Description
In recent years, the contingency-based management accounting literature has been criticized for being fragmentary
and contradictory as a result of methodological limitations. This study adds to this picture by showing that the theoretical
meaning of some commonly used statistical techniques is unclear, i.e. the functional forms are not precise enough
to be able to discriminate between several sometimes even conflicting theories of contingency fit. The study also shows
that the techniques differ significantly in terms of how interaction effects between context and management accounting
are modeled.
The appropriateness of statistical methods for testing
contingency hypotheses in management accounting research
Jonas Gerdin
*
, Jan Greve
Department of Business Administration, O
¨
rebro University, SE-701 82 O
¨
rebro, Sweden
Abstract
In recent years, the contingency-based management accounting literature has been criticized for being fragmentary
and contradictory as a result of methodological limitations. This study adds to this picture by showing that the theo-
retical meaning of some commonly used statistical techniques is unclear, i.e. the functional forms are not precise enough
to be able to discriminate between several sometimes even con?icting theories of contingency ?t. The study also shows
that the techniques di?er signi?cantly in terms of how interaction e?ects between context and management accounting
are modeled. This implies that some methods are only appropriate when theory predicts interaction e?ects in general
while others are only appropriate in cases where theory speci?es a more precise functional form of interaction such as
symmetrical or crossover interactions. Based on these observations, several recommendations for future research are
proposed.
Ó 2007 Elsevier Ltd. All rights reserved.
Introduction
In recent years, several literature reviews have
highlighted that many di?erent ways of conceptu-
alizing ‘contingency ?t’ between context and Man-
agement Accounting System (MAS) have been
used in the literature (Chenhall, 2003; Luft &
Shields, 2003) and that few researchers fully
acknowledge the di?culties of relating these forms
to each other (Gerdin & Greve, 2004). There has
also been a growing interest in (and debate about)
how individual statistical techniques have been
applied in contingency-oriented MAS research
(Dunk, 2003; Gerdin, 2005a, 2005b; Hartmann,
2005; Hartmann & Moers, 1999, 2003). The pur-
pose of this paper is to combine these two streams
of research by providing a systematic analysis of
the appropriateness of commonly used statistical
techniques for testing the di?erent forms of ?t
found in the literature.
In so doing, we propose a conceptual frame-
work which identi?es a number of possible per-
spectives of contingency ?t. Unlike most of the
0361-3682/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.aos.2007.07.003
*
Corresponding author. Tel.: +46 19 30 30 00; fax: +46 19 33
25 46.
E-mail addresses: [email protected] (J. Gerdin), jan.
[email protected] (J. Greve).
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Available online at www.sciencedirect.com
Accounting, Organizations and Society 33 (2008) 995–1009
existing MAS literature (e.g. Chenhall, 2003;
Gerdin & Greve, 2004; Luft & Shields, 2003), the
framework explicitly elaborates on the distinction
between a matching and a multiplicative model
of ?t (Schoonhoven, 1981). The framework also
contributes to the more general discussion about
the use of statistical techniques in contingency
research (Donaldson, 2001; Drazin & Van de
Ven, 1985; Meilich, 2006; Venkatraman, 1989) by
highlighting that the paradigm seems to accommo-
date at least three levels of theory speci?cation.
The paper proceeds as follows. Drawing upon
seminal contingency work, three levels of precision
in the functional form of context/MAS interactions
and four principal and con?icting approaches to
contingency ?t are identi?ed. Next, it is discussed
to what extent statistical methods frequently
applied in contingency-based MAS research can
be used to test the di?erent levels of interaction
and to distinguish between the four approaches.
This results in several conclusions and recommen-
dations for future research which ?nalize the paper.
Levels of theory speci?cation in the contingency
paradigm
The essence of contingency theory is that orga-
nizations must adapt their structure to contingen-
cies such as the environment, organizational size
and business strategy if the organization is to per-
form well (Burns & Stalker, 1961; Donaldson,
2001; Drazin & Van de Ven, 1985; Lawrence &
Lorsch, 1967; Pennings, 1992; Woodward, 1965).
Galbraith (1973, p. 2) formulated this core idea
of contingency theory in the following way:
1. There is no one best way to organize.
2. Any way of organizing is not equally e?ective.
These statements imply that the e?ectiveness
of organization structures is contingent on
context—i.e. there is no universally best way to
organize—and that, in a particular context, certain
structure(s) will outperform other structures.
Schoonhoven (1981, p. 351) referred to this partic-
ular form of relations between variables as
interactions.
Generally, an interaction e?ect exists whenever
the e?ect of an independent variable (structure)
on the dependent variable (performance) varies
due to the values of a third variable (context) (Jac-
card & Turrisi, 2003). As illustrated in Table A,
Fig. 1, an interaction e?ect thus implies that a
change in structure has a more positive (or nega-
tive) e?ect on performance in di?erent contexts
(Luft & Shields, 2003). Given the broad format
of this type of interaction, it will henceforth be
referred to in terms of ‘general interaction’ and
represents the ?rst level of theory speci?cation.
a
C
H
and C
L
denote high and low levels of the contingency factor, respectively.
Structure
Performance
Low High
C
H
C
L
Table A
C
H
C
L
Low High
Performance
Low High
Performance
Table B
C
H
C
L
Structure
Table C
Structure
Fig. 1. Illustration of an interaction (monotonic) function (Table A), a symmetrical interaction (non-monotonic) function (Table B)
and a crossover interaction function (i.e. both non-monotonic and disordinal function) (Table C)
a
.
996 J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009
However, much of the early contingency work,
e.g. Burns and Stalker (1961) and Galbraith
(1973), seems to involve a higher level of theory
speci?cation (henceforth referred to in terms
of the second level) where interaction e?ects
take a symmetrical form (Schoonhoven, 1981).
As illustrated in Table B in Fig. 1, a symmetrical
interaction implies that a certain structure is
high-performing when contingency is low (C
L
),
while another structure is high-performing when
contingency is high (C
H
).
Some contingency theorists have brought the
idea of symmetrical interaction one step further
as they have also speci?ed the relation between
contingency ?t and performance (henceforth
referred to as the third level of theory speci?ca-
tion). For example, Woodward (1965, p. 69), in
her pioneering study of the ?t of span of control
to technology, noted that all ?rms in a state of
?t had equal performance ratings even though
there were three di?erent ?ts, one for each technol-
ogy category. Hence, organizations in states of ?t
outperformed those in mis?t—both within and
between contextual subgroups—which suggests
that it is the degree of ?t between structure and
context that is the principal explanation of
observed variance in organizational performance,
not structure or context alone.
1
Pfe?er (1982, p.
148) referred to this relation in terms of ‘the conso-
nance hypothesis’ implying that ‘‘those organiza-
tions that have structures that more closely
match the requirements of the context are more
e?ective than those that do not’’.
However, when we claim that there are no gen-
erally more e?ective contexts, we need to demon-
strate that the symmetrical interaction e?ect also
is disordinal, i.e. the ranking order of structure
related to performance changes within the obser-
vable range of data (Cohen, Cohen, West, &
Aiken, 2003) (see Table C, Fig. 1). Such e?ect is
sometimes referred to in terms of a ‘crossover
interaction’ (Cohen et al., 2003).
Conceptualizations of contingency ?t
Over the years, there has been considerable
debate in the contingency theory literature (for
overviews see Donaldson, 2001; Drazin & Van de
Ven, 1985; Pennings, 1992; Venkatraman, 1989).
The following three issues of controversy are
directly linked to the conceptualization of contin-
gency ?t:
2
– Congruence vs. contingency. Is ?t postulated, or
must it be explicitly shown that deviations from
optimal context/structure combinations lower
organizational performance?
– Cartesianism vs. con?gurationalism. Is ?t a con-
tinuum between pairs of contingency and struc-
ture dimensions that allows frequent and small
movements by organizations from one state of
?t to another, or is it the internal consistency
of multiple contingency and structural elements
with organizations having to make ‘quantum
jumps’?
– Matching vs. multiplicative relationships. Is ?t a
line with many optimal combinations of context
and structure where any deviations a?ect
performance equally, or is it assumed that there
are only two optima and that the e?ect of devi-
ations di?ers across di?erent levels of context?
While the meanings and implications of the for-
mer two controversies on management accounting
research have been discussed in several previous
1
In fact, some scholars even propose that structural contin-
gency theory, at least in its original form, postulated so-called
iso-performance, i.e. that organizations with structures that
match contexts perform about equally albeit they operate in
di?erent contexts, while organizations in states of mis?t
perform below that level (Donaldson, 2001; Drazin & Van de
Ven, 1985; see also Schoonhoven’s interpretation of Galbraith’s
(1973) theory at p. 353 and also her operationalization of
contingency ?t at p. 352).
2
Note that the terminology in the literature is somewhat
confusing. For example, when Drazin and Van de Ven (1985, p.
514) use the term ‘congruence’, it refers to an unconditional
association between context and structure, while Donaldson
(2001, pp. 186–189) use the same term to denote a speci?c type
of conditional association between context, structure and
performance—an association which yet other researchers have
referred to in terms of matching models (Schoonhoven, 1981;
Venkatraman, 1989). In the present study, we decided to handle
this diversity by using an adapted version of the terminology
proposed by Gerdin and Greve (2004).
J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009 997
studies (see e.g. Chenhall, 2003; Gerdin & Greve,
2004; Luft & Shields, 2003), the third controversy
has received much less attention (but see Hart-
mann & Moers, 1999, p. 299). This is unfortunate
since also the distinction between a matching and a
multiplicative model of contingency ?t has impor-
tant consequences for the choice of appropriate
statistical methods. In the matching form of ?t, it
is assumed that for every value of context, there
is a unique value of structure at which perfor-
mance is maximized. As illustrated by Tables A
and C in Fig. 2, a particular structure optimizes
performance at a low value of contingency (e.g.
low structure at C
1
) while another structure maxi-
mizes performance at a high value of contingency
(e.g. high structure at C
5
). Judging from the math-
ematical operationalizations of this form of ?t in
previous studies (see e.g. Schoonhoven, 1981, p.
352), so-called iso-performance is often assumed,
i.e. all states of ?t produce the same level of perfor-
mance (see also Woodward, 1965, and the discus-
sions in Donaldson, 2001, & Van de Ven &
Drazin, 1985). However, iso-performance is not
an inevitable consequence of the symmetry
assumption (Donaldson, 2001).
Furthermore, Table A illustrates that any devi-
ations in either direction from the unique optimal
value of structure reduce the level of performance.
Put in another way, each point on the ?t line rep-
resents the optimum on a non-linear function
where performance is the dependent variable and
structure is the independent variable (see Table
C, Fig. 2). Thus, the contingency factor acts as a
moderator because it ‘‘determines which charac-
C
5
Structure
Structure
P
e
r
f
o
r
m
a
n
c
e
P
e
r
f
o
r
m
a
n
c
eC
4
C
3
C
2
C
1
C
5
C
4
C
3
C
2
C
1
Low High
Low High
Table C
b
Table D
b
b The indices denote the level of contingency.
2
4
6
8
10
2
4
6
8
10
Low High
High
Low
Contingency
P
6
P
10
P
8
P
4 P
10
P
10
P
8
P
8
P
6
P
6
P
8
P
4
P
8
P
10
P
6
P
8
P
4
P
6
Table A
a
P
8
Structure
P
8
P
6
P
4
P
10
a
The indices denote the level of organizational performance.
P
2
P
2
Low High
High
Low
Contingency
P
8
P
4 P
7
P
6
P
6
P
6
P
6
P
5
P
6
P
4
P
6
P
7
P
5
P
8
P
4
Table B
a
P
8
Structure
P
8
P
6
P
4
P
2
P
2
P
6
P
10
P
10
P
6
Fig. 2. Illustration of a matching form of interaction (Tables A and C) and a multiplicative form of interaction (Tables B and D).
998 J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009
teristic produces high levels of e?ectiveness of the
organization’’ (Donaldson, 2001, p. 6) and it
‘‘e?ectively shifts the curvilinear relationship
between the structural and outcome variables’’
(Meilich, 2006, p. 165).
Finally, matching models seem to imply that a
deviation of one unit from the optimal structure/
contingency combination has the same e?ect on
performance across all levels of the contingency
(see the indices in Table A, Fig. 2).
When Schoonhoven (1981, p. 355) examined
some of Galbraith’s (1973) statements, she con-
cluded that he implicitly understands contingency
relationships as multiplicative forms of ?t. That
is, the e?ect of a structural variable on perfor-
mance increases, or decreases, as a result of
changes of the contingency level (see Fig. 2, Tables
B and D). Contrary to the matching form, multi-
plicative interaction thus assumes that perfor-
mance is a linear function of structure at each
value of contingency. The assumption about line-
arity in conjunction with the assumption about
non-monotonic relationships implies that the con-
tingency factor (moderator) determines both the
direction and amplitude of structure’s e?ect on per-
formance (cf. Table D in Fig. 2 where the struc-
ture-performance relationships at C
2
and C
5
not
only have di?erent slopes, but also di?erent signs).
The con?icting assumptions about linearity in
the matching and the multiplicative form have
important consequences. Note especially that the
multiplicative form implies that only two struc-
tures (the extreme values) are assumed to be opti-
mal (cf. the typical ‘saddle form’ in Table B
(Southwood, 1978)). Implicitly, the multiplicative
interaction form thus postulates so-called hetero-
performance, i.e. that di?erent contingency/struc-
ture combinations produce di?erent maximum
performances. Also note that in contexts around
the in?exion point C
3
in Fig. 2, Table D, all struc-
tures produce about the same level of perfor-
mance. None of these features are compatible
with a matching view, where ?t results from
numerous combinations of contingency and struc-
ture, yet for each value of contingency, only one
structure can be optimal.
It can be concluded that within the contingency
literature, there has been a number of controver-
sial issues in terms of what constitutes ?t between
context and structure and how ?t is attained. In
addition to Cartesian models of ?t (such as the
matching and multiplicative model), there are the-
ories predicting that ?t is the degree of adherence
to con?gurations consisting of multiple context
and structure variables (Drazin & Van de Ven,
1985; Venkatraman, 1989). As mentioned above,
there is also a set of so-called congruence models
that do not aim to explain variations in perfor-
mance in terms of (mis)?t as they typically postu-
late that only high performers exist to be observed.
In the previous section, we also pointed out that
there are at least three broad variants of contin-
gency theory that di?er in terms of their level of
speci?city. Some theories seem to predict interac-
tion e?ects per se between context and structure
(i.e. general interaction), while others prescribe
non-monotonic relationships (i.e. symmetrical
interaction) and, sometimes, also disordinal rela-
tionships (i.e. crossover interaction).
When we combine the di?erent models of ?t
with the di?erent levels of theory speci?cation,
we get a number of possible variants of contin-
gency theory (see Table 1). Arguably, as these the-
oretical variants make very di?erent assumptions
about how ?t is obtained, they typically require
di?erent statistical test methods. More precisely,
the method(s) used should (at least ideally) have
the capacity to test for the assumptions made
at the chosen level of theory speci?cation—no
more, no less—and, at the same time, have a func-
tional form that corresponds with the model of ?t
predicted. The functional form should preferably
also be precise enough to be able to discriminate
between the di?erent models of ?t. As will be dem-
onstrated in the next section, this is not always the
case.
Commonly used statistical techniques in
management accounting studies to conceptualize
contingency ?t
According to several recent literature reviews,
many di?erent statistical techniques have been
used in the literature (see e.g. Chenhall, 2003; Ger-
din & Greve, 2004; Hartmann & Moers, 1999; Luft
J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009 999
& Shields, 2003). In Table 2, frequently occurring
techniques identi?ed in these literature reviews
are outlined.
In the following sections, these statistical tech-
niques will be brie?y described and classi?ed in
terms of their level of theory speci?cation and it
will be discussed to what extent they can discrimi-
nate between the four forms of contingency ?t out-
lined above.
3
Fit as di?erence in means
In congruence-type of studies, this way of con-
ceptualizing contingency ?t implies that a sample
of organizations, subunits or the like is divided
into subgroups and the MAS characteristics of
the subgroups are compared (see e.g. Abernethy
& Lillis, 1995). Since all congruence models seem
to predict symmetrical relationships, but it is
unclear whether crossover interactions are postu-
lated, it will henceforth be argued that signi?cant
results imply (but do not formally test) either of
the two types of interactions.
In contingency-type of MAS research, we have
found two approaches. One is that of Chenhall
and Lang?eld-Smith (1998) who used cluster anal-
ysis to form organizational gestalts and then exam-
Table 1
Variants of contingency theory (the head of the table is an adapted version of that in Gerdin and Greve (2004, p. 318))
a
Forms of fit
Contingency Congruence
Cartesian Configuration
Levels Matching Multiplicative
3. Crossover
interaction
2. Symmetrical
interaction
1. General
interaction
a
As all congruence models seem to predict at least symmetrical relationships (i.e. that di?erent contexts are associated with di?erent
structures), the lower right cell is considered as theoretically not relevant.
Table 2
Commonly used statistical methods in MAS studies to conceptualize and test the existence of contingency ?t
Contingency ?t as: Selected references:
Di?erence in means Abernethy and Brownell (1999), Abernethy and Lillis (1995),
Chenhall and Lang?eld-Smith (1998)
Bivariate correlation Duncan and Moores (1989), Gerdin (2005b), Govindarajan (1988),
Haka (1987), Merchant (1981, 1984), Selto et al. (1995)
Di?erence in correlation
coe?cients (strength)
Abernethy and Brownell (1999), Abernethy and Lillis (1995),
Khandwalla (1972), Merchant (1981, 1984), Simons (1987)
Di?erence in correlation
coe?cients (form)
Macintosh and Daft (1987)
Linear regression coe?cients Brownell (1982), Duncan and Moores (1989), Frucot and
Shearon (1991), Kaplan and Mackey (1992), Simons (1987)
Di?erence in regression
coe?cients
Abernethy and Brownell (1997), Bisbe and Otley (2004),
Brownell and Merchant (1990), Chong (1996), Perera et al. (1997)
An indirect path coe?cient Baines and Lang?eld-Smith (2003), Bouwens and Abernethy (2000),
Chenhall and Morris (1986), Chong and Chong (1997)
3
Note that these techniques will be dealt with separately
below. In many of the empirical studies cited, however, several
ways of testing contingency ?t have been used. This implies that
some of the drawbacks and limitations related to individual
statistical techniques discussed may have been addressed by the
researchers cited insofar as they deliberately have used several
complementary statistical analyses (see also the concluding
discussion).
1000 J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009
ined whether the di?erences in average performance
scores between clusters were statistically signi?cant.
As the authors expected that di?erent strategies
would be associated with di?erent sets of manage-
ment control techniques and practices, this way of
testing contingency ?t implies a con?guration
approach predicting symmetrical interactions.
In the other approach, the typical procedure is
?rst to create subgroups consisting of ?ts and mis-
?ts in two contexts, respectively, and then to show
that the performance score of the ?ts is superior to
that of the mis?ts (see e.g. Abernethy & Brownell,
1999). In our view, this way of conceptualizing ?t
implies that a crossover interaction is predicted
(i.e. relationships are symmetrical and, further-
more, no context is generally more e?ective). How-
ever, this test provides very little information about
the form of the association. For example, is a di?er-
ence in MAS the result of an incremental adapta-
tion to context, or are quantum jumps required
(cf. the Cartesian and the Con?guration approach,
respectively)? Furthermore, is a signi?cant result a
crude expression of a ?t line with numerous opti-
mal solutions, or does it indicate that MAS should
either be maximized or minimized in order to max-
imize performance (cf. the matching and the multi-
plicative form of interaction, respectively)?
So to conclude, the di?erent variants of analyz-
ing means found in the literature may imply both
symmetrical and crossover interactions. Further-
more, for some uses it is clear which form of ?t
is being tested, for others this is not the case.
Fit as bivariate correlation
In some congruence-type of studies, ?t is opera-
tionalized as a statistically signi?cant correlation
between context and MAS (see e.g. Merchant,
1981, 1984). Given that this application of correla-
tion analysis is only used to test predictable corre-
lations between pairs of context and MAS variables,
it can be argued that it focuses on the form of the
relationship. As a result, bivariate correlation
analysis seems to correspond well with a Cartesian
variant of congruence-type of contingency ?t.
In contingency-type of studies, bivariate correla-
tion analysis has been used to test the e?ect of ?t
on performance in so-called deviation-score or
residual analyses (see e.g. Duncan & Moores,
1989; Gerdin, 2005b). The typical procedure is to
?rst compute deviations between a theoretically
or empirically derived ?t line and actual positions,
and then to correlate the deviation-score with
performance.
Arguably, this way of using bivariate correla-
tion analysis is founded on a matching theory inso-
far as the ?t line encompasses an in?nite number
of unique combinations between context and
MAS, each of them assumed to produce maximum
performance, and each unit of deviation from the
?t line a?ects performance equally (see Tables A
and C in Fig. 2). Furthermore, since any deviation
from the optimal line is explained by mis?t alone
(context has no direct e?ect), it implies that a
crossover interaction is predicted.
Notably, however, bivariate correlation analy-
sis has also been used to test symmetrical and gen-
eral interactions. An example of the former type is
the study of Govindarajan (1988) which predicted
a negative correlation between the degree of dis-
tance from ideal con?gurations in two contexts
and organizational performance, but no assump-
tions about ‘context e?ects’ were made (see also
Selto, Renner, & Young, 1995). An example of
the latter type of interaction is the study of Haka
(1987) which expected that ?rms using sophisti-
cated capital budgeting models outperformed
matched non-users in high levels of context but
not in low levels. As Haka used a non-parametric
correlation analysis based on rank order, however,
it is unclear whether the underlying relationship is
expected to be linear (cf. the matching model) or
non-linear (cf. the multiplicative model).
To conclude, bivariate correlation analysis has
been employed for testing congruence theories as
well as matching and con?guration theories at
the crossover and symmetrical interaction levels,
respectively. The technique has also been used to
test the existence of general interactions.
Fit as di?erence in correlation coe?cients: strength
To our knowledge, subgroup correlation analy-
sis focusing on di?erences in strength has above all
been applied in contingency-type of MAS studies
(but see e.g. Khandwalla, 1972). For example,
J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009 1001
Abernethy and Brownell (1999, p. 198) computed
correlation between strategic change and perfor-
mance for two MAS sub-samples (see also Simons,
1987; Merchant, 1981, 1984; Abernethy & Lillis,
1995). In our view, an analysis focusing on di?er-
ences in strength between subgroups does neither
correspond with a matching, nor a con?guration
perspective. The premise is that these theories give
little reason to expect that the predictive ability of
MAS on performance should di?er across di?erent
levels of the contingency variable (see also the dis-
cussion in Drazin & Van de Ven, 1985).
In contrast, this is what a multiplicative form
of ?t implies. That is, for contingency levels
around in the in?exion point in Table D, Fig. 2,
the predictive ability of MAS on performance is
very low, which implies that the correlation is
expected to be low, while the opposite holds for
the extreme values of the contingency variable
(see C
1
and C
5
). Note also that the method repre-
sents the ?rst level of theory speci?cation (i.e. pre-
dicts general interactions), since a signi?cant
di?erence in correlation per se neither shows that
a high-correlation subgroup generally outperforms
a low-correlation group, nor that a certain MAS is
appropriate in certain contexts and another MAS
in others.
Fit as di?erence in correlation coe?cients: form
Congruence-type of studies focusing on the dif-
ferent forms of correlation coe?cients typically
predict that a particular MAS is positively corre-
lated with the extent of one context and negatively
correlated with the extent of another one (e.g.
Macintosh & Daft, 1987). In our view, such a
use of subgroup correlation analysis seems to
imply a Cartesian variant of contingency ?t insofar
as a continuous (and linear) relationship between
context and MAS is predicted.
In Contingency-type of studies, ?t is supported
by demonstrating that there are statistically signif-
icant di?erences between subgroups, produced by
the correlation between MAS and performance
being positive for one contextual subgroup and neg-
ative for the other subgroup. Accordingly, some
information about whether relationships are sym-
metrical is provided, but none about whether a
crossover interaction e?ect is present (see Table
B and C in Fig. 1).
However, it is unclear as to which form of ?t is
supported. To illustrate, again recall the relation-
ships depicted in Fig. 2 above. From both a match-
ing and a multiplicative perspective, we would
expect a negative correlation between MAS and
performance for low levels of the context (see C
1
and C
2
in Tables C and D) and a positive correla-
tion for high levels (C
4
and C
5
). However, while
both models of ?t are supported by di?erent signs
of the subgroup correlation coe?cients, we should
not conclude that the higher the correlations, the
better the support of these types of relationships.
In fact, it could be argued that this use of correla-
tion analysis is better suited to test a speci?c form
of con?guration theory, namely, when it is expected
that ?rms bene?t from the highest possible values
on a set of management control dimensions in one
context, and from the lowest possible values in the
opposite context (see e.g. Govindarajan, 1988).
To conclude, subgroup correlation analysis
focusing on the form of relationships can generally
be used to test the existence of symmetrical interac-
tions, but it cannot di?erentiate between a match-
ing, a multiplicative and a con?guration model.
Fit as linear regression coe?cients
This approach to conceptualizing and testing
contingency ?t typically implies that regression
equations of the following form are ?tted to the
data:
Y ¼ b
0
þ b
1
X
1
þ b
2
X
2
þ b
3
X
3
þ e ð1Þ
In congruence-type of MAS studies, main e?ect
regression analysis has primarily been used to test
whether MAS design/use (Y) is associated with
one or several contingency factors (X
i
) (see e.g.
Kaplan & Mackey, 1992). However, regressions
in the ‘opposite direction’ can also be found in
the literature. For instance, Simons (1987) used a
logit regression model in which competitive strat-
egy was modeled as the dependent variable (Y)
and a number of management control and envi-
ronmental factors were independent variables (X
i
).
Importantly, however, the theoretical interpre-
tation of main e?ect regressions can be unclear.
1002 J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009
For example, the Kaplan and Mackey study cited
above seems to imply a Cartesian variant since each
independent contextual variable is expected to have
an e?ect on the degree of MAS use. The analysis
performed by Simons (1987), in contrast, seems to
imply a con?guration variant as the logit regression
examines whether the overall pattern of control sys-
tem attributes di?ers between strategic types.
In contingency-type of studies, a ‘?t term’ is
often regressed on performance (Brownell, 1982;
Duncan & Moores, 1989; Frucot & Shearon,
1991). Such regression typically has the following
format (Hartmann & Moers, 1999; Venkatraman,
1989):
Y ¼ b
0
þ b
1
X þ b
2
Z þ b
3
jX À Zj þ e ð2Þ
where X is a MAS attribute, Z is context and Y is
performance. The ‘?t term’ jX À Zj is a deviation-
score, indicating the lack of ?t between X and Z.
Arguably, this way of using linear regression
analysis resembles the above discussed use of
bivariate correlation analysis to establish a rela-
tionship between a deviation-score and perfor-
mance. By implication, it means that this method
is not suitable for detecting multiplicative or con-
?gurative relationships between (mis)?t and per-
formance. Unlike the use of bivariate correlation
analysis discussed above, however, linear regres-
sion coe?cients disclose the nature of the relation
(Duncan & Moores, 1989), i.e. the potential con-
textual in?uence on performance is separated from
the interaction e?ect as such in the analysis. This
means that interaction e?ects will be detected also
in situations where performance is strongly in?u-
enced by context, i.e. when the interaction is sym-
metric (but not disordinal). Yet, if b
2
in Eq. (2) is
not signi?cant, or if the variables X and Z are not
included in the equation, and b
3
is still signi?cant,
this indicates a crossover interaction. Accordingly,
depending on how the regression is written and the
results of the test, this statistical technique can be
used to explore the existence of both symmetrical
and crossover interactions.
Fit as di?erence in regression coe?cients
One frequently used technique for testing the
existence of a signi?cant di?erence in regression
coe?cients is the moderated regression analysis
(MRA) (Hartmann & Moers, 1999). An MRA
typically has the following format:
Y ¼ b
0
þ b
1
X þ b
2
Z þ b
3
X Ã Z þ e ð3Þ
where Y is a dependent variable, X is an indepen-
dent variable, Z is a moderator, X
*
Z is the mod-
erating e?ect that Z has on the relationship
between X and Y, and e is the error variable (Co-
hen et al., 2003; Jaccard & Turrisi, 2003).
Although MRA has been used in congruence-
type of studies (e.g. Perera, Harrison, & Poole,
1997), a signi?cant interaction term per se is not
required to conclude that a congruence relation-
ship exists. Rather, the inclusion of such term (in
addition to main e?ect coe?cients) merely implies
that the functional form of the context/MAS rela-
tionship is ‘better’ speci?ed.
In contingency-type of MAS studies (Bisbe &
Otley, 2004; Brownell & Merchant, 1990; Chong,
1996), however, the interaction term is crucial as
it tests the existence of general interaction e?ects.
That is, a signi?cant term indicates that the e?ect
of MAS on performance di?ers across di?erent lev-
els of context, but no information is provided
about whether the e?ect is non-monotonic (sym-
metrical interaction) or disordinal (crossover inter-
action). Furthermore, since this form of MRA is
based on ‘linear by linear’ interactions (Cohen
et al., 2003; Jaccard & Turrisi, 2003), it is unsuit-
able to test the existence of curve linearity predicted
by the matching model (cf. Table C in Fig. 2).
In the MAS literature, there are also examples
of where regression coe?cients in di?erent sub-
groups have been compared in order to test for
interaction e?ects. For example, Abernethy and
Brownell (1997) ?rst divided their sample into four
contextual groups and then regressed simulta-
neously three types of control on managerial per-
formance in each of the four groups. Like MRA,
this way of using main e?ect regression analysis
is inconsistent with matching theory insofar as
matching theory gives little reason to expect that
MAS’s e?ect on performance should di?er across
di?erent levels of context.
So to conclude, both MRA and comparisons of
main e?ect coe?cients between subgroups seem
appropriate for testing a multiplicative model of
J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009 1003
?t. Furthermore, both test for the existence of gen-
eral interactions.
Fit as an indirect path coe?cient
In MAS research, contingency ?t is often ana-
lyzed by the introduction of a mediating variable.
That is, the e?ect of the independent variable on
the dependent variable operates completely or par-
tially through the mediating variable (Gerdin &
Greve, 2004; Luft & Shields, 2003; Venkatraman,
1989). In congruence-type of studies, di?erent
properties of MAS are typically modeled as the
dependent variable (e.g. Bouwens & Abernethy,
2000; Chenhall & Morris, 1986).
Arguably, while a path analysis may reveal asso-
ciations between variables, only direct relations can
express a congruence relationship. Hence, a con-
gruence relationship is supported whenever an
indirect path is prevalent, but only in the sense that
the mediator is signi?cantly associated with MAS.
Also contingency-type of studies using path-
analytical techniques are common in the MAS lit-
erature (e.g. Baines & Lang?eld-Smith, 2003;
Chong & Chong, 1997). However, although these
methods contribute to our understanding about
what determines design and use of MAS, they do
not test for the existence of interaction e?ects
between context and MAS on performance. To
illustrate, consider a theory predicting that high-
performing ?rms in dynamic environments rely
on externally oriented MASs (Proposition A),
and that high-performing ?rms in stable environ-
ments rely on internally oriented MASs (Proposi-
tion B). While a path analysis in a sense could
con?rm Proposition A by showing that dynamism
is positively correlated with externally oriented
MASs which, in turn, is positively correlated with
performance, such a result would contradict Prop-
osition B (because it implies that stability is posi-
tively correlated with an internally oriented MAS
which, in turn, is negatively correlated with perfor-
mance). Accordingly, path analyses cannot explore
the existence of moderated causal relationship(s)
predicted by contingency theory (Donaldson,
2001; Schoonhoven, 1981), i.e. where the relation-
ship between MAS and performance is moderated
by context.
Results of the analysis of statistical methods
In Table 3, the di?erent uses of statistical meth-
ods found in the contingency-style MAS literature
have been sorted into the classi?catory framework
developed above. A method’s row position thus
denotes the level of speci?city of the theory being
tested and the column denotes the particular
model of ?t being tested. A line that crosses several
columns represents the method’s inability to dis-
criminate between the models of ?t in question.
Finally, a dotted line marks that the interaction
e?ect is postulated rather than formally tested.
Several observations can be made based on
Table 3. A ?rst observation is that studies have
been made in most theoretically relevant subcate-
gories of contingency theory. This is noteworthy
in its own right as it reinforces recent claims sug-
gesting that contingency-based MAS research is
diverse (Chenhall, 2003; Gerdin & Greve, 2004;
Luft & Shields, 2003) and, furthermore, suggests
that future research not only should consider the
di?erent forms of ?t present in the literature, but
also the di?erent levels of theory speci?cation.
Given the purpose of this study, however, a more
important conclusion related to this observation
is that, generally, di?erent statistical methods have
been used to test these sub-theories (an exception
is congruence-type of studies in which all methods
have been employed). Overall, this multiplicity is a
necessity as these di?erent variants of contingency
theory make very di?erent assumptions about the
nature of relationships.
A second observation is that some methods
have di?culties in distinguishing between di?erent
forms of ?t. For example, when mean values of
performance between subgroups are compared
and a signi?cant crossover interaction in the pre-
dicted direction is identi?ed, this indicates that
MAS is contingent on context. However, a cross-
over interaction e?ect may be predicted in all
forms. Consequently, such comparison of mean
values helps to identify contingency variables;
however, it does not specify the functional form
of the ?t relationship.
A third observation is that the number and qual-
ity of methods is unequally distributed amongst
sub-theories. For some subcategories, several func-
1004 J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009
tionally precise methods have been used (e.g.
matching theories predicting crossover interac-
tions) while, for others, the opposite is the case
(e.g. for multiplicative type of studies predicting
symmetrical or crossover interactions). As will be
developed in more detail below, these di?erent pre-
requisites imply that researchers sometimes need to
prioritize between several conceivable alternatives
and, sometimes, need to come up with complemen-
tary or ‘new’ techniques in order to compensate for
an existing lack of appropriate ones.
A fourth observation is that one of the methods
previously discussed, i.e. path analysis, can only be
used to test congruence-type of theories. However,
this is not to say that path analysis generally
should be avoided when a contingency-form of ?t
is predicted. After all, there might be situations
where theory suggests a combination of the two
forms of causality (Chenhall, 2003).
A ?fth observation is that all methods can be
used to test for symmetrical/crossover interactions
in congruence-type of studies although, again, the
interaction e?ects are postulated rather than
empirically examined. Interestingly, however, a
closer look suggests that this stream of research
is dominated by two di?erent objectives. One is
to identify the contingency factors as such (see
e.g. Abernethy & Lillis, 1995; Kaplan & Mackey,
1992; Merchant, 1984). The other objective is to
re?ne a congruence model by, for example, specify-
ing under what conditions congruence will occur
(see e.g. Khandwalla, 1972; Perera et al., 1997),
or by further specifying the causal relations (see
e.g. Bouwens & Abernethy, 2000).
Suggestions for future research
Based on these observations, a procedure for
the analysis of the appropriateness of statistical
methods may be sketched. However, before so
doing, the study should be positioned theoretically
by specifying the form of ?t and the level of inter-
action (see Table 3).
Specify the form of ?t. This is an important step
as earlier studies have suggested that the theoreti-
cal assumptions underpinning congruence- and
contingency-type of models, respectively, and
Cartesian- and Con?guration-type of models,
respectively, are so di?erent that they should be
considered as incompatible (see e.g. Chenhall,
2003; Gerdin & Greve, 2004). As mentioned
Table 3
Results of the analysis of statistical methods used in management accounting research
a
Forms of fit Contingency Congruence
Cartesian Configuration
Levels Matching Multiplicative
3. Crossover
interaction
2. Symmetrical
interaction
1. General
interaction
Difference in means
Difference in correlation (form)
Difference in regression coefficients
Difference in correlation (strength)
Regression coefficients
Regression coefficients
All methods
All methods
Bivariate correlation
Difference in means
Bivariate correlation
Bivariate correlation
a
A double-headed line signi?es that the statistical method has been used to test a particular sub-theory. A line that crosses several
columns denotes that the method cannot discriminate between the forms of ?t in question. Finally, an unbroken line means that the
interaction e?ect is formally tested while a broken line signi?es that the interaction e?ect is postulated.
J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009 1005
above, however, the con?icting assumptions
underpinning matching and multiplicative models
of ?t have been less thoroughly discussed, in par-
ticular in the management accounting literature.
We argue that this poses a threat to theory devel-
opment as it is often unclear what the underlying
theory actually looks like (for an excellent excep-
tion, see Bisbe & Otley, 2004). That is, while it is
often clearly stated what type of MAS is expected
at the extreme values of context (i.e. in the contexts
where the two models typically make identical pre-
dictions), little is said about the pattern between
them. There is also a risk that the two models
become mixed within the scope of individual stud-
ies. For example, it may ?rst be proposed that ‘the
higher the level of context, the greater the use of
MAS information if the organization is to perform
well’ and then stated in the formal hypothesis that
‘the higher the level of context, the greater the
e?ect of MAS information on performance’.
Again, however, the ?rst statement has a matching
form as it predicts that the appropriate level of
MAS vis-a` -vis contexts maximizes performance
(cf. the multiplicative form which predicts that per-
formance can be maximized only by maximizing or
minimizing MAS). The latter statement, in con-
trast, represents a multiplicative form as it is
assumed that the e?ect of MAS on performance
increases/decreases at a changing rate across di?er-
ent levels of context (cf. the matching model which
assumes that performance changes at a ?xed rate).
Specify the level of interaction. As mentioned
above, this dimension of theory speci?cation has,
to our knowledge, not been fully recognized in
the contingency literature. Indeed, Schoonhoven
(1981) argued that contingency theory implies sym-
metrical interactions. However, our analysis of the
MAS literature suggests that there are at least two
alternatives which are so di?erent that they should
be explicitly recognized in future studies, namely,
theories predicting general interactions and theo-
ries predicting crossover interactions.
When the form of ?t and the interaction level
has been speci?ed, the next step is to choose or
develop appropriate method(s) for testing hypoth-
eses. Based on the above analysis of Table 3, we
propose the following guidelines for future
research. First, use methods whose functional form
is precise enough to be able to discriminate between
the di?erent forms of ?t. For example, if a match-
ing form of ?t at the crossover interaction level is
predicted, bivariate correlation or regression anal-
ysis should be preferred to an analysis of mean val-
ues since the latter method provides no
information about the form of the underlying con-
text/MAS relationship.
Second, more informative methods should be pre-
ferred to less informative. This implies, for example,
that the sole use of subgroup analysis is recom-
mended only when groups represent true categories
because of the loss of information that follows
when ‘arti?cial’ categories are created on the basis
of continuous variables (Cohen et al., 2003; Jac-
card & Turrisi, 2003). Importantly, however, it also
implies that we should preferably use those methods
that provide the strongest link between the verbal
statements and their mathematical formulation.
And, as we see it, this may imply that some statis-
tical techniques in Table 3 should not be used.
For instance, although it was argued above that a
subgroup correlation analysis focusing on di?er-
ences in strength seems to be consistent with a mul-
tiplicative form of ?t and can be used to test the
existence of general interactions, it would be di?-
cult to argue that such method is more appropriate
than MRA for testing the sub-theory in question.
Indeed, it can be argued that such recommenda-
tions should go without saying. However, our liter-
ature review shows that the choice of statistical test
method is rarely based on explicit and theoretically
grounded arguments explaining why the particular
method(s) used should be preferred to other con-
ceivable alternatives.
Third, and ?nally, in situations where no appro-
priate method can be found in the literature, we
are forced to combine existing methods or to come
up with new ones. Irrespective which alternative is
chosen, however, the general recommendation is
to ensure that the method—or combination of meth-
ods—can both discriminate between di?erent models
of ?t and test for the particular level of interaction
assumed. Accordingly, if a multiplicative model
at the crossover interaction level is predicted, a
method with a precise functional form such as
MRA may well be complemented with (but not
substituted for) an ‘unprecise’ method like
1006 J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009
ANOVA since only the latter tests for the existence
of a crossover interaction e?ect (cf. Table 3).
4
Hopefully, these guidelines can serve as a means
of selecting/developing appropriate statistical tests
in empirical studies. However, at least three
remarks should be made. First, although the clas-
si?catory framework highlights that there are
more variants of contingency theory than has typ-
ically been noted in the MAS literature, it should
be pointed out that also each sub-theory may
include several, possibly competing variants. For
example, matching models may predict both iso-
performance (Schoonhoven, 1981) and hetero-per-
formance (Donaldson, 2001). Importantly, how-
ever, such theoretical variants imply that the
commonly used statistical methods described
above may have to be tailored to the particular
assumptions made. For example, if a matching
model predicts iso-performance, the regression
model depicted in Eq. (2) should preferably be
changed so that this assumption is explicitly recog-
nized and tested (for an example, see e.g. Schoo-
nhoven, 1981, p. 352). Again, such adaptations
are not only necessary to ensure a high correspon-
dence between theory and statistical tests, but will
also reduce the risk of erroneous conclusions. As
Jaccard and Turrisi (2003, p. 21) pointed out;
‘‘failure to obtain a statistically signi?cant interac-
tion [. . .] may re?ect the presence of an alternative
functional form rather than the absence of a mod-
erated relationship.’’
Second, while we have tried to cover the most
commonly applied ways of using the statistical
techniques, we as researchers should be open-
minded to other ways of using them. For example,
subgroup correlation analysis focusing on di?er-
ences in strength criticized above may be used to
show that a lower performing subgroup has signif-
icantly lower correlation between context and
MAS than has a higher performing subgroup
because mis?ts are expected to be more scattered
around the ?t line (cf. the matching form of ?t).
Third, and importantly, the recommendations
above start out from the assumption that existing
theory can be used to develop strong and precise
predictions. While the di?erences between congru-
ence- and contingency-type of models and between
Cartesian- and Con?guration-type of models are
rather obvious, the di?erences between a matching
and a multiplicative model are more subtle.
Indeed, the frequent use of MRA and the scarce
use of matching methods, indicate a preference
for the multiplicative model as the explanation of
observed performance di?erences. However, since
the theoretical arguments for choosing this model
are not always clearly stated and the verbal argu-
ments sometimes seem to correspond better with
a matching model, the speci?c form of ?t seems
to be an open question in many studies. And if this
is the case, we should consider using techniques
such polynomial regression which concurrently
tests for the existence of several models of ?t
(Edwards, 2001; Meilich, 2006).
Conclusion
Our objective has been to examine the appropri-
ateness of commonly used statistical methods in
the contingency-based MAS literature. In so
doing, we developed a framework (Table 1) which
highlights that we need to make more speci?c
choices of theory than has typically been noted.
In particular, we should pay more attention to
the theoretical di?erences between matching- and
multiplicative-type of models, and between inter-
action levels. Given these speci?cations, the analy-
sis summarized in Table 3 can hopefully serve as a
means of selecting/developing appropriate statisti-
cal tests consistent with the particular sub-theory
in question. However, it is important to ensure
that the technique (or set of techniques) has a pre-
cise functional format and cover all the assump-
tions made.
Acknowledgements
The authors gratefully acknowledge the useful
comments made by the anonymous reviewers,
4
An alternative is to perform additional analyses of the
MRA regression to examine whether the interaction e?ect is
non-monotonic (Schoonhoven, 1981, 376–377) and disordinal
(Cohen et al., 2003, p. 288).
J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009 1007
Frank G. H. Hartmann, and participants at work-
shops at CEROC (Centre for Empirical Research
on Organizational Control) at O
¨
rebro University
and at the Fifth EASM conference on New Direc-
tions in Management Accounting, Brussels 2006.
Financial support for this project was provided
by O
¨
rebro University, and the Jan Wallander
and Tom Hedelius Foundation.
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doc_564392793.pdf
In recent years, the contingency-based management accounting literature has been criticized for being fragmentary
and contradictory as a result of methodological limitations. This study adds to this picture by showing that the theoretical
meaning of some commonly used statistical techniques is unclear, i.e. the functional forms are not precise enough
to be able to discriminate between several sometimes even conflicting theories of contingency fit. The study also shows
that the techniques differ significantly in terms of how interaction effects between context and management accounting
are modeled.
The appropriateness of statistical methods for testing
contingency hypotheses in management accounting research
Jonas Gerdin
*
, Jan Greve
Department of Business Administration, O
¨
rebro University, SE-701 82 O
¨
rebro, Sweden
Abstract
In recent years, the contingency-based management accounting literature has been criticized for being fragmentary
and contradictory as a result of methodological limitations. This study adds to this picture by showing that the theo-
retical meaning of some commonly used statistical techniques is unclear, i.e. the functional forms are not precise enough
to be able to discriminate between several sometimes even con?icting theories of contingency ?t. The study also shows
that the techniques di?er signi?cantly in terms of how interaction e?ects between context and management accounting
are modeled. This implies that some methods are only appropriate when theory predicts interaction e?ects in general
while others are only appropriate in cases where theory speci?es a more precise functional form of interaction such as
symmetrical or crossover interactions. Based on these observations, several recommendations for future research are
proposed.
Ó 2007 Elsevier Ltd. All rights reserved.
Introduction
In recent years, several literature reviews have
highlighted that many di?erent ways of conceptu-
alizing ‘contingency ?t’ between context and Man-
agement Accounting System (MAS) have been
used in the literature (Chenhall, 2003; Luft &
Shields, 2003) and that few researchers fully
acknowledge the di?culties of relating these forms
to each other (Gerdin & Greve, 2004). There has
also been a growing interest in (and debate about)
how individual statistical techniques have been
applied in contingency-oriented MAS research
(Dunk, 2003; Gerdin, 2005a, 2005b; Hartmann,
2005; Hartmann & Moers, 1999, 2003). The pur-
pose of this paper is to combine these two streams
of research by providing a systematic analysis of
the appropriateness of commonly used statistical
techniques for testing the di?erent forms of ?t
found in the literature.
In so doing, we propose a conceptual frame-
work which identi?es a number of possible per-
spectives of contingency ?t. Unlike most of the
0361-3682/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.aos.2007.07.003
*
Corresponding author. Tel.: +46 19 30 30 00; fax: +46 19 33
25 46.
E-mail addresses: [email protected] (J. Gerdin), jan.
[email protected] (J. Greve).
www.elsevier.com/locate/aos
Available online at www.sciencedirect.com
Accounting, Organizations and Society 33 (2008) 995–1009
existing MAS literature (e.g. Chenhall, 2003;
Gerdin & Greve, 2004; Luft & Shields, 2003), the
framework explicitly elaborates on the distinction
between a matching and a multiplicative model
of ?t (Schoonhoven, 1981). The framework also
contributes to the more general discussion about
the use of statistical techniques in contingency
research (Donaldson, 2001; Drazin & Van de
Ven, 1985; Meilich, 2006; Venkatraman, 1989) by
highlighting that the paradigm seems to accommo-
date at least three levels of theory speci?cation.
The paper proceeds as follows. Drawing upon
seminal contingency work, three levels of precision
in the functional form of context/MAS interactions
and four principal and con?icting approaches to
contingency ?t are identi?ed. Next, it is discussed
to what extent statistical methods frequently
applied in contingency-based MAS research can
be used to test the di?erent levels of interaction
and to distinguish between the four approaches.
This results in several conclusions and recommen-
dations for future research which ?nalize the paper.
Levels of theory speci?cation in the contingency
paradigm
The essence of contingency theory is that orga-
nizations must adapt their structure to contingen-
cies such as the environment, organizational size
and business strategy if the organization is to per-
form well (Burns & Stalker, 1961; Donaldson,
2001; Drazin & Van de Ven, 1985; Lawrence &
Lorsch, 1967; Pennings, 1992; Woodward, 1965).
Galbraith (1973, p. 2) formulated this core idea
of contingency theory in the following way:
1. There is no one best way to organize.
2. Any way of organizing is not equally e?ective.
These statements imply that the e?ectiveness
of organization structures is contingent on
context—i.e. there is no universally best way to
organize—and that, in a particular context, certain
structure(s) will outperform other structures.
Schoonhoven (1981, p. 351) referred to this partic-
ular form of relations between variables as
interactions.
Generally, an interaction e?ect exists whenever
the e?ect of an independent variable (structure)
on the dependent variable (performance) varies
due to the values of a third variable (context) (Jac-
card & Turrisi, 2003). As illustrated in Table A,
Fig. 1, an interaction e?ect thus implies that a
change in structure has a more positive (or nega-
tive) e?ect on performance in di?erent contexts
(Luft & Shields, 2003). Given the broad format
of this type of interaction, it will henceforth be
referred to in terms of ‘general interaction’ and
represents the ?rst level of theory speci?cation.
a
C
H
and C
L
denote high and low levels of the contingency factor, respectively.
Structure
Performance
Low High
C
H
C
L
Table A
C
H
C
L
Low High
Performance
Low High
Performance
Table B
C
H
C
L
Structure
Table C
Structure
Fig. 1. Illustration of an interaction (monotonic) function (Table A), a symmetrical interaction (non-monotonic) function (Table B)
and a crossover interaction function (i.e. both non-monotonic and disordinal function) (Table C)
a
.
996 J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009
However, much of the early contingency work,
e.g. Burns and Stalker (1961) and Galbraith
(1973), seems to involve a higher level of theory
speci?cation (henceforth referred to in terms
of the second level) where interaction e?ects
take a symmetrical form (Schoonhoven, 1981).
As illustrated in Table B in Fig. 1, a symmetrical
interaction implies that a certain structure is
high-performing when contingency is low (C
L
),
while another structure is high-performing when
contingency is high (C
H
).
Some contingency theorists have brought the
idea of symmetrical interaction one step further
as they have also speci?ed the relation between
contingency ?t and performance (henceforth
referred to as the third level of theory speci?ca-
tion). For example, Woodward (1965, p. 69), in
her pioneering study of the ?t of span of control
to technology, noted that all ?rms in a state of
?t had equal performance ratings even though
there were three di?erent ?ts, one for each technol-
ogy category. Hence, organizations in states of ?t
outperformed those in mis?t—both within and
between contextual subgroups—which suggests
that it is the degree of ?t between structure and
context that is the principal explanation of
observed variance in organizational performance,
not structure or context alone.
1
Pfe?er (1982, p.
148) referred to this relation in terms of ‘the conso-
nance hypothesis’ implying that ‘‘those organiza-
tions that have structures that more closely
match the requirements of the context are more
e?ective than those that do not’’.
However, when we claim that there are no gen-
erally more e?ective contexts, we need to demon-
strate that the symmetrical interaction e?ect also
is disordinal, i.e. the ranking order of structure
related to performance changes within the obser-
vable range of data (Cohen, Cohen, West, &
Aiken, 2003) (see Table C, Fig. 1). Such e?ect is
sometimes referred to in terms of a ‘crossover
interaction’ (Cohen et al., 2003).
Conceptualizations of contingency ?t
Over the years, there has been considerable
debate in the contingency theory literature (for
overviews see Donaldson, 2001; Drazin & Van de
Ven, 1985; Pennings, 1992; Venkatraman, 1989).
The following three issues of controversy are
directly linked to the conceptualization of contin-
gency ?t:
2
– Congruence vs. contingency. Is ?t postulated, or
must it be explicitly shown that deviations from
optimal context/structure combinations lower
organizational performance?
– Cartesianism vs. con?gurationalism. Is ?t a con-
tinuum between pairs of contingency and struc-
ture dimensions that allows frequent and small
movements by organizations from one state of
?t to another, or is it the internal consistency
of multiple contingency and structural elements
with organizations having to make ‘quantum
jumps’?
– Matching vs. multiplicative relationships. Is ?t a
line with many optimal combinations of context
and structure where any deviations a?ect
performance equally, or is it assumed that there
are only two optima and that the e?ect of devi-
ations di?ers across di?erent levels of context?
While the meanings and implications of the for-
mer two controversies on management accounting
research have been discussed in several previous
1
In fact, some scholars even propose that structural contin-
gency theory, at least in its original form, postulated so-called
iso-performance, i.e. that organizations with structures that
match contexts perform about equally albeit they operate in
di?erent contexts, while organizations in states of mis?t
perform below that level (Donaldson, 2001; Drazin & Van de
Ven, 1985; see also Schoonhoven’s interpretation of Galbraith’s
(1973) theory at p. 353 and also her operationalization of
contingency ?t at p. 352).
2
Note that the terminology in the literature is somewhat
confusing. For example, when Drazin and Van de Ven (1985, p.
514) use the term ‘congruence’, it refers to an unconditional
association between context and structure, while Donaldson
(2001, pp. 186–189) use the same term to denote a speci?c type
of conditional association between context, structure and
performance—an association which yet other researchers have
referred to in terms of matching models (Schoonhoven, 1981;
Venkatraman, 1989). In the present study, we decided to handle
this diversity by using an adapted version of the terminology
proposed by Gerdin and Greve (2004).
J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009 997
studies (see e.g. Chenhall, 2003; Gerdin & Greve,
2004; Luft & Shields, 2003), the third controversy
has received much less attention (but see Hart-
mann & Moers, 1999, p. 299). This is unfortunate
since also the distinction between a matching and a
multiplicative model of contingency ?t has impor-
tant consequences for the choice of appropriate
statistical methods. In the matching form of ?t, it
is assumed that for every value of context, there
is a unique value of structure at which perfor-
mance is maximized. As illustrated by Tables A
and C in Fig. 2, a particular structure optimizes
performance at a low value of contingency (e.g.
low structure at C
1
) while another structure maxi-
mizes performance at a high value of contingency
(e.g. high structure at C
5
). Judging from the math-
ematical operationalizations of this form of ?t in
previous studies (see e.g. Schoonhoven, 1981, p.
352), so-called iso-performance is often assumed,
i.e. all states of ?t produce the same level of perfor-
mance (see also Woodward, 1965, and the discus-
sions in Donaldson, 2001, & Van de Ven &
Drazin, 1985). However, iso-performance is not
an inevitable consequence of the symmetry
assumption (Donaldson, 2001).
Furthermore, Table A illustrates that any devi-
ations in either direction from the unique optimal
value of structure reduce the level of performance.
Put in another way, each point on the ?t line rep-
resents the optimum on a non-linear function
where performance is the dependent variable and
structure is the independent variable (see Table
C, Fig. 2). Thus, the contingency factor acts as a
moderator because it ‘‘determines which charac-
C
5
Structure
Structure
P
e
r
f
o
r
m
a
n
c
e
P
e
r
f
o
r
m
a
n
c
eC
4
C
3
C
2
C
1
C
5
C
4
C
3
C
2
C
1
Low High
Low High
Table C
b
Table D
b
b The indices denote the level of contingency.
2
4
6
8
10
2
4
6
8
10
Low High
High
Low
Contingency
P
6
P
10
P
8
P
4 P
10
P
10
P
8
P
8
P
6
P
6
P
8
P
4
P
8
P
10
P
6
P
8
P
4
P
6
Table A
a
P
8
Structure
P
8
P
6
P
4
P
10
a
The indices denote the level of organizational performance.
P
2
P
2
Low High
High
Low
Contingency
P
8
P
4 P
7
P
6
P
6
P
6
P
6
P
5
P
6
P
4
P
6
P
7
P
5
P
8
P
4
Table B
a
P
8
Structure
P
8
P
6
P
4
P
2
P
2
P
6
P
10
P
10
P
6
Fig. 2. Illustration of a matching form of interaction (Tables A and C) and a multiplicative form of interaction (Tables B and D).
998 J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009
teristic produces high levels of e?ectiveness of the
organization’’ (Donaldson, 2001, p. 6) and it
‘‘e?ectively shifts the curvilinear relationship
between the structural and outcome variables’’
(Meilich, 2006, p. 165).
Finally, matching models seem to imply that a
deviation of one unit from the optimal structure/
contingency combination has the same e?ect on
performance across all levels of the contingency
(see the indices in Table A, Fig. 2).
When Schoonhoven (1981, p. 355) examined
some of Galbraith’s (1973) statements, she con-
cluded that he implicitly understands contingency
relationships as multiplicative forms of ?t. That
is, the e?ect of a structural variable on perfor-
mance increases, or decreases, as a result of
changes of the contingency level (see Fig. 2, Tables
B and D). Contrary to the matching form, multi-
plicative interaction thus assumes that perfor-
mance is a linear function of structure at each
value of contingency. The assumption about line-
arity in conjunction with the assumption about
non-monotonic relationships implies that the con-
tingency factor (moderator) determines both the
direction and amplitude of structure’s e?ect on per-
formance (cf. Table D in Fig. 2 where the struc-
ture-performance relationships at C
2
and C
5
not
only have di?erent slopes, but also di?erent signs).
The con?icting assumptions about linearity in
the matching and the multiplicative form have
important consequences. Note especially that the
multiplicative form implies that only two struc-
tures (the extreme values) are assumed to be opti-
mal (cf. the typical ‘saddle form’ in Table B
(Southwood, 1978)). Implicitly, the multiplicative
interaction form thus postulates so-called hetero-
performance, i.e. that di?erent contingency/struc-
ture combinations produce di?erent maximum
performances. Also note that in contexts around
the in?exion point C
3
in Fig. 2, Table D, all struc-
tures produce about the same level of perfor-
mance. None of these features are compatible
with a matching view, where ?t results from
numerous combinations of contingency and struc-
ture, yet for each value of contingency, only one
structure can be optimal.
It can be concluded that within the contingency
literature, there has been a number of controver-
sial issues in terms of what constitutes ?t between
context and structure and how ?t is attained. In
addition to Cartesian models of ?t (such as the
matching and multiplicative model), there are the-
ories predicting that ?t is the degree of adherence
to con?gurations consisting of multiple context
and structure variables (Drazin & Van de Ven,
1985; Venkatraman, 1989). As mentioned above,
there is also a set of so-called congruence models
that do not aim to explain variations in perfor-
mance in terms of (mis)?t as they typically postu-
late that only high performers exist to be observed.
In the previous section, we also pointed out that
there are at least three broad variants of contin-
gency theory that di?er in terms of their level of
speci?city. Some theories seem to predict interac-
tion e?ects per se between context and structure
(i.e. general interaction), while others prescribe
non-monotonic relationships (i.e. symmetrical
interaction) and, sometimes, also disordinal rela-
tionships (i.e. crossover interaction).
When we combine the di?erent models of ?t
with the di?erent levels of theory speci?cation,
we get a number of possible variants of contin-
gency theory (see Table 1). Arguably, as these the-
oretical variants make very di?erent assumptions
about how ?t is obtained, they typically require
di?erent statistical test methods. More precisely,
the method(s) used should (at least ideally) have
the capacity to test for the assumptions made
at the chosen level of theory speci?cation—no
more, no less—and, at the same time, have a func-
tional form that corresponds with the model of ?t
predicted. The functional form should preferably
also be precise enough to be able to discriminate
between the di?erent models of ?t. As will be dem-
onstrated in the next section, this is not always the
case.
Commonly used statistical techniques in
management accounting studies to conceptualize
contingency ?t
According to several recent literature reviews,
many di?erent statistical techniques have been
used in the literature (see e.g. Chenhall, 2003; Ger-
din & Greve, 2004; Hartmann & Moers, 1999; Luft
J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009 999
& Shields, 2003). In Table 2, frequently occurring
techniques identi?ed in these literature reviews
are outlined.
In the following sections, these statistical tech-
niques will be brie?y described and classi?ed in
terms of their level of theory speci?cation and it
will be discussed to what extent they can discrimi-
nate between the four forms of contingency ?t out-
lined above.
3
Fit as di?erence in means
In congruence-type of studies, this way of con-
ceptualizing contingency ?t implies that a sample
of organizations, subunits or the like is divided
into subgroups and the MAS characteristics of
the subgroups are compared (see e.g. Abernethy
& Lillis, 1995). Since all congruence models seem
to predict symmetrical relationships, but it is
unclear whether crossover interactions are postu-
lated, it will henceforth be argued that signi?cant
results imply (but do not formally test) either of
the two types of interactions.
In contingency-type of MAS research, we have
found two approaches. One is that of Chenhall
and Lang?eld-Smith (1998) who used cluster anal-
ysis to form organizational gestalts and then exam-
Table 1
Variants of contingency theory (the head of the table is an adapted version of that in Gerdin and Greve (2004, p. 318))
a
Forms of fit
Contingency Congruence
Cartesian Configuration
Levels Matching Multiplicative
3. Crossover
interaction
2. Symmetrical
interaction
1. General
interaction
a
As all congruence models seem to predict at least symmetrical relationships (i.e. that di?erent contexts are associated with di?erent
structures), the lower right cell is considered as theoretically not relevant.
Table 2
Commonly used statistical methods in MAS studies to conceptualize and test the existence of contingency ?t
Contingency ?t as: Selected references:
Di?erence in means Abernethy and Brownell (1999), Abernethy and Lillis (1995),
Chenhall and Lang?eld-Smith (1998)
Bivariate correlation Duncan and Moores (1989), Gerdin (2005b), Govindarajan (1988),
Haka (1987), Merchant (1981, 1984), Selto et al. (1995)
Di?erence in correlation
coe?cients (strength)
Abernethy and Brownell (1999), Abernethy and Lillis (1995),
Khandwalla (1972), Merchant (1981, 1984), Simons (1987)
Di?erence in correlation
coe?cients (form)
Macintosh and Daft (1987)
Linear regression coe?cients Brownell (1982), Duncan and Moores (1989), Frucot and
Shearon (1991), Kaplan and Mackey (1992), Simons (1987)
Di?erence in regression
coe?cients
Abernethy and Brownell (1997), Bisbe and Otley (2004),
Brownell and Merchant (1990), Chong (1996), Perera et al. (1997)
An indirect path coe?cient Baines and Lang?eld-Smith (2003), Bouwens and Abernethy (2000),
Chenhall and Morris (1986), Chong and Chong (1997)
3
Note that these techniques will be dealt with separately
below. In many of the empirical studies cited, however, several
ways of testing contingency ?t have been used. This implies that
some of the drawbacks and limitations related to individual
statistical techniques discussed may have been addressed by the
researchers cited insofar as they deliberately have used several
complementary statistical analyses (see also the concluding
discussion).
1000 J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009
ined whether the di?erences in average performance
scores between clusters were statistically signi?cant.
As the authors expected that di?erent strategies
would be associated with di?erent sets of manage-
ment control techniques and practices, this way of
testing contingency ?t implies a con?guration
approach predicting symmetrical interactions.
In the other approach, the typical procedure is
?rst to create subgroups consisting of ?ts and mis-
?ts in two contexts, respectively, and then to show
that the performance score of the ?ts is superior to
that of the mis?ts (see e.g. Abernethy & Brownell,
1999). In our view, this way of conceptualizing ?t
implies that a crossover interaction is predicted
(i.e. relationships are symmetrical and, further-
more, no context is generally more e?ective). How-
ever, this test provides very little information about
the form of the association. For example, is a di?er-
ence in MAS the result of an incremental adapta-
tion to context, or are quantum jumps required
(cf. the Cartesian and the Con?guration approach,
respectively)? Furthermore, is a signi?cant result a
crude expression of a ?t line with numerous opti-
mal solutions, or does it indicate that MAS should
either be maximized or minimized in order to max-
imize performance (cf. the matching and the multi-
plicative form of interaction, respectively)?
So to conclude, the di?erent variants of analyz-
ing means found in the literature may imply both
symmetrical and crossover interactions. Further-
more, for some uses it is clear which form of ?t
is being tested, for others this is not the case.
Fit as bivariate correlation
In some congruence-type of studies, ?t is opera-
tionalized as a statistically signi?cant correlation
between context and MAS (see e.g. Merchant,
1981, 1984). Given that this application of correla-
tion analysis is only used to test predictable corre-
lations between pairs of context and MAS variables,
it can be argued that it focuses on the form of the
relationship. As a result, bivariate correlation
analysis seems to correspond well with a Cartesian
variant of congruence-type of contingency ?t.
In contingency-type of studies, bivariate correla-
tion analysis has been used to test the e?ect of ?t
on performance in so-called deviation-score or
residual analyses (see e.g. Duncan & Moores,
1989; Gerdin, 2005b). The typical procedure is to
?rst compute deviations between a theoretically
or empirically derived ?t line and actual positions,
and then to correlate the deviation-score with
performance.
Arguably, this way of using bivariate correla-
tion analysis is founded on a matching theory inso-
far as the ?t line encompasses an in?nite number
of unique combinations between context and
MAS, each of them assumed to produce maximum
performance, and each unit of deviation from the
?t line a?ects performance equally (see Tables A
and C in Fig. 2). Furthermore, since any deviation
from the optimal line is explained by mis?t alone
(context has no direct e?ect), it implies that a
crossover interaction is predicted.
Notably, however, bivariate correlation analy-
sis has also been used to test symmetrical and gen-
eral interactions. An example of the former type is
the study of Govindarajan (1988) which predicted
a negative correlation between the degree of dis-
tance from ideal con?gurations in two contexts
and organizational performance, but no assump-
tions about ‘context e?ects’ were made (see also
Selto, Renner, & Young, 1995). An example of
the latter type of interaction is the study of Haka
(1987) which expected that ?rms using sophisti-
cated capital budgeting models outperformed
matched non-users in high levels of context but
not in low levels. As Haka used a non-parametric
correlation analysis based on rank order, however,
it is unclear whether the underlying relationship is
expected to be linear (cf. the matching model) or
non-linear (cf. the multiplicative model).
To conclude, bivariate correlation analysis has
been employed for testing congruence theories as
well as matching and con?guration theories at
the crossover and symmetrical interaction levels,
respectively. The technique has also been used to
test the existence of general interactions.
Fit as di?erence in correlation coe?cients: strength
To our knowledge, subgroup correlation analy-
sis focusing on di?erences in strength has above all
been applied in contingency-type of MAS studies
(but see e.g. Khandwalla, 1972). For example,
J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009 1001
Abernethy and Brownell (1999, p. 198) computed
correlation between strategic change and perfor-
mance for two MAS sub-samples (see also Simons,
1987; Merchant, 1981, 1984; Abernethy & Lillis,
1995). In our view, an analysis focusing on di?er-
ences in strength between subgroups does neither
correspond with a matching, nor a con?guration
perspective. The premise is that these theories give
little reason to expect that the predictive ability of
MAS on performance should di?er across di?erent
levels of the contingency variable (see also the dis-
cussion in Drazin & Van de Ven, 1985).
In contrast, this is what a multiplicative form
of ?t implies. That is, for contingency levels
around in the in?exion point in Table D, Fig. 2,
the predictive ability of MAS on performance is
very low, which implies that the correlation is
expected to be low, while the opposite holds for
the extreme values of the contingency variable
(see C
1
and C
5
). Note also that the method repre-
sents the ?rst level of theory speci?cation (i.e. pre-
dicts general interactions), since a signi?cant
di?erence in correlation per se neither shows that
a high-correlation subgroup generally outperforms
a low-correlation group, nor that a certain MAS is
appropriate in certain contexts and another MAS
in others.
Fit as di?erence in correlation coe?cients: form
Congruence-type of studies focusing on the dif-
ferent forms of correlation coe?cients typically
predict that a particular MAS is positively corre-
lated with the extent of one context and negatively
correlated with the extent of another one (e.g.
Macintosh & Daft, 1987). In our view, such a
use of subgroup correlation analysis seems to
imply a Cartesian variant of contingency ?t insofar
as a continuous (and linear) relationship between
context and MAS is predicted.
In Contingency-type of studies, ?t is supported
by demonstrating that there are statistically signif-
icant di?erences between subgroups, produced by
the correlation between MAS and performance
being positive for one contextual subgroup and neg-
ative for the other subgroup. Accordingly, some
information about whether relationships are sym-
metrical is provided, but none about whether a
crossover interaction e?ect is present (see Table
B and C in Fig. 1).
However, it is unclear as to which form of ?t is
supported. To illustrate, again recall the relation-
ships depicted in Fig. 2 above. From both a match-
ing and a multiplicative perspective, we would
expect a negative correlation between MAS and
performance for low levels of the context (see C
1
and C
2
in Tables C and D) and a positive correla-
tion for high levels (C
4
and C
5
). However, while
both models of ?t are supported by di?erent signs
of the subgroup correlation coe?cients, we should
not conclude that the higher the correlations, the
better the support of these types of relationships.
In fact, it could be argued that this use of correla-
tion analysis is better suited to test a speci?c form
of con?guration theory, namely, when it is expected
that ?rms bene?t from the highest possible values
on a set of management control dimensions in one
context, and from the lowest possible values in the
opposite context (see e.g. Govindarajan, 1988).
To conclude, subgroup correlation analysis
focusing on the form of relationships can generally
be used to test the existence of symmetrical interac-
tions, but it cannot di?erentiate between a match-
ing, a multiplicative and a con?guration model.
Fit as linear regression coe?cients
This approach to conceptualizing and testing
contingency ?t typically implies that regression
equations of the following form are ?tted to the
data:
Y ¼ b
0
þ b
1
X
1
þ b
2
X
2
þ b
3
X
3
þ e ð1Þ
In congruence-type of MAS studies, main e?ect
regression analysis has primarily been used to test
whether MAS design/use (Y) is associated with
one or several contingency factors (X
i
) (see e.g.
Kaplan & Mackey, 1992). However, regressions
in the ‘opposite direction’ can also be found in
the literature. For instance, Simons (1987) used a
logit regression model in which competitive strat-
egy was modeled as the dependent variable (Y)
and a number of management control and envi-
ronmental factors were independent variables (X
i
).
Importantly, however, the theoretical interpre-
tation of main e?ect regressions can be unclear.
1002 J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009
For example, the Kaplan and Mackey study cited
above seems to imply a Cartesian variant since each
independent contextual variable is expected to have
an e?ect on the degree of MAS use. The analysis
performed by Simons (1987), in contrast, seems to
imply a con?guration variant as the logit regression
examines whether the overall pattern of control sys-
tem attributes di?ers between strategic types.
In contingency-type of studies, a ‘?t term’ is
often regressed on performance (Brownell, 1982;
Duncan & Moores, 1989; Frucot & Shearon,
1991). Such regression typically has the following
format (Hartmann & Moers, 1999; Venkatraman,
1989):
Y ¼ b
0
þ b
1
X þ b
2
Z þ b
3
jX À Zj þ e ð2Þ
where X is a MAS attribute, Z is context and Y is
performance. The ‘?t term’ jX À Zj is a deviation-
score, indicating the lack of ?t between X and Z.
Arguably, this way of using linear regression
analysis resembles the above discussed use of
bivariate correlation analysis to establish a rela-
tionship between a deviation-score and perfor-
mance. By implication, it means that this method
is not suitable for detecting multiplicative or con-
?gurative relationships between (mis)?t and per-
formance. Unlike the use of bivariate correlation
analysis discussed above, however, linear regres-
sion coe?cients disclose the nature of the relation
(Duncan & Moores, 1989), i.e. the potential con-
textual in?uence on performance is separated from
the interaction e?ect as such in the analysis. This
means that interaction e?ects will be detected also
in situations where performance is strongly in?u-
enced by context, i.e. when the interaction is sym-
metric (but not disordinal). Yet, if b
2
in Eq. (2) is
not signi?cant, or if the variables X and Z are not
included in the equation, and b
3
is still signi?cant,
this indicates a crossover interaction. Accordingly,
depending on how the regression is written and the
results of the test, this statistical technique can be
used to explore the existence of both symmetrical
and crossover interactions.
Fit as di?erence in regression coe?cients
One frequently used technique for testing the
existence of a signi?cant di?erence in regression
coe?cients is the moderated regression analysis
(MRA) (Hartmann & Moers, 1999). An MRA
typically has the following format:
Y ¼ b
0
þ b
1
X þ b
2
Z þ b
3
X Ã Z þ e ð3Þ
where Y is a dependent variable, X is an indepen-
dent variable, Z is a moderator, X
*
Z is the mod-
erating e?ect that Z has on the relationship
between X and Y, and e is the error variable (Co-
hen et al., 2003; Jaccard & Turrisi, 2003).
Although MRA has been used in congruence-
type of studies (e.g. Perera, Harrison, & Poole,
1997), a signi?cant interaction term per se is not
required to conclude that a congruence relation-
ship exists. Rather, the inclusion of such term (in
addition to main e?ect coe?cients) merely implies
that the functional form of the context/MAS rela-
tionship is ‘better’ speci?ed.
In contingency-type of MAS studies (Bisbe &
Otley, 2004; Brownell & Merchant, 1990; Chong,
1996), however, the interaction term is crucial as
it tests the existence of general interaction e?ects.
That is, a signi?cant term indicates that the e?ect
of MAS on performance di?ers across di?erent lev-
els of context, but no information is provided
about whether the e?ect is non-monotonic (sym-
metrical interaction) or disordinal (crossover inter-
action). Furthermore, since this form of MRA is
based on ‘linear by linear’ interactions (Cohen
et al., 2003; Jaccard & Turrisi, 2003), it is unsuit-
able to test the existence of curve linearity predicted
by the matching model (cf. Table C in Fig. 2).
In the MAS literature, there are also examples
of where regression coe?cients in di?erent sub-
groups have been compared in order to test for
interaction e?ects. For example, Abernethy and
Brownell (1997) ?rst divided their sample into four
contextual groups and then regressed simulta-
neously three types of control on managerial per-
formance in each of the four groups. Like MRA,
this way of using main e?ect regression analysis
is inconsistent with matching theory insofar as
matching theory gives little reason to expect that
MAS’s e?ect on performance should di?er across
di?erent levels of context.
So to conclude, both MRA and comparisons of
main e?ect coe?cients between subgroups seem
appropriate for testing a multiplicative model of
J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009 1003
?t. Furthermore, both test for the existence of gen-
eral interactions.
Fit as an indirect path coe?cient
In MAS research, contingency ?t is often ana-
lyzed by the introduction of a mediating variable.
That is, the e?ect of the independent variable on
the dependent variable operates completely or par-
tially through the mediating variable (Gerdin &
Greve, 2004; Luft & Shields, 2003; Venkatraman,
1989). In congruence-type of studies, di?erent
properties of MAS are typically modeled as the
dependent variable (e.g. Bouwens & Abernethy,
2000; Chenhall & Morris, 1986).
Arguably, while a path analysis may reveal asso-
ciations between variables, only direct relations can
express a congruence relationship. Hence, a con-
gruence relationship is supported whenever an
indirect path is prevalent, but only in the sense that
the mediator is signi?cantly associated with MAS.
Also contingency-type of studies using path-
analytical techniques are common in the MAS lit-
erature (e.g. Baines & Lang?eld-Smith, 2003;
Chong & Chong, 1997). However, although these
methods contribute to our understanding about
what determines design and use of MAS, they do
not test for the existence of interaction e?ects
between context and MAS on performance. To
illustrate, consider a theory predicting that high-
performing ?rms in dynamic environments rely
on externally oriented MASs (Proposition A),
and that high-performing ?rms in stable environ-
ments rely on internally oriented MASs (Proposi-
tion B). While a path analysis in a sense could
con?rm Proposition A by showing that dynamism
is positively correlated with externally oriented
MASs which, in turn, is positively correlated with
performance, such a result would contradict Prop-
osition B (because it implies that stability is posi-
tively correlated with an internally oriented MAS
which, in turn, is negatively correlated with perfor-
mance). Accordingly, path analyses cannot explore
the existence of moderated causal relationship(s)
predicted by contingency theory (Donaldson,
2001; Schoonhoven, 1981), i.e. where the relation-
ship between MAS and performance is moderated
by context.
Results of the analysis of statistical methods
In Table 3, the di?erent uses of statistical meth-
ods found in the contingency-style MAS literature
have been sorted into the classi?catory framework
developed above. A method’s row position thus
denotes the level of speci?city of the theory being
tested and the column denotes the particular
model of ?t being tested. A line that crosses several
columns represents the method’s inability to dis-
criminate between the models of ?t in question.
Finally, a dotted line marks that the interaction
e?ect is postulated rather than formally tested.
Several observations can be made based on
Table 3. A ?rst observation is that studies have
been made in most theoretically relevant subcate-
gories of contingency theory. This is noteworthy
in its own right as it reinforces recent claims sug-
gesting that contingency-based MAS research is
diverse (Chenhall, 2003; Gerdin & Greve, 2004;
Luft & Shields, 2003) and, furthermore, suggests
that future research not only should consider the
di?erent forms of ?t present in the literature, but
also the di?erent levels of theory speci?cation.
Given the purpose of this study, however, a more
important conclusion related to this observation
is that, generally, di?erent statistical methods have
been used to test these sub-theories (an exception
is congruence-type of studies in which all methods
have been employed). Overall, this multiplicity is a
necessity as these di?erent variants of contingency
theory make very di?erent assumptions about the
nature of relationships.
A second observation is that some methods
have di?culties in distinguishing between di?erent
forms of ?t. For example, when mean values of
performance between subgroups are compared
and a signi?cant crossover interaction in the pre-
dicted direction is identi?ed, this indicates that
MAS is contingent on context. However, a cross-
over interaction e?ect may be predicted in all
forms. Consequently, such comparison of mean
values helps to identify contingency variables;
however, it does not specify the functional form
of the ?t relationship.
A third observation is that the number and qual-
ity of methods is unequally distributed amongst
sub-theories. For some subcategories, several func-
1004 J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009
tionally precise methods have been used (e.g.
matching theories predicting crossover interac-
tions) while, for others, the opposite is the case
(e.g. for multiplicative type of studies predicting
symmetrical or crossover interactions). As will be
developed in more detail below, these di?erent pre-
requisites imply that researchers sometimes need to
prioritize between several conceivable alternatives
and, sometimes, need to come up with complemen-
tary or ‘new’ techniques in order to compensate for
an existing lack of appropriate ones.
A fourth observation is that one of the methods
previously discussed, i.e. path analysis, can only be
used to test congruence-type of theories. However,
this is not to say that path analysis generally
should be avoided when a contingency-form of ?t
is predicted. After all, there might be situations
where theory suggests a combination of the two
forms of causality (Chenhall, 2003).
A ?fth observation is that all methods can be
used to test for symmetrical/crossover interactions
in congruence-type of studies although, again, the
interaction e?ects are postulated rather than
empirically examined. Interestingly, however, a
closer look suggests that this stream of research
is dominated by two di?erent objectives. One is
to identify the contingency factors as such (see
e.g. Abernethy & Lillis, 1995; Kaplan & Mackey,
1992; Merchant, 1984). The other objective is to
re?ne a congruence model by, for example, specify-
ing under what conditions congruence will occur
(see e.g. Khandwalla, 1972; Perera et al., 1997),
or by further specifying the causal relations (see
e.g. Bouwens & Abernethy, 2000).
Suggestions for future research
Based on these observations, a procedure for
the analysis of the appropriateness of statistical
methods may be sketched. However, before so
doing, the study should be positioned theoretically
by specifying the form of ?t and the level of inter-
action (see Table 3).
Specify the form of ?t. This is an important step
as earlier studies have suggested that the theoreti-
cal assumptions underpinning congruence- and
contingency-type of models, respectively, and
Cartesian- and Con?guration-type of models,
respectively, are so di?erent that they should be
considered as incompatible (see e.g. Chenhall,
2003; Gerdin & Greve, 2004). As mentioned
Table 3
Results of the analysis of statistical methods used in management accounting research
a
Forms of fit Contingency Congruence
Cartesian Configuration
Levels Matching Multiplicative
3. Crossover
interaction
2. Symmetrical
interaction
1. General
interaction
Difference in means
Difference in correlation (form)
Difference in regression coefficients
Difference in correlation (strength)
Regression coefficients
Regression coefficients
All methods
All methods
Bivariate correlation
Difference in means
Bivariate correlation
Bivariate correlation
a
A double-headed line signi?es that the statistical method has been used to test a particular sub-theory. A line that crosses several
columns denotes that the method cannot discriminate between the forms of ?t in question. Finally, an unbroken line means that the
interaction e?ect is formally tested while a broken line signi?es that the interaction e?ect is postulated.
J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009 1005
above, however, the con?icting assumptions
underpinning matching and multiplicative models
of ?t have been less thoroughly discussed, in par-
ticular in the management accounting literature.
We argue that this poses a threat to theory devel-
opment as it is often unclear what the underlying
theory actually looks like (for an excellent excep-
tion, see Bisbe & Otley, 2004). That is, while it is
often clearly stated what type of MAS is expected
at the extreme values of context (i.e. in the contexts
where the two models typically make identical pre-
dictions), little is said about the pattern between
them. There is also a risk that the two models
become mixed within the scope of individual stud-
ies. For example, it may ?rst be proposed that ‘the
higher the level of context, the greater the use of
MAS information if the organization is to perform
well’ and then stated in the formal hypothesis that
‘the higher the level of context, the greater the
e?ect of MAS information on performance’.
Again, however, the ?rst statement has a matching
form as it predicts that the appropriate level of
MAS vis-a` -vis contexts maximizes performance
(cf. the multiplicative form which predicts that per-
formance can be maximized only by maximizing or
minimizing MAS). The latter statement, in con-
trast, represents a multiplicative form as it is
assumed that the e?ect of MAS on performance
increases/decreases at a changing rate across di?er-
ent levels of context (cf. the matching model which
assumes that performance changes at a ?xed rate).
Specify the level of interaction. As mentioned
above, this dimension of theory speci?cation has,
to our knowledge, not been fully recognized in
the contingency literature. Indeed, Schoonhoven
(1981) argued that contingency theory implies sym-
metrical interactions. However, our analysis of the
MAS literature suggests that there are at least two
alternatives which are so di?erent that they should
be explicitly recognized in future studies, namely,
theories predicting general interactions and theo-
ries predicting crossover interactions.
When the form of ?t and the interaction level
has been speci?ed, the next step is to choose or
develop appropriate method(s) for testing hypoth-
eses. Based on the above analysis of Table 3, we
propose the following guidelines for future
research. First, use methods whose functional form
is precise enough to be able to discriminate between
the di?erent forms of ?t. For example, if a match-
ing form of ?t at the crossover interaction level is
predicted, bivariate correlation or regression anal-
ysis should be preferred to an analysis of mean val-
ues since the latter method provides no
information about the form of the underlying con-
text/MAS relationship.
Second, more informative methods should be pre-
ferred to less informative. This implies, for example,
that the sole use of subgroup analysis is recom-
mended only when groups represent true categories
because of the loss of information that follows
when ‘arti?cial’ categories are created on the basis
of continuous variables (Cohen et al., 2003; Jac-
card & Turrisi, 2003). Importantly, however, it also
implies that we should preferably use those methods
that provide the strongest link between the verbal
statements and their mathematical formulation.
And, as we see it, this may imply that some statis-
tical techniques in Table 3 should not be used.
For instance, although it was argued above that a
subgroup correlation analysis focusing on di?er-
ences in strength seems to be consistent with a mul-
tiplicative form of ?t and can be used to test the
existence of general interactions, it would be di?-
cult to argue that such method is more appropriate
than MRA for testing the sub-theory in question.
Indeed, it can be argued that such recommenda-
tions should go without saying. However, our liter-
ature review shows that the choice of statistical test
method is rarely based on explicit and theoretically
grounded arguments explaining why the particular
method(s) used should be preferred to other con-
ceivable alternatives.
Third, and ?nally, in situations where no appro-
priate method can be found in the literature, we
are forced to combine existing methods or to come
up with new ones. Irrespective which alternative is
chosen, however, the general recommendation is
to ensure that the method—or combination of meth-
ods—can both discriminate between di?erent models
of ?t and test for the particular level of interaction
assumed. Accordingly, if a multiplicative model
at the crossover interaction level is predicted, a
method with a precise functional form such as
MRA may well be complemented with (but not
substituted for) an ‘unprecise’ method like
1006 J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009
ANOVA since only the latter tests for the existence
of a crossover interaction e?ect (cf. Table 3).
4
Hopefully, these guidelines can serve as a means
of selecting/developing appropriate statistical tests
in empirical studies. However, at least three
remarks should be made. First, although the clas-
si?catory framework highlights that there are
more variants of contingency theory than has typ-
ically been noted in the MAS literature, it should
be pointed out that also each sub-theory may
include several, possibly competing variants. For
example, matching models may predict both iso-
performance (Schoonhoven, 1981) and hetero-per-
formance (Donaldson, 2001). Importantly, how-
ever, such theoretical variants imply that the
commonly used statistical methods described
above may have to be tailored to the particular
assumptions made. For example, if a matching
model predicts iso-performance, the regression
model depicted in Eq. (2) should preferably be
changed so that this assumption is explicitly recog-
nized and tested (for an example, see e.g. Schoo-
nhoven, 1981, p. 352). Again, such adaptations
are not only necessary to ensure a high correspon-
dence between theory and statistical tests, but will
also reduce the risk of erroneous conclusions. As
Jaccard and Turrisi (2003, p. 21) pointed out;
‘‘failure to obtain a statistically signi?cant interac-
tion [. . .] may re?ect the presence of an alternative
functional form rather than the absence of a mod-
erated relationship.’’
Second, while we have tried to cover the most
commonly applied ways of using the statistical
techniques, we as researchers should be open-
minded to other ways of using them. For example,
subgroup correlation analysis focusing on di?er-
ences in strength criticized above may be used to
show that a lower performing subgroup has signif-
icantly lower correlation between context and
MAS than has a higher performing subgroup
because mis?ts are expected to be more scattered
around the ?t line (cf. the matching form of ?t).
Third, and importantly, the recommendations
above start out from the assumption that existing
theory can be used to develop strong and precise
predictions. While the di?erences between congru-
ence- and contingency-type of models and between
Cartesian- and Con?guration-type of models are
rather obvious, the di?erences between a matching
and a multiplicative model are more subtle.
Indeed, the frequent use of MRA and the scarce
use of matching methods, indicate a preference
for the multiplicative model as the explanation of
observed performance di?erences. However, since
the theoretical arguments for choosing this model
are not always clearly stated and the verbal argu-
ments sometimes seem to correspond better with
a matching model, the speci?c form of ?t seems
to be an open question in many studies. And if this
is the case, we should consider using techniques
such polynomial regression which concurrently
tests for the existence of several models of ?t
(Edwards, 2001; Meilich, 2006).
Conclusion
Our objective has been to examine the appropri-
ateness of commonly used statistical methods in
the contingency-based MAS literature. In so
doing, we developed a framework (Table 1) which
highlights that we need to make more speci?c
choices of theory than has typically been noted.
In particular, we should pay more attention to
the theoretical di?erences between matching- and
multiplicative-type of models, and between inter-
action levels. Given these speci?cations, the analy-
sis summarized in Table 3 can hopefully serve as a
means of selecting/developing appropriate statisti-
cal tests consistent with the particular sub-theory
in question. However, it is important to ensure
that the technique (or set of techniques) has a pre-
cise functional format and cover all the assump-
tions made.
Acknowledgements
The authors gratefully acknowledge the useful
comments made by the anonymous reviewers,
4
An alternative is to perform additional analyses of the
MRA regression to examine whether the interaction e?ect is
non-monotonic (Schoonhoven, 1981, 376–377) and disordinal
(Cohen et al., 2003, p. 288).
J. Gerdin, J. Greve / Accounting, Organizations and Society 33 (2008) 995–1009 1007
Frank G. H. Hartmann, and participants at work-
shops at CEROC (Centre for Empirical Research
on Organizational Control) at O
¨
rebro University
and at the Fifth EASM conference on New Direc-
tions in Management Accounting, Brussels 2006.
Financial support for this project was provided
by O
¨
rebro University, and the Jan Wallander
and Tom Hedelius Foundation.
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