motivation,
for
example,
would
increase achievement
indefinitely
even
if current
activity
remained the same.
The
logged
form
implies
that each
factor
has
diminishing
returns when the
others are
fixed
because all three factor
coefficients are less than
one;
increasing
motivation
beyond
a
point,
for
example,
would be less
productive
than
also
increasing
current
activity.
It
further
implies,
however,
increasing
returns to
scale because
the
factor
coefficients
sum
to
greater
than
one,
and
doubling
them
all,
perhaps
by
increasing
the scale of both motivation and
lifelong
education
or
perhaps
by
personal specialization,
would more than
double achievement.
Because
the
efficient allocation of
scarce
resources to
competing goals requires
knowledge
of
the
production
function,
it
would be
useful to know
the true form
of
the
equation.
The
limitations
of
educational
measures
are
likely
to
continue to
make the
resolution
of the issues difficult.
CONCLUSIONS
Within
the
constraints of the
cross-sectional
data,
it
appears
that
general
science
achievement
among young
adults
depends
on
relevant
prior
educa-
tional
background,
current
educative
activity,
and
motivation;
and
that
educational
background,
including
psychological aspects
of environments
experienced
in
schools,
ethnic
and
socioeconomic
groups,
and families
weighs
most
heavily.
The three
factors,
even
though
each
makes
a
significant
contribution to the
accountable
variance,
are
colinear;
those
advantaged
on
one are
likely
to be
advantaged
on the other two. The
advantages
are
not
only
colinear but
cumulative,
because
prior
educational
background
predicts
current educative
activity
and
motivation and
all
three contribute
to
achieve-
ment.
Thus,
two
aspects
of the
Matthew effect are
supported.
The
data,
however,
show no
clear-cut
superiority
of the
Cobb-Douglas
multiplicative,
diminishing-returns
model over
an
additive,
linear
model.
Thus,
whether
achievement
is
determined
by
processes
of
multiplicative
efficiency
or
additive
compensation
remains
for
subsequent
research
to
371
WALBERG
AND TSAI
answer.
Furthermore,
the
possibility
of
reverse
causation,
for
example,
motivation and
activity
enhanced
by
achievement,
should also be acknowl-
edged
and
investigated. Longitudinal
achievement data with
daily logs
of
activities
of a
large,
diversified
sample
would be difficult and
expensive
to
obtain but would
permit
a better
assessment of
these
latter
questions.
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372
MATTHEW EFFECTS
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AUTHORS
HERBERT
J.
WALBERG,
Research
Professor
of
Urban
Education,
Uni-
versity
of
Illinois,
Chicago,
College
of
Education,
Box
4348,
Chicago,
IL
60680.
Specialization:
Educational
productivity
and
psychology.
SHIOW-LING
TSAI,
Research
Assistant,
University
of
Illinois,
Chicago,
College
of
Education,
Box
4348,
Chicago,
IL
60680.
Specializations:
Measurement,
evaluation,
and
statistical
analysis;
economics.
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