Description
In the contingency literature on the behavioral and organizational eects of budgeting, use of the Moderated
Regression Analysis (MRA) technique is prevalent. This technique is used to test contingency hypotheses that predict
interaction eects between budgetary and contextual variables. This paper critically evaluates the application of this
technique in budgetary research over the last two decades. The results of the analysis indicate that the use and inter-
pretation of MRA often do not conform to proper methodology and theory. The paper further demonstrates that these
problems seriously aect the interpretability and conclusions of individual budgetary research papers, and may also
aect the budgetary research paradigm as a whole.
Mini-review
Testing contingency hypotheses in budgetary research: an
evaluation of the use of moderated regression analysis
$
Frank G.H. Hartmann
a
, Frank Moers
b,
*
a
Department of Financial Management, Faculty of Economics and Econometrics, University of Amsterdam,
Roetersstraat 11, 1018 WB Amsterdam, The Netherlands
b
Department of Accounting, Faculty of Economics and Business Administration, Maastricht University, P.O. Box 616, 6200 MD
Maastricht, The Netherlands
Abstract
In the contingency literature on the behavioral and organizational e?ects of budgeting, use of the Moderated
Regression Analysis (MRA) technique is prevalent. This technique is used to test contingency hypotheses that predict
interaction e?ects between budgetary and contextual variables. This paper critically evaluates the application of this
technique in budgetary research over the last two decades. The results of the analysis indicate that the use and inter-
pretation of MRA often do not conform to proper methodology and theory. The paper further demonstrates that these
problems seriously a?ect the interpretability and conclusions of individual budgetary research papers, and may also
a?ect the budgetary research paradigm as a whole. #1999 Elsevier Science Ltd. All rights reserved.
Keywords: Budgetary research; Reliance on accounting performance measures; Budgetary participation; Methodology; Moderated
regression analysis; Interaction.
1. Introduction
Over the last 40 years a research paradigm has
developed in the management accounting litera-
ture that focuses on the use of budgets in organi-
zations. An early study by Argyris (1952) provided
a ®rst attempt to describe the e?ects of using
budgets on the behavior of employees. Whereas
Argyris and other researchers in the 1950s and
1960s often studied budget-related issues following
a case-study methodology, later studies pre-
dominantly relied upon survey data. In the 1970s
two such survey studies on budgeting appeared
that have become particularly in¯uential. These
studies, by Hopwood (1972) and Otley (1978),
focused on the behavioral and attitudinal e?ects of
using budgetary information to evaluate the per-
formance of subordinate managers. Hopwood
(1972) found that a high reliance on budgetary
performance led to a high degree of stress, as well
as to dysfunctional managerial behavior. Believing
that Hopwood's results were likely contingent on
other organizational variables, Otley (1978)
designed a study that involved a research site
where it was expected that Hopwood's results
Accounting, Organizations and Society 24 (1999) 291±315
0361-3682/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved.
PII: S0361-3682(99)00002-1
* Corresponding author. Fax: +31-20-525-5285.
$
The authors gratefully acknowledge the comments made by
Ken Merchant, David Otley and two anonymous reviewers. This
paper has further bene®ted from presentations at Maastricht Uni-
versity, the 21st annual EAA meeting, the Fourth International
Management Control Systems Research Conference, the EIASM
workshop on New Directions in Management Accounting, and
the 1999 AAA Management Accounting Research Conference.
would not hold. Indeed, Otley obtained results
that were contrary to those of Hopwood. He did
not ®nd negative relationships between the use of
budgetary performance information and sub-
ordinates' attitudes and behaviors; instead he
found either no correlation or positive correla-
tions. The con¯icting results of these two studies
provided an important stimulus to other research-
ers to adopt contingency perspectives in studying
the e?ects of the formalized construct Reliance on
Accounting Performance Measures (RAPM). For
example, Brownell (1982a) expected that the dif-
ference in results could be explained by a construct
labeled Budget Participation that relates to sub-
ordinate managers' involvement in budget setting.
This variable had also received ample attention in
the literature during the sixties and the seventies
(cf. Shields & Shields, 1998). Generally, such con-
tingency studies have aimed to ®nd a match
between the use of budgets and the context in
which they are used. Together, they form a body
of literature which has attained a dominant posi-
tion in contemporary management accounting
research (cf. Chapman, 1997). Brownell and Dunk
(1991, p. 703) characterize the development of this
paradigm as:
The continuing stream of research devoted to
this issue constitutes, in our view, the only
organized critical mass of empirical work in
management accounting at present.
Over the last decade, several papers have pro-
vided overviews and evaluations of di?erent
aspects of this contingency literature on budgeting
(e.g. Briers & Hirst, 1990; Fisher, 1995; Hart-
mann, in press; Kren & Liao, 1988; Shields &
Shields, 1998). The purpose of the present paper is
to address and critically evaluate the statistical
method used in this literature to test contingency
hypotheses. It focuses on the use of Moderated
Regression Analysis (MRA), which has become
the dominant statistical technique in budgetary
research for testing contingency hypotheses. The
use of techniques such as MRA has received only
little attention in the overview papers mentioned.
Yet, such attention seems warranted for at least
two reasons. First, since the introduction of the
contingency theory paradigm in budgeting, statis-
tical techniques have become increasingly important
(cf. Briers & Hirst, 1990, p. 385). They not only
a?ect the design, execution and success of indivi-
dual studies, but also determine the paradigm's
overall success (cf. Lindsay, 1995). Second, atten-
tion to the MRA technique seems particularly
warranted given the complexity and speci®city of
the technique, and the problems associated with
its use (e.g. Arnold, 1982, 1984; Jaccard, Turrisi &
Wan, 1990). As will be shown in detail below,
budgetary papers often appear to neglect these
complexities, which causes ¯aws in the applica-
tion of MRA and in the interpretation of
results.
The remainder of the paper is structured as fol-
lows. Section 2 begins with a short explanation of
the concept of `®t' in contingency theory. It con-
tinues with an explanation of the basic properties
of MRA. Section 3 discusses the selection of bud-
getary research papers for analysis. Section 4
describes speci®c characteristics of MRA and pre-
sents the ®ndings of the analysis of the use of
MRA in the selected research papers. Finally,
Section 5 discusses the implications of the ®ndings
for both the current state and required future
developments of budgetary research.
2. Testing contingency theories of budgeting
Contingency theories of accounting are the
opposites of universal theories of accounting in
that they link the e?ects or the optimality of
accounting systems to the environment and con-
text in which these systems operate. In a summary
of early management accounting studies that used
contingency frameworks, Otley (1980) concluded
that much needed to be done in the development
of a contingency theory of accounting, and he
outlined some minimal requirements for such a
theory, stating that:
(. . .) a contingency theory must identify spe-
ci®c aspects of an accounting system which
are associated with certain de®ned circum-
stances and demonstrate an appropriate
matching (Otley, 1980, p. 413).
292 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
Three elements in this prescription are essential,
relating to: (1) the `speci®c aspects' (2) the `de®ned
circumstances'; and (3) the `appropriate match-
ing'. The ®rst element (i.e. speci®c aspects) points
to the demand for speci®city of the accounting
system variables in the formulation and test of
theories. The second element (i.e. de®ned circum-
stances) points to the conceptual di?erence
between a universal theory and a contingency
theory. The third and last element (i.e. appropriate
matching) forms the core of this paper, as it points
to the empirical di?erence between a universal
theory and a contingency theory. Otley (1980)
does not show how an `appropriate matching' is to
be de®ned theoretically, nor does he prescribe how
it is to be determined empirically. Such prescrip-
tions and illustrations can be found, however, in
the organizational literature, which has a larger
history in contingency methodology (cf. Chapman,
1997) and pays ample attention to the theoretical
and empirical aspects of determining the `appro-
priate matching'. In the remainder of this paper, this
`appropriate matching' element will be addressed
with the more common term `contingency ®t'.
An overview of the organizational literature
reveals several di?erent concepts of `contingency
®t' (see, e.g. Drazin & Van de Ven, 1985; Schoon-
hoven, 1981; Venkatraman, 1989). These concepts
of ®t are each associated with a di?erent theore-
tical interpretation, and each require a di?erent
statistical test. In this paper, the discussion is
restricted to a type of contingency ®t called the
interaction type of ®t, which is the dominant con-
ceptualization of contingency ®t in budgetary
research. The appropriate statistical technique to
test the interaction type of ®t is through Moder-
ated Regression Analysis (MRA), that will be
explained below. Appendix A brie¯y outlines sev-
eral other common types of ®t, stating both the
typical format of the underlying contingency
hypothesis and the appropriate statistical test.
2.1. Moderated Regression Analysis, the basic
format
Moderated Regression Analysis (MRA) is a
speci®c application of multiple linear regression
analysis, in which the regression equation contains
an `interaction term' (e.g. Champoux & Peters,
1987; Southwood, 1978). A typical equation for the
multiple regression of a dependent variable (Y) on
two independent variables (X
1
and X
2
) is presented
in Eq. (1):
Y ?
0
?
1
X
1
?
2
X
2
?" ?1?
In contrast, a typical regression equation used in
MRA has the format of Eq. (2):
Y ?
0
?
1
X
1
?
2
X
2
?
3
X
1
ÂX
2
?" ?2?
Eq. (2) di?ers from Eq. (1) by the inclusion of the
product of the two independent variables (X
1
 X
2
).
This product termis said to represent the moderating
e?ect of variable X
2
on the relationship between X
1
and Y. In contrast, the other terms in the equation
(X
1
and X
2
) are said to represent the main e?ects of
variables X
1
and X
2
on Y. The meaning of this pro-
duct term in establishing a moderating e?ect can be
illustrated by taking the partial derivative of Eq. (2)
with respect to X
1
?@Y=@X
1
?, which has the format
expressed by Eq. (3):
@Y=@X
1
?
1
?
3
X
2
?3?
As Eq. (3) illustrates, the term representing the
partial derivative (@Y=@X
1
) is a function of X
2
.
This means that the `form' of the relationship
between Y and X
1
is a function of X
2
, or in short,
that variable X
2
moderates the form of the rela-
tionship between X
1
and Y (cf. Champoux &
Peters, 1987, p. 244; Jaccard et al., 1990, p. 22). A
moderating e?ect can be graphically illustrated as
a variation in the slope of the regression line of Y
and X
1
as a function of X
2
. Fig. 1 below depicts a
situation in which the slope of the regression line
between X
1
and Y is more positive for higher
values of X
2
. This is expressed by stating that Y is
a function of the interaction between X
1
and X
2
.
Alternatively, it is said that the relationship
between Y and X
1
is contingent upon X
2
. To prove
the contingency hypothesis, therefore, one must
prove that X
2
in¯uences the relationship between
X
1
and Y, or that X
1
and X
2
interact to a?ect Y.
Although X
2
is considered the moderator in the
example above, a similar analysis applies if X
1
is
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 293
considered the moderator of the relationship
between X
2
and Y. Then, illustrated with Eq. (3a),
the partial derivative is taken with respect to X
2
?@Y=@X
2
?, and it follows that the relationship
between X
2
and Y is a function of X
1
.
@Y=@X
2
?
2
?
3
X
1
?3a?
For this reason, the moderating e?ect expressed
by the interaction term in Eq. (2) is called `sym-
metrical' (cf. Arnold, 1982; Southwood, 1978).
This implies that if X
2
moderates the relationship
between X
1
and Y, then X
1
necessarily also mod-
erates the relationship between X
2
and Y. It is
because of this symmetry that the neutral expres-
sion refers to an `interaction' of X
1
and X
2
to
a?ect Y. Whether an independent variable is
labeled as a moderator or an independent variable
is a matter of theory rather than statistics. A
moderator variable theoretically a?ects the rela-
tionship between the independent variable and the
dependent variable, but is not itself theoretically
related with either the dependent or independent
variables (e.g. Arnold, 1982, p. 154; 1984, p. 216;
Shields & Shields, 1998, p. 51). Typically, variables
are labeled moderators that are exogenous or
uncontrollable (e.g. Cohen & Cohen, 1983, p. 305).
Sharma, Durand, and Gur-Arie (1981) provide an
overview and taxonomy of moderator variables.
In empirical contingency research, MRA is used
to establish the existence of a statistically sig-
ni®cant interaction e?ect. A method to do so is
through hierarchical regression analysis (e.g.
Arnold & Evans, 1979; Cohen & Cohen, 1983;
Cronbach, 1987; Southwood, 1978). This method
requires running two regressions, one with the
main-e?ects-only [cf. Eq. (1)] and a second with
both main e?ects and the interaction term [cf. Eq.
(2)]. A signi®cant interaction e?ect is con®rmed by
the statistical signi®cance of the additional var-
iance explained by the inclusion of the interaction
term (i.e. the signi®cance of the increase in R
2
).
This method is equivalent to the simpler and more
direct assessment of the signi®cance of the t-value
associated with the coecient of the product term
(see Southwood, 1978, p. 1168; Arnold, 1982,
p. 157; Jaccard et al., 1990, p. 22). The equivalence
of these two methods is illustrated by Cohen and
Cohen (1983), who show that the F-statistic for the
increase in R
2
equals the square of the t-statistic for
the interaction term.
1
The equivalence of these two methods is illu-
strated by Cohen and Cohen (1983), who show
that the F-statistic for the increase in R
2
equals the
square of the t-statistic for the interaction term. In
the example used above, this means that a test for
a statistically signi®cant moderating e?ect of X
2
on the relationship between X
1
and Y implies a
test whether the coecient of the interaction term
?
3
? in Eq. (2) is statistically signi®cant. The sym-
metry applies here as well; a signi®cant t-value of
the coecient of the interaction term thus simul-
taneously implies a signi®cant moderating e?ect of
X
1
on the relationship between X
2
and Y.
Fig. 1. Moderating e?ect.
1
See, for example, Chenhall (1986) for a redundant test for
the signi®cance in incremental explanatory power after testing
for the signi®cance of the interaction term. Surprisingly, the F-
statistic of incremental explanatory power and the squared t-
statistic of the interaction in this study do not match (F equals
7.27, t-square equals 28.30). The only explanation seems to be a
calculation error.
294 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
The interaction in Eq. (2) above is commonly
called a two-way interaction, since the equation
contains two variables and their interaction.
Moreover, given that in the example (see Fig. 1)
the relationship between X
1
and Y is more positive
(or: less negative) for higher values of X
2
, it is
called a `positive interaction' between X
1
and X
2
. A
`negative interaction' signi®es that the relationship
between X
1
and Y is more negative (or: less positive)
for higher values of X
2
. Additionally, the interaction
can be either monotonic or non-monotonic. A mono-
tonic interaction exists when the partial derivative
does not `cross' the horizontal axis. This means that
the moderating e?ect of X
2
changes the slope of the
relationship between X
1
and Y within positive
values, or negative values, only (cf. Schoonhoven,
1981). Appendix A presents verbal examples of both
monotonic and non-monotonic interactions.
2.2. Moderated Regression Analysis with a dummy
variable
A special and often used form of MRA is
obtained when the moderator variable is a dummy
variable, taking on only discrete values (e.g. 0 and
1). If, for the example above, the moderator X
2
has only values of 0 and 1, the original equation
expressing the interaction e?ect between X
1
and
X
2
in Eq. (2), can be rewritten in the formats of
Eq. (2a) and Eq. (2b) below.
Y ?
0
?
1
X
1
?
2
X
2
?
3
X
1
ÂX
2
?" ?2?
Y ?
0
?
1
X
1
?" ?for X
2
? 0? ?2a?
Y ? ?
0
?
2
? ??
1
?
3
?X
1
?" ?for X
2
? 1?
?2b?
While this does not change the interpretation of
the coecient of the interaction term (
3
), the
decomposition illustrates that an analysis is done
for two subgroups. Therefore, the MRA with a
dummy variable is sometimes called `subgroup
regression analysis' (e.g. Stone & Hollenbeck,
1984) in which the `subgroups' are distinguished
based on extreme (e.g. high and low) values of the
moderator variable. Arnold (1984, pp. 219±221)
argues that the label `subgroup regression analy-
sis' may lead to the incorrect belief that this
method di?ers from general MRA. In fact, MRA
is always concerned with di?erent `subgroups',
however, introducing a dummy variable reduces
the number of `subgroups' to two. A graphical
example of MRA when the moderator variable is
a dummy variable is presented in Fig. 2.
Fig. 2 shows two regression lines, one for each
of the two values of X
2
. The ®gure illustrates a
positive interaction, which means that the coe-
cient (
3
) of the interaction term is positive. From
comparing Eqs. (2a) and (2b) above, it follows
that a positive and signi®cant coecient (
3
) sug-
gests that the slope of the regression line for the
`X
2
=1' subgroup is signi®cantly `more positive'
than the slope of the regression line for the `X
2
=0'
subgroup. It should be noted that the associated
label `positive interaction
0
is only meaningful if the
dummy values 0 and 1 re¯ect underlying values
(e.g. low and high) of the moderator variable.
However, MRA is also meaningfully applied if a
dummy does not re¯ect an underlying quantitative
variable, for example, if it re¯ects a natural dummy
Fig. 2. Interaction e?ect when the moderator is a dummy variable.
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 295
(e.g. male±female). Despite the prevalence of such
`natural dummies', subgroup regression analysis is
commonly performed based on a categorization of
the scores on an underlying continuous variable.
Such categorization has been argued to be unadvi-
sable, since it implies a loss of information (e.g.
Cohen & Cohen, 1983, p. 310; Pedhazur & Pedha-
zur-Schmelkin, 1991, p. 539), yet it has substantial
advantages relating to the understandability of the
MRA outcomes and the statistical power of the
MRA technique (Arnold, 1984, pp. 221±222).
These advantages are especially important when
the analysis incorporates interactions of a higher
order than the two-way interactions discussed so
far. Such higher-order interactions are discussed
further below.
3. Selection of the budgetary research papers
The budgetary research papers were selected for
analysis using four criteria. These were: (1)
research method; (2) publication date; (3) journal
of publication; and (4) subject of study. The ®rst
criterion aimed at the selection of papers that used
a survey methodology using questionnaires. The
second criterion resulted in papers published in the
period from 1980 to 1998. This period was chosen
because it lies after the in¯uential conceptual
paper of Otley (1980). The third criterion aimed at
selecting papers from high-quality accounting
journals. This criterion was applied to limit the
total number of papers, as well as to exclude
`lower journal quality' as a potential explanation
for the ®ndings. Based on an examination by
Brown and Huefner (1994) of the perceived qual-
ity of accounting journals among di?erent respon-
dents, papers were selected from The Accounting
Review, Journal of Accounting Research, and
Accounting, Organizations and Society.
2
Finally,
regarding the subject of study, papers were selected
that hypothesize and test contingency ®t concern-
ing budget-related variables, such as RAPM and
Budgetary Participation, using an `interaction'
concept of ®t. The application of these criteria
resulted in the selection of 28 papers. Table 1
shows the dispersion of the papers over the three
journals. Appendix B provides an overview of the
28 papers that meet the selection criteria.
4. Analysis of the budgetary research papers
This section analyzes the application and inter-
pretation of MRA in the 28 budgetary research
papers reviewed. In addition to the basic format of
MRA discussed above, here di?erent subsections
explain di?erent speci®c characteristics of MRA.
These speci®c characteristics relate to interaction
and (1) the strength of relationships; (2) the for-
mulation of hypotheses; (3) lower-order e?ects; (4)
multiple and higher-order interactions; (5) e?ect size;
and (6) (non-) monotonicity. Each subsection illus-
trates and discusses how these MRA characteristics
appear in the individual studies.
4.1. Interaction and the strength of relationships
In Section 2.2 above, a reference was made to
the `subgroup' method for illustrating the di?er-
ence in the slope of the regression line for two
subgroups. The literature uncovers another use of
subgroup analysis which tests for di?erences
between subgroups in the strength of the relation-
ships between the independent and dependent
variables (e.g. Champoux & Peters, 1987, p. 243;
Stone & Hollenbeck, 1984). Within the context of
the example, this `subgroup correlation analysis'
implies that a test is made for di?erences between
the correlation of X
1
and Y for extreme values of
2
The Journal of Accounting and Economics belongs to the
four journals with the highest perceived quality in the Brown
and Huefner (1994) study. It has not published, however, con-
tingency studies of budgeting.
Table 1
Dispersion of reviewed budgetary articles over journals
Journal (acronym used) Number of
articles
The Accounting Review (TAR) 5
Journal of Accounting Research (JAR) 6
Accounting, Organizations and Society (AOS) 17
Total 28
296 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
X
2
. The di?erence in substantive meaning of the
two kinds of analyses is graphically illustrated in
Fig. 3. In this ®gure, the shaded areas represent
the `clouds' of observations (scatter diagrams) of
the relationship between X and Y. A `wide' cloud
indicates a low correlation and a `narrow' cloud
indicates a high correlation. For each cloud the
appropriate regression lines are depicted as well.
Panel A of Fig. 3 shows no sign of interaction,
since both correlations and regression lines are
equal for the two subgroups. Panel B illustrates a
`form' interaction since the slope of the regression
line is di?erent for the two subgroups. No indica-
tion of interaction for `strength' exists, since X
appears to predict Y in both subgroups equally
well, evidenced by the absolute values of the corre-
lation coecients being equal. Panel C is the oppo-
site of panel B since there is no di?erence in slope,
but there is a di?erence in `strength'. This means
that in subgroup 1, X is a better predictor of Y than
in subgroup 2. Panel D shows a combination of
`form' and `strength' interactions, since both the
slope of the regression line and the correlation of X
and Y are di?erent for the two subgroups.
There has been some confusion in the literature
about whether contingency hypotheses re¯ect dif-
ferences in `form' or in `strength' (see, e.g. Arnold,
1982, 1984; Stone & Hollenbeck, 1984). The com-
mon understanding, however, now seems to be
that contingency hypotheses are of the form type
(panels B and D, Fig. 3), and it is even argued that
di?erences in strength are commonly meaningless
(Arnold, 1982, pp. 153±154; Schmidt & Hunter,
1978, p. 216). A problem, therefore, exists with
respect to the relationships hypothesized and tes-
ted in many budgetary studies. In 15 of the 28
papers used in this paper there is either no
hypothesis explicitly stated (Brownell & Dunk,
1991; Brownell & Hirst, 1986; Brownell & Mer-
chant, 1990) or it is stated in a null form predicting
that there is `no interaction' between the measured
variables (Brownell, 1982a, b, 1983, 1985; Chen-
hall, 1986; Dunk, 1989, 1990, 1993; Frucot &
Shearon, 1991; Harrison, 1992, 1993; Mia &
Chenhall, 1994). This raises the question about the
meaning of the word `interaction' in these cases, in
particular whether it relates to the strength of the
relationship or the form of the relationship. Since
these types of ®t are not equivalent for either the
theoretical interpretation or the statistical test,
null hypotheses are inadequate for describing the
speci®c contingency formulations and statistical
test to be used. Obviously, if an author states that
there is an `interaction' (e.g. Hirst & Lowy, 1990),
Fig. 3. Interaction as strength and as form.
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 297
this hypothesis has the same shortcomings as the
null hypothesis described above.
Despite the dominance of form interactions in
contingency research, budgetary researchers have
investigated hypotheses that seem to express
strength interactions. If there is a theory supporting
such relationships, the appropriate statistical ana-
lysis consists of calculating z-scores of the corre-
lation coecients. Since the interest is in the
di?erence in predictive power between subgroups,
it is important that the z-scores are calculated
using absolute values of the correlation coe-
cients. Obviously, their sign does not contain
information about predictive power. Merchant
(1981, 1984, 1990) and Govindarajan (1984) test
for di?erences in correlation coecients, but do
not calculate nor speci®cally mention the `abso-
lute' z-score.
4.2. Interaction and the formulation of hypotheses
The examples above point to a weak link
between the verbal and statistical format of
hypotheses, which has been noted and discussed
before by Schoonhoven (1981). She criticizes stud-
ies in the organizational literature for their lack
of clarity in stating contingency hypotheses, which
a?ects the obviousness of the statistical test to be
used. Above, a reference was made to Govindar-
ajan (1984), who tests a strength hypothesis. A
further problem with Govindarajan's (1984) analy-
sis relates to the substantive content of his con-
tingency hypothesis, which is incompatible with
his theoretical arguments.
3
His hypothesis predicts
that `organizational e?ectiveness' a?ects the
strength of the relationship between `environ-
mental uncertainty' and `evaluation style'. The
format of the statistical analysis is in conformity
with this hypothesis, since it compares the corre-
lation coecients for the two subgroups. The
subsequent interpretation of these results, how-
ever, is not. Govindarajan (1984, p. 133) concludes
that environmental uncertainty has a `signi®cant
moderating e?ect' on the relationship between
evaluation style and organizational e?ectiveness.
This is a peculiar interpretation since the subgroup
correlation analysis is based on high and low `e?ec-
tiveness' subgroups. This suggests that `e?ective-
ness' is the moderator instead of the theoretically
relevant moderator `environmental uncertainty'.
4
Overall, therefore, there is no match between the
theoretical arguments, the formulation of the
hypothesis, and the interpretation of the statistical
analysis of the hypothesis. Govindarajan's (1984)
conclusion about the moderating e?ect of `envir-
onmental uncertainty' is clearly unfounded.
In another six of the 28 papers (Merchant, 1981;
1984; Brownell, 1982b; Imoisili, 1989; Frucot &
Shearon, 1991; Dunk, 1992), obvious di?erences
exist between the hypothesis and the statistical test
used, which makes the conclusions by the authors
debatable.
5
Merchant (1981, 1984) hypothesizes
an interaction a?ecting the form of the relation-
ship, as shown by an example of the following
hypothesis:
Organizational performance tends to be
higher where there is a `®t' between the use of
budgeting and the situational factors, as
described in Hypotheses 1±4. (Merchant,
1984, p. 294; emphasis added.)
6
Recall from the previous section that the statis-
tical test used is a correlation per subgroup and
relates to the strength of the relationship. The results
of the analysis are therefore of little relevance and
value to the contingency hypothesis stated.
A second example of a di?erence between the
hypothetical and measured ®t are the papers of
3
Govindarajan's (1984) theoretical arguments indicate an
interaction of the form type. Govindarajan even speci®cally
proposes a non-monotonic relationship (see Fig. 1, p.128)
4
Note that labeling an independent variable the `moderator' in
MRA is a question of theory because of the symmetry mentioned
earlier. Yet, Govindarajan does not switch the moderator and the
independent variable, but switches the moderator and the depen-
dent variable. In this case, the symmetry does not apply.
5
The papers of Imoisili (1989) and Dunk (1992) will be dis-
cussed in Sections 4.4 and 4.5, respectively.
6
This hypothesis is the ®fth in Merchant's paper and refers
to hypotheses 1±4. In these hypotheses, Merchant applies the
selection type of ®t and uses correlation analysis. For example
hypothesis 4 states: ``Larger, more diverse departments tend to
place greater emphasis on formal budgeting.''
298 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
Brownell (1982b) and Frucot and Shearon (1991,
p. 85). Frucot and Shearon (1991) state a null
hypothesis in the following form:
In Mexico, locus of control does not have,
through an interaction e?ect with budget-
ary participation, a signi®cant e?ect on
performance.
Subsequently the following equation is statistically
tested:
Y ?
0
?
1
X
1
?
2
X
2
?
3
X
1
ÀX
2
?" ?4?
This equation does not, however, measure ®t as
interaction but ®t as matching (Venkatraman,
1989, p. 431). Because ®t as interaction (i.e. form)
is hypothesized, the verbal statement and statis-
tical measure are not compatible.
7
Given this
incompatibility, the conclusion cannot be inter-
preted and the statistical results become explora-
tory at best. The reason the authors give for using
the matching variable is that:
(. . .) the multiplicative interaction term does
not provide a good measure of this matching
condition'' (Frucot & Shearon, 1991, p. 90).
Although this is true, the hypothesis expresses `®t'
as interaction and simply does not predict the
matching condition. Frucot and Shearon (1991,
p. 90) also state that the variable should be mea-
sured by the absolute di?erence, arguing that this
better re¯ects the relationship among the three vari-
ables. If so, the hypothesis should have been altered
to state the matching condition, and the alternative
and only proper formulation would have been:
8
In Mexico, given the value of locus of con-
trol, there is a unique value of budgetary par-
ticipation that produces the highest value of
performance; deviations from this relationship
in either direction reduce the value of perfor-
mance. (cf. Schoonhoven, 1981).
9
4.3. Interaction and lower-order e?ects
As illustrated above, the equation representing
an interaction e?ect [Eq. (2)] includes not only
the interaction term (X
1
 X
2
), but also the two
main e?ects (X
1
) and (X
2
). At least three topics
related to the inclusion of lower-order e?ects
warrant discussion. These are (1) the reason for
including lower-order e?ects; (2) the interpreta-
tion of the coecients for lower-order e?ects
found in the regression analysis; and (3) the
potential problem of multicollinearity. First, the
reason for the inclusion of lower-order e?ects in
MRA is to prevent conclusions of the existence of
an interaction e?ect when such an e?ect is solely
due to lower-order e?ects. An example is found
with Hirst (1983) who tests a model represented
by Eq. (5) below that does not include main
e?ects:
Y ?
0
?
1
X
1
ÂX
2
?" ?5?
In this case, ®nding a signi®cant coecient
1
does
not necessarily indicate the existence of an inter-
action e?ect, since it could be due to a signi®cant
relationship between X
1
and Y regardless of X
2
. In
other words, because the interaction term is the
product of the two main e?ects, it is likely to `steal
variance' from its constituting parts (cf. Cohen &
Cohen, 1983, p. 305). Stone and Hollenbeck (1984,
p. 201) argue in this respect:
(. . .) while the cross-product term in a
regression equation ``carries'' the interaction,
the same cross-product term is not the inter-
action.
This implies that when testing for an interaction
e?ect, the lower-order e?ects should be `partialed
out' by including them in the regression equation
(Southwood, 1978, p. 1164; Cohen & Cohen,
7
The authors also state that the relationship is `accentuated'
and `attenuated' (p. 85). This refers to accelerating and decel-
erating e?ects and thus to the form of the relationship.
8
The same line of reasoning applies to Brownell (1982b).
9
For a discussion of the use of di?erence scores, see
Bedeian, Day, Edwards, Tisak, and Smith (1994).
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 299
1983, p. 348; Stone & Hollenbeck, 1984, p. 201).
Consequently, Hirst's (1983) conclusion based on
the results of Eq. (5) is unfounded.
10
A second issue relates to the proper interpreta-
tion of coecients obtained for lower-order e?ects
in MRA. Southwood (1978, p. 1168) argues that
such coecients generally have no theoretical
meaning. The reason is that in the behavioral sci-
ences the variables are usually measured using
interval scales, and not ratio scales. This means
that scale origins and thus linear transformations
of variable scores are arbitrary, and have no sub-
stantive meaning. Southwood (1978, p. 1668, pp.
1198±1201) shows that such linear transforma-
tions do change the coecient of the lower-order
e?ects in the MRA equations, and therefore, these
coecients cannot be easily interpreted. This does
not imply that the coecients of the lower-order
e?ects in an interaction model are lacking all
meaning. In particular, they signify the main e?ect
of the variable (e.g. X
1
) when the value of the
other variable (X
2
) is zero (Jaccard et al., 1990).
Only for ratio scale variables is this zero `mean-
ingful' (Southwood, 1978, p. 1165). For interval
scale variables, the zero value obtains a speci®c
meaning if the variables are `centered' around
their respective means. In this case, the coecients
of the main e?ects represent the e?ect of one
variable at the (sample) average of the other (Jac-
card et al., 1990, p. 34). Despite this meaning, it is
important to point out that the coecients
obtained for the main e?ects when applying MRA
are, in general, di?erent from those that would be
obtained through a regression model without the
interaction term. Furthermore, it is important to
note that linear transformations do not change the
coecient of the interaction term, nor its t-statistic
and level of signi®cance (Cohen & Cohen, 1983,
pp. 305±306; Southwood, 1978, p. 1168). Thus,
Brownell (1982a), Chenhall (1986) and Mia (1988)
are wrong in assuming that `centering' the vari-
ables provides a:
clearer basis for predicting the sign of (. . .) the
coecient of the interaction term (Brownell,
1982a, p. 20; emphasis added).
Since the coecient of the interaction term is not
sensitive to the scale origins, it also follows that for
tests of an interaction e?ect using MRA the inde-
pendent variables need not be ratio±scaled (South-
wood, 1978, p. 1167; Arnold & Evans, 1979).
The analysis of the budgetary papers shows that
the interpretation of lower-order e?ects is subject
to both Type-I and Type-II errors; interpretation
of invalid lower-order e?ects and no interpretation
of valid lower-order e?ects. First, ®ve papers show
an invalid interpretation of main e?ects in two-way
interactions (Brownell, 1982a, 1983, 1985; Chen-
hall, 1986; Mia, 1989). For example, Brownell
(1982a) studies (among others) the moderating
e?ect of Budget Emphasis on the relationship
between Budgetary Participation and Performance.
He interprets the interaction e?ect, and both main
e?ects [see Eq. (2)]. The Budgetary Participation
variable in the MRA equation is measured as a
`deviation score' from the overall mean (i.e. cen-
tered). A linear transformation of the raw score of
one independent variable leads to a change in the
regression coecient of the other independent
variable. This implies that the coecient of the
main e?ect of Budget Emphasis changes. As a
result, the coecient of Budget Emphasis illustrates
10
Hirst (1983, p. 600) claims to have found an interaction
e?ect of the form-type based on subgroup regression-analysis.
Since the regression coecients are standardized, and since
standardized regression coecients in simple linear regression
equals correlation coecients, the subgroup analysis is in fact
subgroup correlation-analysis. This latter statistical format,
however, tests strength and not form, so that Hirst's ®ndings
seem unfounded. However, in this speci®c case additional
information suggests the existence of a form interaction for one
of the two dependent variables (job-related tension). The corre-
lation coecients between RAPM and job-related tension for
low and high task uncertainty are À0.33 and 0.53 respectively.
Both coecients are statistically signi®cant, which means that
the regression coecients per subgroup are also signi®cant. As a
result, there will be a signi®cant negative coecient for the low
task uncertainty subgroup and a signi®cant positive coecient
for the high task uncertainty subgroup. Since signi®cant means
signi®cantly di?erent from zero, a positive (negative) signi®cant
coecient is also signi®cantly di?erent from any negative (posi-
tive) coecient. Thus, the di?erence between these two regres-
sion coecients is also signi®cant. The signi®cance of this
di?erence is equal to the signi®cance of the interaction term in
MRA and the ®t as interaction (form) is supported. Note that
Hirst's (1983) paper, as it is published, thus does not prove a ®t
as interaction (form); the above analysis does.
300 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
the e?ect of Budget Emphasis on Performance at
the average level of Budgetary Participation.
11
This
interpretation di?ers from Brownell's (1982a, pp.
20±21) who incorrectly interprets the regression
coecient unconditional on Budgetary Participation.
Further, the Budget Emphasis variable is not centered
around its mean, which makes the coecient of
Budgetary Participation uninterpretable. Brow-
nell's conclusion regarding Budgetary Participa-
tion is therefore unfounded.
12
In studies using
higher-order interactions, similar problems are
found (e.g. Brownell & Hirst, 1986; Imoisili,
1989). These studies are discussed below in the
section on higher-order interactions.
The above ®ve studies precede the introduction
of the Southwood (1978) paper into the manage-
ment accounting research literature.
13
The more
recent and uncritical use of Southwood's paper,
however, has led to the reverse situation; no
interpretation of valid lower-order e?ects. Exam-
ples include the following. Mia and Chenhall
(1994) study the moderating e?ect of Function on
the relationship between the Use of Broad Scope
MAS and Managerial Performance. The MAS
variable is a `di?erence score' from the overall
mean (i.e. centered). This means that the coe-
cient of the main e?ect of Function is interpretable.
The authors refer to Southwood and state:
No attempt was made to interpret the coef-
®cients (. . .) that related to extent of use of
broad scope Management Accounting System
(MAS) information or function. (p. 9; empha-
sis added.)
Thus, they incorrectly state that the coecient of
Function cannot be interpreted and therefore lose
information. Using this information would have
allowed the supplementary conclusion that Func-
tion by itself has a direct in¯uence on managerial
performance, in that marketing managers perform
better than production managers at the `average'
MAS. In Lau, Low and Eggleton (1995) all inde-
pendent variables are centered. This means that
the lower-order e?ects in their interaction models
could have been interpreted. The authors, how-
ever, refer to Southwood and reject the inter-
pretation of lower-order e?ects (p. 369).
Although, the papers of Mia and Chenhall (1994)
and Lau et al. (1995) are the only concrete and
explicit examples of a Type-II error, seven other
studies speci®cally refer to Southwood and a
priori reject the interpretation of lower-order
e?ects (Brownell & Dunk, 1991; Dunk, 1990,
1992, 1993; Harrison, 1992, 1993; Gul & Chia,
1994). The conclusion seems warranted that
researchers are unaware of the possibilities and
problems of interpreting lower-order e?ects in
MRA. In a way, Southwood's paper has had both
a positive and a negative e?ect on this. The posi-
tive e?ect is that main e?ects indeed cannot
usually be interpreted, while the negative e?ect has
been that it is believed that they should never be
interpreted in MRA. Unfortunately, this false idea
even shows up in handbooks aimed at novice
management accounting researchers (Brownell,
1995). Here it says that:
It is now widely understood that the esti-
mated coecients for variables, included in
an equation along with their cross product
with another variable, are not interpretable.
(Brownell, 1995, p. 55; emphasis added.)
It also says that Southwood has shown that if a
constant is added to interval scale data that:
(. . .) this will alter the estimated coecient for
the variable to which the constant was added
(p. 55; emphasis added).
This is, of course, incorrect. The coecient of the
variable to which the constant is not added, chan-
ges. The `easy' reference to papers like South-
wood's, without critically evaluating its wisdom, is
remarkable at least.
11
More speci®cally, the results show that at the average
level of Budgetary Participation, lower Budget Emphasis leads
to increased Performance.
12
Brownell concludes that higher Budgetary Participation is
associated with higher Performance.
13
Schoonhoven (1981) explicitly incorporates several main
e?ects in her multiple interaction equation and incorrectly
interprets them all. This is peculiar since Southwood (1978) is
among her references.
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 301
The third and ®nal point related to lower-order
e?ects in MRA is the potential problem of multi-
collinearity, caused by the fact that the lower-
order e?ects (e.g. X
1
and X
2
) and their product are
likely to be correlated (e.g. Drazin & Van de Ven,
1985). Yet, from the same arguments that show
the insensitivity of the coecient of the interaction
term in MRA (X
1
 X
2
) to changes in scale origins
of X
1
and X
2
, it follows that multicollinearity is
not a problem when applying MRA (cf. Dunlap &
Kemery, 1987). In particular, it is possible to use
linear transformations of X
1
and X
2
that remove
the correlation between the main terms and the
interaction term (Southwood, 1978, p. 1167; Jac-
card et al., 1990, p. 22). The `correct' linear trans-
formation of variable scores to minimize the
correlation between the independent variables and
their product is the centering procedure discussed
before (e.g. Jaccard et al., 1990, p. 34). Recall that
since no such linear transformation ever a?ects the
coecient of the interaction term, the coecient
of the interaction term is always interpretable, and
centering is not required. As was illustrated, this is
not always recognized in budgetary studies
(Brownell, 1982a, 1983; Chenhall, 1986; Mia,
1988, 1989; Lau et al., 1995). As an example, Lau et
al. (1995) use deviation scores from the mean
because, as they state, it reduces the `problem' of
multicollinearity (p. 368). However, no such problem
exists.
14
4.4. Multiple and higher-order interactions
The previous sections discussed the general for-
mat of MRA and focused on the analysis of a
single two-way interaction. MRA, however, is not
restricted to the analysis of a single two-way
interaction. It can also be used to analyze (1)
multiple two-way interactions, and (2) any n-way
interaction. First, multiple two-way interactions
can be tested by extending Eq. (2) to include an
additional main and interaction e?ect, as shown
by the example of Eq. (6a):
Y ?
0
?
1
X
1
?
2
X
2
?
3
X
3
?
4
X
1
ÂX
2
?
5
X
1
ÂX
3
?"
?6a?
As for any equation, the inclusion of an additional
two-way interaction in MRA should be based on
theory (Jaccard et al., 1990, p.40±41). More speci-
®cally, the theory should state that the relation-
ship between X
1
and Y is not only a function of
X
2
, but also of X
3
. In other words,
@Y=@X
1
?
1
?
4
X
2
?
5
X
3
?6b?
Imoisili (1989, p. 327) exactly hypothesizes the
relationship depicted by Eqs. (6a) and (6b). How-
ever, this hypothesis is incorrectly tested, since the
equation analyzed also includes a redundant two-
way interaction term X
2
 X
3
, and a redundant
three-way interaction term X
1
 X
2
 X
3
. The
result of analyzing this equation does not provide
an answer to the hypothesis, since the partial deri-
vative ?@Y=@X
1
? of the function that Imoisili uses is
given by Eq. (7), which contains an `interaction
e?ect' ?X
2
 X
3
? not hypothesized.
@Y=@X
1
?
1
?
4
X
2
?
5
X
3
?
7
X
2
ÂX
3
?7?
The only correct statistical test would have been
Eq. (6a). Harrison (1992, 1993) provides an
example of similar problems. Harrison (1992) uses
Eq. (8) to test for the existence of two-way inter-
actions between Budgetary Participation (X
1
),
RAPM (X
2
), and the dummy variable Nation (X
3
)
to a?ect Job-Related Tension (Y):
Y ?
0
?
1
X
1
?
2
X
2
?
3
X
3
?
4
X
1
ÂX
2
?
5
X
1
ÂX
3
?
6
X
2
ÂX
3
?"
?8?
Harrison (1992, p. 11) is only interested in the
moderating e?ect of X
1
on the relationship
between X
2
and Y, and his analysis is therefore
¯awed for two reasons.
15
First, there is no theore-
tical foundation for using the multiple interaction
equation. Only the ®rst interaction (X
1
 X
2
) is
hypothesized by Harrison, both other interactions
14
The only `problem' that multicollinearity can cause is that
the statistical program is unable to calculate the regression
coecients due to singularity of the matrix.
15
The same conclusion can be made with respect to Imoisili
(1989).
302 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
(X
2
 X
3
and X
1
 X
3
) are not.
16
Second, this
equation has a chance of being overspeci®ed,
which means that extra predictor variables are
unnecessarily included. Overspeci®cation of the
model leads to an increased standard error of the
regression coecients (Cryer & Miller, 1991,
p. 639), in¯uencing the signi®cance test of the
coecient. Harrison states that:
4
, as the (highest order) interaction term, is
both stable and interpretable for its standard
error and signi®cance test. (Harrison, 1992,
p. 11; emphasis added.)
Although the interaction term, standard error
and signi®cance test may be stable, they are hardly
interpretable if the model is a?ected by an unne-
cessary overspeci®cation. A standard error in¯u-
enced by overspeci®cation is not interpretable, no
matter how stable it is. In this case, therefore, the
signi®cance of coecient
4
is not interpretable.
Moreover, the partial derivative of this equation
?@Y=@X
2
? is:
@Y=@X
2
?
2
?
4
X
1
?
5
X
3
?9?
This reveals that the relationship between X
2
and Y
is not a linear function of X
1
, but a linear function
of both X
1
and X
3
. As a result, the hypothesis
remains unanswered because the coecient
4
is
not a measure of the hypothesized moderating
e?ect of X
1
on the relationship between X
2
and Y.
17
Apart from the use of multiple two-way inter-
actions, MRA can be used to analyze n-way
interactions. As an example of higher-order inter-
actions, a three-way interaction generally has the
format of Eq. (10):
Y ?
0
?
1
X
1
?
2
X
2
?
3
X
3
?
4
X
1
ÂX
2
?
5
X
1
ÂX
3
?
6
X
2
ÂX
3
?
7
X
1
ÂX
2
ÂX
3
?"
?10?
In conformity with the interpretation of the pro-
duct term for two-way interactions, the product
term ?X
1
 X
2
 X
3
? in Eq. (10) represents the
three-way interaction among the (three) indepen-
dent variables. The issues discussed above regard-
ing use and interpretation of MRA for two-way
interactions are also important for three-way
interactions. Regarding the inclusion of main
e?ects in MRA, for a three-way interaction equa-
tion, all two-way interactions should be included,
and the user should observe that the coecients
obtained for these two-way interactions are not
directly interpretable (Cohen & Cohen, 1983,
p. 348).
18,19
In general, for an n-way interaction,
the main e?ects and all possible interactions of a
lower-than-n order should be included. The di?er-
ence between two-way and higher-order interactions
16
Harrison (1992) refers to both Schoonhoven (1981) and
Jaccard et al. (1990) for using the multiple interaction equation.
Schoonhoven's statistical analysis is incorrect, and referring to
her analysis may have caused the incorporation of similar
shortcomings. The reference to Jaccard et al. (1990, pp. 40±41)
is intriguing, since here the importance of theory when using
multiple interactions is stressed. Harrison seems to selectively
use this passage to only eliminate the theoretically irrelevant
three-way interaction (1992, p. 11), while leaving two theoreti-
cally irrelevant two-way interactions.
17
The same line of reasoning applies to Harrison (1993).
18
Once again, `not interpretable' means that the coecients
found in the interaction model are not the same as those found
in the main-e?ects-only model. Although the main e?ects are
not interpretable in a three-way interaction equation, the two-
way interactions are if the variables are centered. The inter-
pretation is in conformity with the interpretation stated in pre-
vious sections, i.e.
4
is the interaction e?ect X
1
 X
2
on Y at
the (sample) average of X
3
.
19
Brownell and Hirst (1986) use a three-way interaction
equation and interpret a main e?ect [Participation (P)], a two-
way interaction [PÂBudget Emphasis (B)], and the three-way
interaction [PÂBÂTask Uncertainty (T)]. The authors assume
that every variable in the equation is interpretable. However, as
was shown before, the coecients of the main e?ects in a three-
way interaction are normally not interpretable. Because only
variable P is centered, only the two-way interaction without
component P can be interpreted. This means that only the
interaction of B Â T can be interpreted. Brownell and Hirst (1986)
on the other hand, interpret the coecient of P Â B, which is
statistically incorrect. Conclusion of the regression results
should only have been based on the two-way interaction B Â T
and the three-way interaction (P Â B Â T). More problematic
even is the analysis of Imoisili (1989, p. 330). Imoisili examines
two-way interactions and uses a three-way interaction equation
[see Eq. (10) above], where Y=a.o. Performance; X
1
=Budget
style; X
2
=Task Interdependence; and X
3
=Task Uncertainty.
The author is interested in the coecients
4
and
5
. Their
interpretation is hindered because of, among others, the use of
raw scores instead of centred variables. The results therefore do
not provide support for, nor allow rejection, of the hypothesis.
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 303
therefore does not lie in its mathematics or statis-
tics, but in the interpretation of its meaning. Cohen
and Cohen (1983, p. 306) note in this respect:
The fact that the mathematics can rigorously
support the analysis of interactions of high
order, however, does not mean that they
should necessarily be constructed and used:
interactions greater than three-way are most
dicult to conceptualize, not likely to exist,
and are costly in statistical inference (. . .)
However, even for a three-way interaction the
problems noted by Cohen and Cohen (1983) exist.
First, Schmidt and Hunter (1978) and Champoux
and Peters (1987), for example, note that the sam-
ple sizes typical in (organizational) research lack
the power to ®nd the hypothesized interactions of
a high-order. Budgetary studies are no exception,
with sample sizes often far below 100 (cf. Young,
1996). Second, the diculty of conceptualizing
three-way interactions becomes clear if one con-
siders that a three-way interaction means that a
two-way interaction is a function of a third vari-
able. In terms of Eq. (10), this means that a sig-
ni®cant coecient of the three-way interaction
term (
7
) indicates that the interaction e?ect of X
1
and X
2
on Y is a function of X
3
. However, because
of the symmetry mentioned earlier, a three-way
interaction therefore simultaneously expresses:
(a) the moderating e?ect of X
3
on the X
1
 X
2
interaction a?ecting Y;
(b) the moderating e?ect of X
2
on the X
1
 X
3
interaction a?ecting Y; and,
(c) the moderating e?ect of X
1
on the X
2
 X
3
interaction a?ecting Y.
The complexity is evident if it is further con-
sidered that (a) implies that X
3
is `moderating the
moderating e?ect' that X
2
has on the relationship
between X
1
and Y, and that also here the sym-
metry applies that was mentioned earlier. Because
of the complexity, it seems even more important
here that theory should dictate which variables are
labeled the moderators.
A three-way interaction is graphically illustrated
in Fig. 4, which depicts a three-way interaction for
one continuous and two dichotomous independent
variables. Panel A and B both show a two-way
interaction, and illustrate how the relationship
between X
1
and Y is di?erent for high and low
values of X
2
. Panel A shows the two-way interac-
tion for low values of X
3
. Panel B shows the two-
way interaction for high values of X
3
. The three-
way interaction signi®es the di?erence between the
two changes in slope for high and low values of
X
3
. A signi®cant three-way interaction does not
indicate that a two-way interaction is signi®cant
for some values of X
3
, and not for others. Indeed,
a three-way interaction can be signi®cant, both
when the `underlying' two-way interactions are
signi®cant, and when they are not.
20
Note that
here and in many (graphical) examples in this
paper, the analysis is simpli®ed by using dichoto-
mic variables. For three continuous variables, the
graphical depiction and explanation of three-way
interactions are far more complex. In sum, Cohen
and Cohen (1983, pp. 347±348) therefore advocate
a restricted use of higher-order interactions, and
state:
No interaction set should be included in the
IV's (independent variables) unless it is ser-
iously entertained on substantive grounds
(. . .). This requires as a minimum condition
that it be understood by the investigator and
on practical grounds that it can be clearly
explicable to his audience.
Of the 28 papers analyzed, six papers speci®-
cally study three-way interactions (Brownell &
Dunk, 1991; Brownell & Hirst, 1986; Dunk, 1993;
Gul & Chia, 1994; Harrison, 1993; Lau et al.,
1995). Three of these six papers decompose the
three-way interaction into two-way interactions
(Brownell & Dunk, 1991, pp. 700±701; Brownell &
Hirst, 1986, pp. 247±248; Lau et al., 1995, p. 372).
In this way the authors can ascertain that the sig-
ni®cant three-way interaction is indeed a `real'
20
Thus, a signi®cant universal relationship may exist
between the independent and dependent variables, while the
three-way interaction is also signi®cant. An example of (hypo-
thetical) data that exhibit this relationship is available from the
authors upon request.
304 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
relationship and not fallacious.
21
As stated before,
a signi®cant three-way interaction does not con-
tain any information about the signi®cance of the
underlying two-way interactions. To establish the
latter, the additional analysis is required.
22
The
other three papers mentioned (Dunk, 1993; Gul &
Chia, 1994; Harrison, 1993) do not check the sig-
ni®cance of the two-way interaction e?ects under-
lying the three-way interactions found. Solely
based on the signi®cance of the three-way interac-
tion, the authors draw conclusions with respect to
the underlying relationship at the level of two-way
interactions (Dunk, 1993, p. 407; Harrison, 1993,
p. 333) and even at the level of main e?ects (Gul &
Chia, 1994, p. 422), Gul &Chia (1994), for example,
measure the three-way interaction of Management
Accounting System Scope, Perceived Environmental
Uncertainty and Decentralization on Managerial
Performance. They use the partial derivative of the
three-way interaction Eq. (10) to analyze two-way
interactions and main e?ects. The result of their
analysis is theoretically uninterpretable, since they
do not establish whether two-way interactions
exist at all. The same conclusion holds for the
papers of Dunk (1993) and Harrison (1993).
It seems clear that Cohen and Cohen's (1983)
warning concerning higher-order interactions is
not heard in the budgetary research paradigm. A
reviewer of Gul and Chia's paper suggested the use
of a four-way interaction (1994, footnote 10). It is
easy to consider the problems and complexities
associated with this format.
4.5. Interaction, e?ect size, and the Johnson±
Neyman technique
A further issue related to the interpretation of
the outcomes of MRA is that a (signi®cant) coef-
®cient of the interaction only contains information
about changes in the relationship between vari-
ables, and does not contain information about the
optimal value of the dependent variable (i.e. e?ect
size, see Champoux & Peters, 1987). This is illu-
strated in Fig. 5. In panel A, Y has the highest
(lowest) value when both X
1
and X
2
are high (low).
In contrast, in panel B, Y has the highest (lowest)
value when X
1
is high (low) and X
2
is low (high).
Note that in both cases the interactions (X
1
 X
2
)
are equal with respect to both direction and size.
This means that in both cases, an increase in the
value of X
2
has an equal positive e?ect on the
form of the relationship between X
1
and Y. The
di?erence between the cases is due to a main e?ect
of the moderating variable on the dependent vari-
able (cf. Kren & Kerr, 1993). The proper inter-
pretation of a positive interaction therefore is not
that Y achieves the highest values for the highest
values of X
1
and X
2
, but that for higher values of
X
1
; X
2
has a more positive e?ect on Y. Hence,
MRA cannot be used to test expectations about
Fig. 4. Three-way interactions for two dichotomous moderators.
21
Lau et al. (1995) provide a clear example of such a
decomposition. A ¯aw in their analysis, however, is that they
de®ne a null hypothesis and alternative hypotheses (pp. 363±
364), which are not mutually exclusive. This means that the
statistical results could have supported both the null hypothesis
and the alternative hypotheses.
22
Brownell and Dunk (1991) do the additional analysis to
con®rm the expected form and sign of the two-way interactions
(p. 701). Finding a signi®cant three-way interaction does not
warrant such speci®c expectations.
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 305
the values of X
1
and X
2
for which Y will have the
highest value. This is the consequence of MRA
testing the signi®cance of the interaction e?ect,
and not testing for a combined e?ect of the main
e?ects and the interaction e?ect on the dependent
variable.
The di?erence between a signi®cant interaction
and e?ect size is not always recognized in the
papers examined. For example, Dunk (1992)
hypothesizes that:
(. . .) the higher (lower) the level of manu-
facturing process automation and the higher
(lower) the reliance on budgetary control, the
higher will be production subunit perfor-
mance (p. 198; emphasis added).
This hypothesis states that high/high and low/low
combinations of the independent variables max-
imize the dependent variable. Dunk (1992) uses
MRA to test this hypothesis and thus incorrectly
assumes that the signi®cant interaction contains
information about e?ect size. Further, Brownell
(1983), Brownell and Hirst (1986), Mia (1989),
Dunk (1989, 1990, 1993) and Brownell and Dunk
(1991) also assume that a signi®cant interaction
means that a certain combination of variables
maximizes the dependent variable. For example,
Dunk (1993) states the following about the sig-
ni®cance of the coecient of the three-way inter-
action term (b
7
):
As b-(. . .) is signi®cant and negative, it
appears that slack is low when participation,
information asymmetry, and budget emphasis
are all high (pp. 405±406; emphasis added).
Such a statement is not only incorrect, the ques-
tion of the `highest Y' is likely to be irrelevant in
testing contingency models, especially when the
main e?ects are due to uncontrollable, exogenous
contingency factors.
Two papers apply a formal analysis of e?ect
sizes by using the so-called Johnson±Neyman
technique (Brownell, 1982a; Lau et al., 1995). This
technique can be used to ®nd the `region of sig-
ni®cance' for the di?erence between the e?ects of
di?erent values of the moderator at a given value
of the independent variable (Pedhazur & Pedha-
zur-Schmelkin, 1991). In other words, the techni-
que provides a measure to establish whether the
e?ect of the moderator is `large enough' to lead to
signi®cant di?erent values of the dependent vari-
able. The Johnson±Neyman technique can be illu-
strated more clearly by returning to Fig. 5. The
question is whether for a given value of X
1
, there
is a signi®cant di?erence between the value of Y
for subgroup 1 and 2 (i.e. for X
2
=low and
X
2
=high). In panel A, the `region of signi®cance'
will relate to higher values of X
1
, since the di?er-
ence between the two regression lines increases
with increases in X
1
. In panel B, on the other
hand, the `region of signi®cance' will relate to
lower values of X
1
. Despite this di?erence in
`region of signi®cance', the interactions are equal
with respect to both direction and size, as stated
before. The use of the Johnson±Neyman technique
in MRA is therefore questionable, since it plays no
Fig. 5. Interaction contains no information on value independent variable.
306 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
role in the test of hypotheses of the interaction
format. Since the interaction contains no infor-
mation on e?ect sizes (i.e. values of the dependent
variable), the results of this technique are of no
relevance to the interpretation of the interaction
e?ect. The formula used to ®nd the `region of sig-
ni®cance' is not only determined by the moderating
e?ect (i.e. e?ect on slope) of the contingency vari-
able, but also by its e?ect on the intercept. The
region of signi®cance could be very large even if the
interaction e?ect is very small and insigni®cant,
because of a large di?erence in the intercept (and
vice versa). Further, looking at Eqs. (2a) and (2b),
one sees that the di?erence between intercepts is
in¯uenced by the `main e?ect of the moderator' (cf.
Kren & Kerr, 1993). As a result, the Johnson±Ney-
man technique mixes main e?ects and moderating
e?ects, and thus seems of little value to explore the
nature of the interaction e?ect alone, as stated and
done by Brownell (1982a) and Lau et al. (1995).
4.6. Interaction and (non-)monotonicity
Both in formulating and in testing contingency
hypotheses of the interaction format, it is impor-
tant to consider the (non-)monotonicity of the
hypothesized relationship. A statistically sig-
ni®cant coecient of the interaction term does not
contain information about whether the relation-
ship found is monotonic or non-monotonic, nor
does contingency theory have an a priori `pre-
ference' for monotonic or non-monotonic rela-
tionships. Since, however, the substantive
implications are di?erent for monotonic and non-
monotonic relationships, studies should explicitly
state whether the aim is to investigate and test
(non-)monotonicity.
23,24
Six of the 28 papers use
the method of the partial derivative to analyze
the (non-)monotonicity of relationships found
(Govindarajan & Gupta, 1985; Gul & Chia, 1994;
Harrison, 1993; Lau et al., 1995
25
; Mia, 1988,
1989). For example, Govindarajan and Gupta
(1985) measure the partial derivative of two two-
way interactions and provide graphs of these
equations. The resulting two graphs are examples
of an almost perfect non-monotonic relationship
in which the line crosses the X-axis near zero. The
conclusion is that for one extreme value of the mod-
erator (i.e. Strategy) the organization will be e?ective
if, here, accounting information is used in perfor-
mance evaluation, while being ine?ective for the
other extreme value of the moderator. Harrison
(1993) and Gul and Chia (1994) both measure the
partial derivative of the three-way interaction Eq.
(10). However, as the above analysis shows that their
results are uninterpretable because of a misspeci®ed
model, the conclusions about non-monotonicity are
invalid as well.
The graph of the partial derivative is one test for
non-monotonic e?ects but non-monotonicity can
also be measured by a regression per subgroup.
Four of the 28 papers use subgroup regression
analysis and all indicate that a non-monotonic
relationship exists (Brownell, 1983, 1985; Brownell
& Merchant, 1990; Mia & Chenhall, 1994). A fur-
ther strong point of these studies is that, except for
Brownell and Merchant (1990), they all measure
the statistical signi®cance for the di?erent sub-
groups, which allows a better understanding of the
higher-order interaction. In the majority of
papers, however, the issue of (non-)monotonicity
is not addressed.
5. Summary of ®ndings, conclusions and
implications
The evidence in the previous sections leads to
the initial conclusion that the use of MRA in the
papers reviewed is seriously ¯awed, caused by the
uncritical application of this statistical technique
and too little knowledge of its speci®c require-
ments and underlying assumptions. Table 2 pre-
sents an overview of the ®ndings. Generally, it
appears that six major types of errors in MRA use
23
Only Mia (1988, 1989) explicitly states a non-monotonic
form hypothesis.
24
Recall that an important reason for budgetary research to
adopt a contingency perspective were the opposite results of
Hopwood (1972) and Otley (1978). Hopwood (1972) found a
positive e?ect of budget emphasis, whereas Otley (1978) found a
negative e?ect. A contingency hypothesis that attempts to
explain these opposite e?ects of budget emphasis can only do so
by predicting a non-monotonic interaction e?ect.
25
Lau et al. (1995) only mention the result of the non-
monotonic test in a footnote (p. 374).
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 307
frequently occur in budgetary studies. These are:
(1) format of statistical test not in conformity with
hypothesis; (2) faulty use of tests for interactions of
the `strength' type when hypothesizing interactions
of the `form' type; (3) incorrect interpretation of
main e?ects; (4) incorrect speci®cation of the
MRA equation; (5) incorrect use of higher-order
interactions equations to test lower-order interac-
tions; and, (6) incorrect conclusions about e?ect
sizes from MRA. Overall, 27 of the 28 papers
(96%) exhibit at least one of the above errors.
26
Although the summary of ®ndings reveals that
only one paper appears free from errors, this does
not imply that the statistical results presented in
all other papers are meaningless, nor that the
conclusions drawn and presented in these papers
are not supported by the data. Regarding the for-
mer, although researchers may have applied MRA
incorrectly, and may have interpreted the MRA
results incorrectly, it may be that the statistical
results presented in these studies are interpretable
and useful. Therefore, an additional analysis was
done to evaluate the interpretability of the statis-
tical results as presented. This further analysis
reveals that the statistical results of 12 of the 28
papers (43%) can still not be interpreted. For
these papers, the uninterpretability of statistical
results is due to: (a) the use of subgroup correla-
tion analysis instead of the required MRA
(Govindarajan, 1984; Merchant, 1981, 1984,
1990); (b) the incorrect speci®cation of the MRA
equation (Brownell, 1982b; Frucot & Shearon,
1991; Harrison, 1992, 1993; Hirst, 1983; Imoisili,
1989); and (c) the de®cient analysis of a three-way
interaction (Dunk, 1993; Gul & Chia, 1994).
Regarding the latter, the analysis in the present
paper does also not prove that the conclusions
drawn and presented in the reviewed papers are
incorrect and unsupported by the data. It may be
that the statistical results presented in these papers
are robust and insensitive to the analytical ¯aws
and model misspeci®cations found. To check the
robustness of the results, another additional ana-
lysis would be required. Such an analysis would
imply the re-analysis of the original data using
MRA in conformity with the methodology and a
subsequent comparison of the results with those
presented in the original papers. Thus far, the
authors have not been able to conduct this test.
27
Table 2
Summary and overview of ®ndings
Major types of errors in MRA use Number of articles
1. Format of statistical test not in conformity with hypothesis 21 (75%)
2. Faulty use of tests for interactions of the `strength' type 4 (14%)
3. Incorrect interpretation of main e?ects 8 (29%)
4. Incorrect speci®cation of the MRA equation 4 (14%)
5. Incorrect use of higher-order interactions 3 (11%)
6. Incorrect conclusions about e?ect sizes from MRA 10 (36%)
Number of articles containing at least one of the above errors 27 (96%)
26
The paper of Govindarajan and Gupta (1985) does not
contain any errors with respect to the application and inter-
pretation of MRA.
27
To conduct such an analysis, the authors asked, at the
outset of the paper, for the data from two recent papers in the
sample. These two papers explicitly stated that the data `were
available upon request'. The authors of the two papers were
approached by both regular mail and e-mail. The letter and e-
mail stated the subject of the present paper and the purpose of
the request, which was to analyze the data for strictly methodo-
logical reasons. The results of this request were disappointing.
The author(s) of one paper replied that the data were lost due to
a move to a new university. The author(s) of the second paper
did not reply at all. After these two `answers', data were asked
from a third budgetary control paper. This was not included in
the sample (since it did not test `interaction'), but was compar-
able and deemed useful for the additional data-analysis. Also
here it said that the data were available. In this case the author
quickly replied but stated that the data were lost due to a `com-
puter crash'. Overall, this raises suspicion about the actual data
availability and, consequently, of the value of a `data avail-
ability policy'. Although the aim of this paper is not to investi-
gate the e?ectiveness of data availability policy proposed by
some journals, such an investigation does seem in order.
308 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
In sum, the ®ndings in this paper provide clear
evidence that the use of statistics in the budgetary
contingency literature does not indicate a high
level of technical quality. Many studies show too
little knowledge of the characteristics and pitfalls
of MRA, and do not display the expertise and
care required in the interpretation of its out-
comes. Moreover, budgetary studies contain little
rigor in their use of contingency theory, since it is
also found that many studies do not provide a
good link between the verbal (substantive) format
of the hypothesis and the statistical format sub-
sequently used to test the hypothesis. The reason
for this apparent negligence is not obvious, but it
may be an additional ground to be critical at
theoretical advancement in this area of the litera-
ture (cf. Chapman, 1997; Lindsay & Ehrenberg,
1993; Hartmann, in press; Young, 1996). Earlier
Briers and Hirst (1990, p. 385) have sharply criti-
cized the underdevelopment of contingency the-
ory in many budgetary and RAPM studies. They
stated:
Of particular concern is the inclusion of vari-
ables in hypothesis with little supporting
explanation. For example, some studies use
box diagrams with arrows indicating causally
related variables. Although this is a parsimo-
nious way of communicating connections, the
supporting argument in some studies is only
suggestive (. . .).
This apparent lack of ambition to develop a true
contingency theory of management accounting
was noted before by Otley, who suggested that in
many studies:
. . .[t]he contingency approach is invoked, so it
seems, in order to cover up some of the
embarrassing ambiguities that exist in the
universalistic approach (Otley, 1980, p. 414).
Indeed, many of the papers that have appeared
since then still su?er from the defects at which
Otley was hinting. These two main conclusions
provide ample reason to be worried about the
current state of budgetary contingency research
for at least three reasons. First, the analysis only
included papers from high-quality accounting
journals. Second, the analysis referred to an area
of research considered to be of great importance
to the broad area of management accounting
research. Third, the analysis examined a research
methodology which has become typical for this
and related research ®elds. The dangers of the
impact and persistence of errors in MRA found
for the state of knowledge in this speci®c ®eld of
research are large given the lack of successful
replication studies here (cf. Lindsay & Ehrenberg,
1993), and the lack of large sample studies
(Lindsay, 1995).
The main implication for future research is that
major advancements in this ®eld can be made.
Regarding the technical failures in MRA, the
®ndings in this study provide strong support for
earlier pleas for the improvement of the methodo-
logical quality of management accounting
research (cf. Lindsay & Ehrenberg, 1993; Lindsay,
1995; Young, 1996). In itself, MRA is a method
that is well-regarded and well-described in the lit-
erature. Regarding the ¯aws that a?ect both MRA
and contingency theory, authors should strive for
better and more explicit articulations of con-
tingency hypotheses. Moreover, additional care is
required in linking the form of the theoretical
proposition with the format of the statistical test.
This could also mean an increased focus on other
than simply `interaction' types of contingency ®t
(see e.g. Venkatraman, 1989). Such more con-
sciously matched theories, hypotheses and tests
are the necessary ingredients to develop a `true'
contingency theory of management accounting (cf.
Chapman, 1997). Since it is the theory that dic-
tates the format of `contingency ®t', it should also
be theory that dictates the appropriate way of
testing `contingency ®t'.
Appendix A
Selected forms and types of contingency ®t
Appendix B
Overview of reviewed articles
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 309
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F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 313
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F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 315
doc_219803784.pdf
In the contingency literature on the behavioral and organizational eects of budgeting, use of the Moderated
Regression Analysis (MRA) technique is prevalent. This technique is used to test contingency hypotheses that predict
interaction eects between budgetary and contextual variables. This paper critically evaluates the application of this
technique in budgetary research over the last two decades. The results of the analysis indicate that the use and inter-
pretation of MRA often do not conform to proper methodology and theory. The paper further demonstrates that these
problems seriously aect the interpretability and conclusions of individual budgetary research papers, and may also
aect the budgetary research paradigm as a whole.
Mini-review
Testing contingency hypotheses in budgetary research: an
evaluation of the use of moderated regression analysis
$
Frank G.H. Hartmann
a
, Frank Moers
b,
*
a
Department of Financial Management, Faculty of Economics and Econometrics, University of Amsterdam,
Roetersstraat 11, 1018 WB Amsterdam, The Netherlands
b
Department of Accounting, Faculty of Economics and Business Administration, Maastricht University, P.O. Box 616, 6200 MD
Maastricht, The Netherlands
Abstract
In the contingency literature on the behavioral and organizational e?ects of budgeting, use of the Moderated
Regression Analysis (MRA) technique is prevalent. This technique is used to test contingency hypotheses that predict
interaction e?ects between budgetary and contextual variables. This paper critically evaluates the application of this
technique in budgetary research over the last two decades. The results of the analysis indicate that the use and inter-
pretation of MRA often do not conform to proper methodology and theory. The paper further demonstrates that these
problems seriously a?ect the interpretability and conclusions of individual budgetary research papers, and may also
a?ect the budgetary research paradigm as a whole. #1999 Elsevier Science Ltd. All rights reserved.
Keywords: Budgetary research; Reliance on accounting performance measures; Budgetary participation; Methodology; Moderated
regression analysis; Interaction.
1. Introduction
Over the last 40 years a research paradigm has
developed in the management accounting litera-
ture that focuses on the use of budgets in organi-
zations. An early study by Argyris (1952) provided
a ®rst attempt to describe the e?ects of using
budgets on the behavior of employees. Whereas
Argyris and other researchers in the 1950s and
1960s often studied budget-related issues following
a case-study methodology, later studies pre-
dominantly relied upon survey data. In the 1970s
two such survey studies on budgeting appeared
that have become particularly in¯uential. These
studies, by Hopwood (1972) and Otley (1978),
focused on the behavioral and attitudinal e?ects of
using budgetary information to evaluate the per-
formance of subordinate managers. Hopwood
(1972) found that a high reliance on budgetary
performance led to a high degree of stress, as well
as to dysfunctional managerial behavior. Believing
that Hopwood's results were likely contingent on
other organizational variables, Otley (1978)
designed a study that involved a research site
where it was expected that Hopwood's results
Accounting, Organizations and Society 24 (1999) 291±315
0361-3682/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved.
PII: S0361-3682(99)00002-1
* Corresponding author. Fax: +31-20-525-5285.
$
The authors gratefully acknowledge the comments made by
Ken Merchant, David Otley and two anonymous reviewers. This
paper has further bene®ted from presentations at Maastricht Uni-
versity, the 21st annual EAA meeting, the Fourth International
Management Control Systems Research Conference, the EIASM
workshop on New Directions in Management Accounting, and
the 1999 AAA Management Accounting Research Conference.
would not hold. Indeed, Otley obtained results
that were contrary to those of Hopwood. He did
not ®nd negative relationships between the use of
budgetary performance information and sub-
ordinates' attitudes and behaviors; instead he
found either no correlation or positive correla-
tions. The con¯icting results of these two studies
provided an important stimulus to other research-
ers to adopt contingency perspectives in studying
the e?ects of the formalized construct Reliance on
Accounting Performance Measures (RAPM). For
example, Brownell (1982a) expected that the dif-
ference in results could be explained by a construct
labeled Budget Participation that relates to sub-
ordinate managers' involvement in budget setting.
This variable had also received ample attention in
the literature during the sixties and the seventies
(cf. Shields & Shields, 1998). Generally, such con-
tingency studies have aimed to ®nd a match
between the use of budgets and the context in
which they are used. Together, they form a body
of literature which has attained a dominant posi-
tion in contemporary management accounting
research (cf. Chapman, 1997). Brownell and Dunk
(1991, p. 703) characterize the development of this
paradigm as:
The continuing stream of research devoted to
this issue constitutes, in our view, the only
organized critical mass of empirical work in
management accounting at present.
Over the last decade, several papers have pro-
vided overviews and evaluations of di?erent
aspects of this contingency literature on budgeting
(e.g. Briers & Hirst, 1990; Fisher, 1995; Hart-
mann, in press; Kren & Liao, 1988; Shields &
Shields, 1998). The purpose of the present paper is
to address and critically evaluate the statistical
method used in this literature to test contingency
hypotheses. It focuses on the use of Moderated
Regression Analysis (MRA), which has become
the dominant statistical technique in budgetary
research for testing contingency hypotheses. The
use of techniques such as MRA has received only
little attention in the overview papers mentioned.
Yet, such attention seems warranted for at least
two reasons. First, since the introduction of the
contingency theory paradigm in budgeting, statis-
tical techniques have become increasingly important
(cf. Briers & Hirst, 1990, p. 385). They not only
a?ect the design, execution and success of indivi-
dual studies, but also determine the paradigm's
overall success (cf. Lindsay, 1995). Second, atten-
tion to the MRA technique seems particularly
warranted given the complexity and speci®city of
the technique, and the problems associated with
its use (e.g. Arnold, 1982, 1984; Jaccard, Turrisi &
Wan, 1990). As will be shown in detail below,
budgetary papers often appear to neglect these
complexities, which causes ¯aws in the applica-
tion of MRA and in the interpretation of
results.
The remainder of the paper is structured as fol-
lows. Section 2 begins with a short explanation of
the concept of `®t' in contingency theory. It con-
tinues with an explanation of the basic properties
of MRA. Section 3 discusses the selection of bud-
getary research papers for analysis. Section 4
describes speci®c characteristics of MRA and pre-
sents the ®ndings of the analysis of the use of
MRA in the selected research papers. Finally,
Section 5 discusses the implications of the ®ndings
for both the current state and required future
developments of budgetary research.
2. Testing contingency theories of budgeting
Contingency theories of accounting are the
opposites of universal theories of accounting in
that they link the e?ects or the optimality of
accounting systems to the environment and con-
text in which these systems operate. In a summary
of early management accounting studies that used
contingency frameworks, Otley (1980) concluded
that much needed to be done in the development
of a contingency theory of accounting, and he
outlined some minimal requirements for such a
theory, stating that:
(. . .) a contingency theory must identify spe-
ci®c aspects of an accounting system which
are associated with certain de®ned circum-
stances and demonstrate an appropriate
matching (Otley, 1980, p. 413).
292 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
Three elements in this prescription are essential,
relating to: (1) the `speci®c aspects' (2) the `de®ned
circumstances'; and (3) the `appropriate match-
ing'. The ®rst element (i.e. speci®c aspects) points
to the demand for speci®city of the accounting
system variables in the formulation and test of
theories. The second element (i.e. de®ned circum-
stances) points to the conceptual di?erence
between a universal theory and a contingency
theory. The third and last element (i.e. appropriate
matching) forms the core of this paper, as it points
to the empirical di?erence between a universal
theory and a contingency theory. Otley (1980)
does not show how an `appropriate matching' is to
be de®ned theoretically, nor does he prescribe how
it is to be determined empirically. Such prescrip-
tions and illustrations can be found, however, in
the organizational literature, which has a larger
history in contingency methodology (cf. Chapman,
1997) and pays ample attention to the theoretical
and empirical aspects of determining the `appro-
priate matching'. In the remainder of this paper, this
`appropriate matching' element will be addressed
with the more common term `contingency ®t'.
An overview of the organizational literature
reveals several di?erent concepts of `contingency
®t' (see, e.g. Drazin & Van de Ven, 1985; Schoon-
hoven, 1981; Venkatraman, 1989). These concepts
of ®t are each associated with a di?erent theore-
tical interpretation, and each require a di?erent
statistical test. In this paper, the discussion is
restricted to a type of contingency ®t called the
interaction type of ®t, which is the dominant con-
ceptualization of contingency ®t in budgetary
research. The appropriate statistical technique to
test the interaction type of ®t is through Moder-
ated Regression Analysis (MRA), that will be
explained below. Appendix A brie¯y outlines sev-
eral other common types of ®t, stating both the
typical format of the underlying contingency
hypothesis and the appropriate statistical test.
2.1. Moderated Regression Analysis, the basic
format
Moderated Regression Analysis (MRA) is a
speci®c application of multiple linear regression
analysis, in which the regression equation contains
an `interaction term' (e.g. Champoux & Peters,
1987; Southwood, 1978). A typical equation for the
multiple regression of a dependent variable (Y) on
two independent variables (X
1
and X
2
) is presented
in Eq. (1):
Y ?
0
?
1
X
1
?
2
X
2
?" ?1?
In contrast, a typical regression equation used in
MRA has the format of Eq. (2):
Y ?
0
?
1
X
1
?
2
X
2
?
3
X
1
ÂX
2
?" ?2?
Eq. (2) di?ers from Eq. (1) by the inclusion of the
product of the two independent variables (X
1
 X
2
).
This product termis said to represent the moderating
e?ect of variable X
2
on the relationship between X
1
and Y. In contrast, the other terms in the equation
(X
1
and X
2
) are said to represent the main e?ects of
variables X
1
and X
2
on Y. The meaning of this pro-
duct term in establishing a moderating e?ect can be
illustrated by taking the partial derivative of Eq. (2)
with respect to X
1
?@Y=@X
1
?, which has the format
expressed by Eq. (3):
@Y=@X
1
?
1
?
3
X
2
?3?
As Eq. (3) illustrates, the term representing the
partial derivative (@Y=@X
1
) is a function of X
2
.
This means that the `form' of the relationship
between Y and X
1
is a function of X
2
, or in short,
that variable X
2
moderates the form of the rela-
tionship between X
1
and Y (cf. Champoux &
Peters, 1987, p. 244; Jaccard et al., 1990, p. 22). A
moderating e?ect can be graphically illustrated as
a variation in the slope of the regression line of Y
and X
1
as a function of X
2
. Fig. 1 below depicts a
situation in which the slope of the regression line
between X
1
and Y is more positive for higher
values of X
2
. This is expressed by stating that Y is
a function of the interaction between X
1
and X
2
.
Alternatively, it is said that the relationship
between Y and X
1
is contingent upon X
2
. To prove
the contingency hypothesis, therefore, one must
prove that X
2
in¯uences the relationship between
X
1
and Y, or that X
1
and X
2
interact to a?ect Y.
Although X
2
is considered the moderator in the
example above, a similar analysis applies if X
1
is
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 293
considered the moderator of the relationship
between X
2
and Y. Then, illustrated with Eq. (3a),
the partial derivative is taken with respect to X
2
?@Y=@X
2
?, and it follows that the relationship
between X
2
and Y is a function of X
1
.
@Y=@X
2
?
2
?
3
X
1
?3a?
For this reason, the moderating e?ect expressed
by the interaction term in Eq. (2) is called `sym-
metrical' (cf. Arnold, 1982; Southwood, 1978).
This implies that if X
2
moderates the relationship
between X
1
and Y, then X
1
necessarily also mod-
erates the relationship between X
2
and Y. It is
because of this symmetry that the neutral expres-
sion refers to an `interaction' of X
1
and X
2
to
a?ect Y. Whether an independent variable is
labeled as a moderator or an independent variable
is a matter of theory rather than statistics. A
moderator variable theoretically a?ects the rela-
tionship between the independent variable and the
dependent variable, but is not itself theoretically
related with either the dependent or independent
variables (e.g. Arnold, 1982, p. 154; 1984, p. 216;
Shields & Shields, 1998, p. 51). Typically, variables
are labeled moderators that are exogenous or
uncontrollable (e.g. Cohen & Cohen, 1983, p. 305).
Sharma, Durand, and Gur-Arie (1981) provide an
overview and taxonomy of moderator variables.
In empirical contingency research, MRA is used
to establish the existence of a statistically sig-
ni®cant interaction e?ect. A method to do so is
through hierarchical regression analysis (e.g.
Arnold & Evans, 1979; Cohen & Cohen, 1983;
Cronbach, 1987; Southwood, 1978). This method
requires running two regressions, one with the
main-e?ects-only [cf. Eq. (1)] and a second with
both main e?ects and the interaction term [cf. Eq.
(2)]. A signi®cant interaction e?ect is con®rmed by
the statistical signi®cance of the additional var-
iance explained by the inclusion of the interaction
term (i.e. the signi®cance of the increase in R
2
).
This method is equivalent to the simpler and more
direct assessment of the signi®cance of the t-value
associated with the coecient of the product term
(see Southwood, 1978, p. 1168; Arnold, 1982,
p. 157; Jaccard et al., 1990, p. 22). The equivalence
of these two methods is illustrated by Cohen and
Cohen (1983), who show that the F-statistic for the
increase in R
2
equals the square of the t-statistic for
the interaction term.
1
The equivalence of these two methods is illu-
strated by Cohen and Cohen (1983), who show
that the F-statistic for the increase in R
2
equals the
square of the t-statistic for the interaction term. In
the example used above, this means that a test for
a statistically signi®cant moderating e?ect of X
2
on the relationship between X
1
and Y implies a
test whether the coecient of the interaction term
?
3
? in Eq. (2) is statistically signi®cant. The sym-
metry applies here as well; a signi®cant t-value of
the coecient of the interaction term thus simul-
taneously implies a signi®cant moderating e?ect of
X
1
on the relationship between X
2
and Y.
Fig. 1. Moderating e?ect.
1
See, for example, Chenhall (1986) for a redundant test for
the signi®cance in incremental explanatory power after testing
for the signi®cance of the interaction term. Surprisingly, the F-
statistic of incremental explanatory power and the squared t-
statistic of the interaction in this study do not match (F equals
7.27, t-square equals 28.30). The only explanation seems to be a
calculation error.
294 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
The interaction in Eq. (2) above is commonly
called a two-way interaction, since the equation
contains two variables and their interaction.
Moreover, given that in the example (see Fig. 1)
the relationship between X
1
and Y is more positive
(or: less negative) for higher values of X
2
, it is
called a `positive interaction' between X
1
and X
2
. A
`negative interaction' signi®es that the relationship
between X
1
and Y is more negative (or: less positive)
for higher values of X
2
. Additionally, the interaction
can be either monotonic or non-monotonic. A mono-
tonic interaction exists when the partial derivative
does not `cross' the horizontal axis. This means that
the moderating e?ect of X
2
changes the slope of the
relationship between X
1
and Y within positive
values, or negative values, only (cf. Schoonhoven,
1981). Appendix A presents verbal examples of both
monotonic and non-monotonic interactions.
2.2. Moderated Regression Analysis with a dummy
variable
A special and often used form of MRA is
obtained when the moderator variable is a dummy
variable, taking on only discrete values (e.g. 0 and
1). If, for the example above, the moderator X
2
has only values of 0 and 1, the original equation
expressing the interaction e?ect between X
1
and
X
2
in Eq. (2), can be rewritten in the formats of
Eq. (2a) and Eq. (2b) below.
Y ?
0
?
1
X
1
?
2
X
2
?
3
X
1
ÂX
2
?" ?2?
Y ?
0
?
1
X
1
?" ?for X
2
? 0? ?2a?
Y ? ?
0
?
2
? ??
1
?
3
?X
1
?" ?for X
2
? 1?
?2b?
While this does not change the interpretation of
the coecient of the interaction term (
3
), the
decomposition illustrates that an analysis is done
for two subgroups. Therefore, the MRA with a
dummy variable is sometimes called `subgroup
regression analysis' (e.g. Stone & Hollenbeck,
1984) in which the `subgroups' are distinguished
based on extreme (e.g. high and low) values of the
moderator variable. Arnold (1984, pp. 219±221)
argues that the label `subgroup regression analy-
sis' may lead to the incorrect belief that this
method di?ers from general MRA. In fact, MRA
is always concerned with di?erent `subgroups',
however, introducing a dummy variable reduces
the number of `subgroups' to two. A graphical
example of MRA when the moderator variable is
a dummy variable is presented in Fig. 2.
Fig. 2 shows two regression lines, one for each
of the two values of X
2
. The ®gure illustrates a
positive interaction, which means that the coe-
cient (
3
) of the interaction term is positive. From
comparing Eqs. (2a) and (2b) above, it follows
that a positive and signi®cant coecient (
3
) sug-
gests that the slope of the regression line for the
`X
2
=1' subgroup is signi®cantly `more positive'
than the slope of the regression line for the `X
2
=0'
subgroup. It should be noted that the associated
label `positive interaction
0
is only meaningful if the
dummy values 0 and 1 re¯ect underlying values
(e.g. low and high) of the moderator variable.
However, MRA is also meaningfully applied if a
dummy does not re¯ect an underlying quantitative
variable, for example, if it re¯ects a natural dummy
Fig. 2. Interaction e?ect when the moderator is a dummy variable.
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 295
(e.g. male±female). Despite the prevalence of such
`natural dummies', subgroup regression analysis is
commonly performed based on a categorization of
the scores on an underlying continuous variable.
Such categorization has been argued to be unadvi-
sable, since it implies a loss of information (e.g.
Cohen & Cohen, 1983, p. 310; Pedhazur & Pedha-
zur-Schmelkin, 1991, p. 539), yet it has substantial
advantages relating to the understandability of the
MRA outcomes and the statistical power of the
MRA technique (Arnold, 1984, pp. 221±222).
These advantages are especially important when
the analysis incorporates interactions of a higher
order than the two-way interactions discussed so
far. Such higher-order interactions are discussed
further below.
3. Selection of the budgetary research papers
The budgetary research papers were selected for
analysis using four criteria. These were: (1)
research method; (2) publication date; (3) journal
of publication; and (4) subject of study. The ®rst
criterion aimed at the selection of papers that used
a survey methodology using questionnaires. The
second criterion resulted in papers published in the
period from 1980 to 1998. This period was chosen
because it lies after the in¯uential conceptual
paper of Otley (1980). The third criterion aimed at
selecting papers from high-quality accounting
journals. This criterion was applied to limit the
total number of papers, as well as to exclude
`lower journal quality' as a potential explanation
for the ®ndings. Based on an examination by
Brown and Huefner (1994) of the perceived qual-
ity of accounting journals among di?erent respon-
dents, papers were selected from The Accounting
Review, Journal of Accounting Research, and
Accounting, Organizations and Society.
2
Finally,
regarding the subject of study, papers were selected
that hypothesize and test contingency ®t concern-
ing budget-related variables, such as RAPM and
Budgetary Participation, using an `interaction'
concept of ®t. The application of these criteria
resulted in the selection of 28 papers. Table 1
shows the dispersion of the papers over the three
journals. Appendix B provides an overview of the
28 papers that meet the selection criteria.
4. Analysis of the budgetary research papers
This section analyzes the application and inter-
pretation of MRA in the 28 budgetary research
papers reviewed. In addition to the basic format of
MRA discussed above, here di?erent subsections
explain di?erent speci®c characteristics of MRA.
These speci®c characteristics relate to interaction
and (1) the strength of relationships; (2) the for-
mulation of hypotheses; (3) lower-order e?ects; (4)
multiple and higher-order interactions; (5) e?ect size;
and (6) (non-) monotonicity. Each subsection illus-
trates and discusses how these MRA characteristics
appear in the individual studies.
4.1. Interaction and the strength of relationships
In Section 2.2 above, a reference was made to
the `subgroup' method for illustrating the di?er-
ence in the slope of the regression line for two
subgroups. The literature uncovers another use of
subgroup analysis which tests for di?erences
between subgroups in the strength of the relation-
ships between the independent and dependent
variables (e.g. Champoux & Peters, 1987, p. 243;
Stone & Hollenbeck, 1984). Within the context of
the example, this `subgroup correlation analysis'
implies that a test is made for di?erences between
the correlation of X
1
and Y for extreme values of
2
The Journal of Accounting and Economics belongs to the
four journals with the highest perceived quality in the Brown
and Huefner (1994) study. It has not published, however, con-
tingency studies of budgeting.
Table 1
Dispersion of reviewed budgetary articles over journals
Journal (acronym used) Number of
articles
The Accounting Review (TAR) 5
Journal of Accounting Research (JAR) 6
Accounting, Organizations and Society (AOS) 17
Total 28
296 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
X
2
. The di?erence in substantive meaning of the
two kinds of analyses is graphically illustrated in
Fig. 3. In this ®gure, the shaded areas represent
the `clouds' of observations (scatter diagrams) of
the relationship between X and Y. A `wide' cloud
indicates a low correlation and a `narrow' cloud
indicates a high correlation. For each cloud the
appropriate regression lines are depicted as well.
Panel A of Fig. 3 shows no sign of interaction,
since both correlations and regression lines are
equal for the two subgroups. Panel B illustrates a
`form' interaction since the slope of the regression
line is di?erent for the two subgroups. No indica-
tion of interaction for `strength' exists, since X
appears to predict Y in both subgroups equally
well, evidenced by the absolute values of the corre-
lation coecients being equal. Panel C is the oppo-
site of panel B since there is no di?erence in slope,
but there is a di?erence in `strength'. This means
that in subgroup 1, X is a better predictor of Y than
in subgroup 2. Panel D shows a combination of
`form' and `strength' interactions, since both the
slope of the regression line and the correlation of X
and Y are di?erent for the two subgroups.
There has been some confusion in the literature
about whether contingency hypotheses re¯ect dif-
ferences in `form' or in `strength' (see, e.g. Arnold,
1982, 1984; Stone & Hollenbeck, 1984). The com-
mon understanding, however, now seems to be
that contingency hypotheses are of the form type
(panels B and D, Fig. 3), and it is even argued that
di?erences in strength are commonly meaningless
(Arnold, 1982, pp. 153±154; Schmidt & Hunter,
1978, p. 216). A problem, therefore, exists with
respect to the relationships hypothesized and tes-
ted in many budgetary studies. In 15 of the 28
papers used in this paper there is either no
hypothesis explicitly stated (Brownell & Dunk,
1991; Brownell & Hirst, 1986; Brownell & Mer-
chant, 1990) or it is stated in a null form predicting
that there is `no interaction' between the measured
variables (Brownell, 1982a, b, 1983, 1985; Chen-
hall, 1986; Dunk, 1989, 1990, 1993; Frucot &
Shearon, 1991; Harrison, 1992, 1993; Mia &
Chenhall, 1994). This raises the question about the
meaning of the word `interaction' in these cases, in
particular whether it relates to the strength of the
relationship or the form of the relationship. Since
these types of ®t are not equivalent for either the
theoretical interpretation or the statistical test,
null hypotheses are inadequate for describing the
speci®c contingency formulations and statistical
test to be used. Obviously, if an author states that
there is an `interaction' (e.g. Hirst & Lowy, 1990),
Fig. 3. Interaction as strength and as form.
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 297
this hypothesis has the same shortcomings as the
null hypothesis described above.
Despite the dominance of form interactions in
contingency research, budgetary researchers have
investigated hypotheses that seem to express
strength interactions. If there is a theory supporting
such relationships, the appropriate statistical ana-
lysis consists of calculating z-scores of the corre-
lation coecients. Since the interest is in the
di?erence in predictive power between subgroups,
it is important that the z-scores are calculated
using absolute values of the correlation coe-
cients. Obviously, their sign does not contain
information about predictive power. Merchant
(1981, 1984, 1990) and Govindarajan (1984) test
for di?erences in correlation coecients, but do
not calculate nor speci®cally mention the `abso-
lute' z-score.
4.2. Interaction and the formulation of hypotheses
The examples above point to a weak link
between the verbal and statistical format of
hypotheses, which has been noted and discussed
before by Schoonhoven (1981). She criticizes stud-
ies in the organizational literature for their lack
of clarity in stating contingency hypotheses, which
a?ects the obviousness of the statistical test to be
used. Above, a reference was made to Govindar-
ajan (1984), who tests a strength hypothesis. A
further problem with Govindarajan's (1984) analy-
sis relates to the substantive content of his con-
tingency hypothesis, which is incompatible with
his theoretical arguments.
3
His hypothesis predicts
that `organizational e?ectiveness' a?ects the
strength of the relationship between `environ-
mental uncertainty' and `evaluation style'. The
format of the statistical analysis is in conformity
with this hypothesis, since it compares the corre-
lation coecients for the two subgroups. The
subsequent interpretation of these results, how-
ever, is not. Govindarajan (1984, p. 133) concludes
that environmental uncertainty has a `signi®cant
moderating e?ect' on the relationship between
evaluation style and organizational e?ectiveness.
This is a peculiar interpretation since the subgroup
correlation analysis is based on high and low `e?ec-
tiveness' subgroups. This suggests that `e?ective-
ness' is the moderator instead of the theoretically
relevant moderator `environmental uncertainty'.
4
Overall, therefore, there is no match between the
theoretical arguments, the formulation of the
hypothesis, and the interpretation of the statistical
analysis of the hypothesis. Govindarajan's (1984)
conclusion about the moderating e?ect of `envir-
onmental uncertainty' is clearly unfounded.
In another six of the 28 papers (Merchant, 1981;
1984; Brownell, 1982b; Imoisili, 1989; Frucot &
Shearon, 1991; Dunk, 1992), obvious di?erences
exist between the hypothesis and the statistical test
used, which makes the conclusions by the authors
debatable.
5
Merchant (1981, 1984) hypothesizes
an interaction a?ecting the form of the relation-
ship, as shown by an example of the following
hypothesis:
Organizational performance tends to be
higher where there is a `®t' between the use of
budgeting and the situational factors, as
described in Hypotheses 1±4. (Merchant,
1984, p. 294; emphasis added.)
6
Recall from the previous section that the statis-
tical test used is a correlation per subgroup and
relates to the strength of the relationship. The results
of the analysis are therefore of little relevance and
value to the contingency hypothesis stated.
A second example of a di?erence between the
hypothetical and measured ®t are the papers of
3
Govindarajan's (1984) theoretical arguments indicate an
interaction of the form type. Govindarajan even speci®cally
proposes a non-monotonic relationship (see Fig. 1, p.128)
4
Note that labeling an independent variable the `moderator' in
MRA is a question of theory because of the symmetry mentioned
earlier. Yet, Govindarajan does not switch the moderator and the
independent variable, but switches the moderator and the depen-
dent variable. In this case, the symmetry does not apply.
5
The papers of Imoisili (1989) and Dunk (1992) will be dis-
cussed in Sections 4.4 and 4.5, respectively.
6
This hypothesis is the ®fth in Merchant's paper and refers
to hypotheses 1±4. In these hypotheses, Merchant applies the
selection type of ®t and uses correlation analysis. For example
hypothesis 4 states: ``Larger, more diverse departments tend to
place greater emphasis on formal budgeting.''
298 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
Brownell (1982b) and Frucot and Shearon (1991,
p. 85). Frucot and Shearon (1991) state a null
hypothesis in the following form:
In Mexico, locus of control does not have,
through an interaction e?ect with budget-
ary participation, a signi®cant e?ect on
performance.
Subsequently the following equation is statistically
tested:
Y ?
0
?
1
X
1
?
2
X
2
?
3
X
1
ÀX
2
?" ?4?
This equation does not, however, measure ®t as
interaction but ®t as matching (Venkatraman,
1989, p. 431). Because ®t as interaction (i.e. form)
is hypothesized, the verbal statement and statis-
tical measure are not compatible.
7
Given this
incompatibility, the conclusion cannot be inter-
preted and the statistical results become explora-
tory at best. The reason the authors give for using
the matching variable is that:
(. . .) the multiplicative interaction term does
not provide a good measure of this matching
condition'' (Frucot & Shearon, 1991, p. 90).
Although this is true, the hypothesis expresses `®t'
as interaction and simply does not predict the
matching condition. Frucot and Shearon (1991,
p. 90) also state that the variable should be mea-
sured by the absolute di?erence, arguing that this
better re¯ects the relationship among the three vari-
ables. If so, the hypothesis should have been altered
to state the matching condition, and the alternative
and only proper formulation would have been:
8
In Mexico, given the value of locus of con-
trol, there is a unique value of budgetary par-
ticipation that produces the highest value of
performance; deviations from this relationship
in either direction reduce the value of perfor-
mance. (cf. Schoonhoven, 1981).
9
4.3. Interaction and lower-order e?ects
As illustrated above, the equation representing
an interaction e?ect [Eq. (2)] includes not only
the interaction term (X
1
 X
2
), but also the two
main e?ects (X
1
) and (X
2
). At least three topics
related to the inclusion of lower-order e?ects
warrant discussion. These are (1) the reason for
including lower-order e?ects; (2) the interpreta-
tion of the coecients for lower-order e?ects
found in the regression analysis; and (3) the
potential problem of multicollinearity. First, the
reason for the inclusion of lower-order e?ects in
MRA is to prevent conclusions of the existence of
an interaction e?ect when such an e?ect is solely
due to lower-order e?ects. An example is found
with Hirst (1983) who tests a model represented
by Eq. (5) below that does not include main
e?ects:
Y ?
0
?
1
X
1
ÂX
2
?" ?5?
In this case, ®nding a signi®cant coecient
1
does
not necessarily indicate the existence of an inter-
action e?ect, since it could be due to a signi®cant
relationship between X
1
and Y regardless of X
2
. In
other words, because the interaction term is the
product of the two main e?ects, it is likely to `steal
variance' from its constituting parts (cf. Cohen &
Cohen, 1983, p. 305). Stone and Hollenbeck (1984,
p. 201) argue in this respect:
(. . .) while the cross-product term in a
regression equation ``carries'' the interaction,
the same cross-product term is not the inter-
action.
This implies that when testing for an interaction
e?ect, the lower-order e?ects should be `partialed
out' by including them in the regression equation
(Southwood, 1978, p. 1164; Cohen & Cohen,
7
The authors also state that the relationship is `accentuated'
and `attenuated' (p. 85). This refers to accelerating and decel-
erating e?ects and thus to the form of the relationship.
8
The same line of reasoning applies to Brownell (1982b).
9
For a discussion of the use of di?erence scores, see
Bedeian, Day, Edwards, Tisak, and Smith (1994).
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 299
1983, p. 348; Stone & Hollenbeck, 1984, p. 201).
Consequently, Hirst's (1983) conclusion based on
the results of Eq. (5) is unfounded.
10
A second issue relates to the proper interpreta-
tion of coecients obtained for lower-order e?ects
in MRA. Southwood (1978, p. 1168) argues that
such coecients generally have no theoretical
meaning. The reason is that in the behavioral sci-
ences the variables are usually measured using
interval scales, and not ratio scales. This means
that scale origins and thus linear transformations
of variable scores are arbitrary, and have no sub-
stantive meaning. Southwood (1978, p. 1668, pp.
1198±1201) shows that such linear transforma-
tions do change the coecient of the lower-order
e?ects in the MRA equations, and therefore, these
coecients cannot be easily interpreted. This does
not imply that the coecients of the lower-order
e?ects in an interaction model are lacking all
meaning. In particular, they signify the main e?ect
of the variable (e.g. X
1
) when the value of the
other variable (X
2
) is zero (Jaccard et al., 1990).
Only for ratio scale variables is this zero `mean-
ingful' (Southwood, 1978, p. 1165). For interval
scale variables, the zero value obtains a speci®c
meaning if the variables are `centered' around
their respective means. In this case, the coecients
of the main e?ects represent the e?ect of one
variable at the (sample) average of the other (Jac-
card et al., 1990, p. 34). Despite this meaning, it is
important to point out that the coecients
obtained for the main e?ects when applying MRA
are, in general, di?erent from those that would be
obtained through a regression model without the
interaction term. Furthermore, it is important to
note that linear transformations do not change the
coecient of the interaction term, nor its t-statistic
and level of signi®cance (Cohen & Cohen, 1983,
pp. 305±306; Southwood, 1978, p. 1168). Thus,
Brownell (1982a), Chenhall (1986) and Mia (1988)
are wrong in assuming that `centering' the vari-
ables provides a:
clearer basis for predicting the sign of (. . .) the
coecient of the interaction term (Brownell,
1982a, p. 20; emphasis added).
Since the coecient of the interaction term is not
sensitive to the scale origins, it also follows that for
tests of an interaction e?ect using MRA the inde-
pendent variables need not be ratio±scaled (South-
wood, 1978, p. 1167; Arnold & Evans, 1979).
The analysis of the budgetary papers shows that
the interpretation of lower-order e?ects is subject
to both Type-I and Type-II errors; interpretation
of invalid lower-order e?ects and no interpretation
of valid lower-order e?ects. First, ®ve papers show
an invalid interpretation of main e?ects in two-way
interactions (Brownell, 1982a, 1983, 1985; Chen-
hall, 1986; Mia, 1989). For example, Brownell
(1982a) studies (among others) the moderating
e?ect of Budget Emphasis on the relationship
between Budgetary Participation and Performance.
He interprets the interaction e?ect, and both main
e?ects [see Eq. (2)]. The Budgetary Participation
variable in the MRA equation is measured as a
`deviation score' from the overall mean (i.e. cen-
tered). A linear transformation of the raw score of
one independent variable leads to a change in the
regression coecient of the other independent
variable. This implies that the coecient of the
main e?ect of Budget Emphasis changes. As a
result, the coecient of Budget Emphasis illustrates
10
Hirst (1983, p. 600) claims to have found an interaction
e?ect of the form-type based on subgroup regression-analysis.
Since the regression coecients are standardized, and since
standardized regression coecients in simple linear regression
equals correlation coecients, the subgroup analysis is in fact
subgroup correlation-analysis. This latter statistical format,
however, tests strength and not form, so that Hirst's ®ndings
seem unfounded. However, in this speci®c case additional
information suggests the existence of a form interaction for one
of the two dependent variables (job-related tension). The corre-
lation coecients between RAPM and job-related tension for
low and high task uncertainty are À0.33 and 0.53 respectively.
Both coecients are statistically signi®cant, which means that
the regression coecients per subgroup are also signi®cant. As a
result, there will be a signi®cant negative coecient for the low
task uncertainty subgroup and a signi®cant positive coecient
for the high task uncertainty subgroup. Since signi®cant means
signi®cantly di?erent from zero, a positive (negative) signi®cant
coecient is also signi®cantly di?erent from any negative (posi-
tive) coecient. Thus, the di?erence between these two regres-
sion coecients is also signi®cant. The signi®cance of this
di?erence is equal to the signi®cance of the interaction term in
MRA and the ®t as interaction (form) is supported. Note that
Hirst's (1983) paper, as it is published, thus does not prove a ®t
as interaction (form); the above analysis does.
300 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
the e?ect of Budget Emphasis on Performance at
the average level of Budgetary Participation.
11
This
interpretation di?ers from Brownell's (1982a, pp.
20±21) who incorrectly interprets the regression
coecient unconditional on Budgetary Participation.
Further, the Budget Emphasis variable is not centered
around its mean, which makes the coecient of
Budgetary Participation uninterpretable. Brow-
nell's conclusion regarding Budgetary Participa-
tion is therefore unfounded.
12
In studies using
higher-order interactions, similar problems are
found (e.g. Brownell & Hirst, 1986; Imoisili,
1989). These studies are discussed below in the
section on higher-order interactions.
The above ®ve studies precede the introduction
of the Southwood (1978) paper into the manage-
ment accounting research literature.
13
The more
recent and uncritical use of Southwood's paper,
however, has led to the reverse situation; no
interpretation of valid lower-order e?ects. Exam-
ples include the following. Mia and Chenhall
(1994) study the moderating e?ect of Function on
the relationship between the Use of Broad Scope
MAS and Managerial Performance. The MAS
variable is a `di?erence score' from the overall
mean (i.e. centered). This means that the coe-
cient of the main e?ect of Function is interpretable.
The authors refer to Southwood and state:
No attempt was made to interpret the coef-
®cients (. . .) that related to extent of use of
broad scope Management Accounting System
(MAS) information or function. (p. 9; empha-
sis added.)
Thus, they incorrectly state that the coecient of
Function cannot be interpreted and therefore lose
information. Using this information would have
allowed the supplementary conclusion that Func-
tion by itself has a direct in¯uence on managerial
performance, in that marketing managers perform
better than production managers at the `average'
MAS. In Lau, Low and Eggleton (1995) all inde-
pendent variables are centered. This means that
the lower-order e?ects in their interaction models
could have been interpreted. The authors, how-
ever, refer to Southwood and reject the inter-
pretation of lower-order e?ects (p. 369).
Although, the papers of Mia and Chenhall (1994)
and Lau et al. (1995) are the only concrete and
explicit examples of a Type-II error, seven other
studies speci®cally refer to Southwood and a
priori reject the interpretation of lower-order
e?ects (Brownell & Dunk, 1991; Dunk, 1990,
1992, 1993; Harrison, 1992, 1993; Gul & Chia,
1994). The conclusion seems warranted that
researchers are unaware of the possibilities and
problems of interpreting lower-order e?ects in
MRA. In a way, Southwood's paper has had both
a positive and a negative e?ect on this. The posi-
tive e?ect is that main e?ects indeed cannot
usually be interpreted, while the negative e?ect has
been that it is believed that they should never be
interpreted in MRA. Unfortunately, this false idea
even shows up in handbooks aimed at novice
management accounting researchers (Brownell,
1995). Here it says that:
It is now widely understood that the esti-
mated coecients for variables, included in
an equation along with their cross product
with another variable, are not interpretable.
(Brownell, 1995, p. 55; emphasis added.)
It also says that Southwood has shown that if a
constant is added to interval scale data that:
(. . .) this will alter the estimated coecient for
the variable to which the constant was added
(p. 55; emphasis added).
This is, of course, incorrect. The coecient of the
variable to which the constant is not added, chan-
ges. The `easy' reference to papers like South-
wood's, without critically evaluating its wisdom, is
remarkable at least.
11
More speci®cally, the results show that at the average
level of Budgetary Participation, lower Budget Emphasis leads
to increased Performance.
12
Brownell concludes that higher Budgetary Participation is
associated with higher Performance.
13
Schoonhoven (1981) explicitly incorporates several main
e?ects in her multiple interaction equation and incorrectly
interprets them all. This is peculiar since Southwood (1978) is
among her references.
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 301
The third and ®nal point related to lower-order
e?ects in MRA is the potential problem of multi-
collinearity, caused by the fact that the lower-
order e?ects (e.g. X
1
and X
2
) and their product are
likely to be correlated (e.g. Drazin & Van de Ven,
1985). Yet, from the same arguments that show
the insensitivity of the coecient of the interaction
term in MRA (X
1
 X
2
) to changes in scale origins
of X
1
and X
2
, it follows that multicollinearity is
not a problem when applying MRA (cf. Dunlap &
Kemery, 1987). In particular, it is possible to use
linear transformations of X
1
and X
2
that remove
the correlation between the main terms and the
interaction term (Southwood, 1978, p. 1167; Jac-
card et al., 1990, p. 22). The `correct' linear trans-
formation of variable scores to minimize the
correlation between the independent variables and
their product is the centering procedure discussed
before (e.g. Jaccard et al., 1990, p. 34). Recall that
since no such linear transformation ever a?ects the
coecient of the interaction term, the coecient
of the interaction term is always interpretable, and
centering is not required. As was illustrated, this is
not always recognized in budgetary studies
(Brownell, 1982a, 1983; Chenhall, 1986; Mia,
1988, 1989; Lau et al., 1995). As an example, Lau et
al. (1995) use deviation scores from the mean
because, as they state, it reduces the `problem' of
multicollinearity (p. 368). However, no such problem
exists.
14
4.4. Multiple and higher-order interactions
The previous sections discussed the general for-
mat of MRA and focused on the analysis of a
single two-way interaction. MRA, however, is not
restricted to the analysis of a single two-way
interaction. It can also be used to analyze (1)
multiple two-way interactions, and (2) any n-way
interaction. First, multiple two-way interactions
can be tested by extending Eq. (2) to include an
additional main and interaction e?ect, as shown
by the example of Eq. (6a):
Y ?
0
?
1
X
1
?
2
X
2
?
3
X
3
?
4
X
1
ÂX
2
?
5
X
1
ÂX
3
?"
?6a?
As for any equation, the inclusion of an additional
two-way interaction in MRA should be based on
theory (Jaccard et al., 1990, p.40±41). More speci-
®cally, the theory should state that the relation-
ship between X
1
and Y is not only a function of
X
2
, but also of X
3
. In other words,
@Y=@X
1
?
1
?
4
X
2
?
5
X
3
?6b?
Imoisili (1989, p. 327) exactly hypothesizes the
relationship depicted by Eqs. (6a) and (6b). How-
ever, this hypothesis is incorrectly tested, since the
equation analyzed also includes a redundant two-
way interaction term X
2
 X
3
, and a redundant
three-way interaction term X
1
 X
2
 X
3
. The
result of analyzing this equation does not provide
an answer to the hypothesis, since the partial deri-
vative ?@Y=@X
1
? of the function that Imoisili uses is
given by Eq. (7), which contains an `interaction
e?ect' ?X
2
 X
3
? not hypothesized.
@Y=@X
1
?
1
?
4
X
2
?
5
X
3
?
7
X
2
ÂX
3
?7?
The only correct statistical test would have been
Eq. (6a). Harrison (1992, 1993) provides an
example of similar problems. Harrison (1992) uses
Eq. (8) to test for the existence of two-way inter-
actions between Budgetary Participation (X
1
),
RAPM (X
2
), and the dummy variable Nation (X
3
)
to a?ect Job-Related Tension (Y):
Y ?
0
?
1
X
1
?
2
X
2
?
3
X
3
?
4
X
1
ÂX
2
?
5
X
1
ÂX
3
?
6
X
2
ÂX
3
?"
?8?
Harrison (1992, p. 11) is only interested in the
moderating e?ect of X
1
on the relationship
between X
2
and Y, and his analysis is therefore
¯awed for two reasons.
15
First, there is no theore-
tical foundation for using the multiple interaction
equation. Only the ®rst interaction (X
1
 X
2
) is
hypothesized by Harrison, both other interactions
14
The only `problem' that multicollinearity can cause is that
the statistical program is unable to calculate the regression
coecients due to singularity of the matrix.
15
The same conclusion can be made with respect to Imoisili
(1989).
302 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
(X
2
 X
3
and X
1
 X
3
) are not.
16
Second, this
equation has a chance of being overspeci®ed,
which means that extra predictor variables are
unnecessarily included. Overspeci®cation of the
model leads to an increased standard error of the
regression coecients (Cryer & Miller, 1991,
p. 639), in¯uencing the signi®cance test of the
coecient. Harrison states that:
4
, as the (highest order) interaction term, is
both stable and interpretable for its standard
error and signi®cance test. (Harrison, 1992,
p. 11; emphasis added.)
Although the interaction term, standard error
and signi®cance test may be stable, they are hardly
interpretable if the model is a?ected by an unne-
cessary overspeci®cation. A standard error in¯u-
enced by overspeci®cation is not interpretable, no
matter how stable it is. In this case, therefore, the
signi®cance of coecient
4
is not interpretable.
Moreover, the partial derivative of this equation
?@Y=@X
2
? is:
@Y=@X
2
?
2
?
4
X
1
?
5
X
3
?9?
This reveals that the relationship between X
2
and Y
is not a linear function of X
1
, but a linear function
of both X
1
and X
3
. As a result, the hypothesis
remains unanswered because the coecient
4
is
not a measure of the hypothesized moderating
e?ect of X
1
on the relationship between X
2
and Y.
17
Apart from the use of multiple two-way inter-
actions, MRA can be used to analyze n-way
interactions. As an example of higher-order inter-
actions, a three-way interaction generally has the
format of Eq. (10):
Y ?
0
?
1
X
1
?
2
X
2
?
3
X
3
?
4
X
1
ÂX
2
?
5
X
1
ÂX
3
?
6
X
2
ÂX
3
?
7
X
1
ÂX
2
ÂX
3
?"
?10?
In conformity with the interpretation of the pro-
duct term for two-way interactions, the product
term ?X
1
 X
2
 X
3
? in Eq. (10) represents the
three-way interaction among the (three) indepen-
dent variables. The issues discussed above regard-
ing use and interpretation of MRA for two-way
interactions are also important for three-way
interactions. Regarding the inclusion of main
e?ects in MRA, for a three-way interaction equa-
tion, all two-way interactions should be included,
and the user should observe that the coecients
obtained for these two-way interactions are not
directly interpretable (Cohen & Cohen, 1983,
p. 348).
18,19
In general, for an n-way interaction,
the main e?ects and all possible interactions of a
lower-than-n order should be included. The di?er-
ence between two-way and higher-order interactions
16
Harrison (1992) refers to both Schoonhoven (1981) and
Jaccard et al. (1990) for using the multiple interaction equation.
Schoonhoven's statistical analysis is incorrect, and referring to
her analysis may have caused the incorporation of similar
shortcomings. The reference to Jaccard et al. (1990, pp. 40±41)
is intriguing, since here the importance of theory when using
multiple interactions is stressed. Harrison seems to selectively
use this passage to only eliminate the theoretically irrelevant
three-way interaction (1992, p. 11), while leaving two theoreti-
cally irrelevant two-way interactions.
17
The same line of reasoning applies to Harrison (1993).
18
Once again, `not interpretable' means that the coecients
found in the interaction model are not the same as those found
in the main-e?ects-only model. Although the main e?ects are
not interpretable in a three-way interaction equation, the two-
way interactions are if the variables are centered. The inter-
pretation is in conformity with the interpretation stated in pre-
vious sections, i.e.
4
is the interaction e?ect X
1
 X
2
on Y at
the (sample) average of X
3
.
19
Brownell and Hirst (1986) use a three-way interaction
equation and interpret a main e?ect [Participation (P)], a two-
way interaction [PÂBudget Emphasis (B)], and the three-way
interaction [PÂBÂTask Uncertainty (T)]. The authors assume
that every variable in the equation is interpretable. However, as
was shown before, the coecients of the main e?ects in a three-
way interaction are normally not interpretable. Because only
variable P is centered, only the two-way interaction without
component P can be interpreted. This means that only the
interaction of B Â T can be interpreted. Brownell and Hirst (1986)
on the other hand, interpret the coecient of P Â B, which is
statistically incorrect. Conclusion of the regression results
should only have been based on the two-way interaction B Â T
and the three-way interaction (P Â B Â T). More problematic
even is the analysis of Imoisili (1989, p. 330). Imoisili examines
two-way interactions and uses a three-way interaction equation
[see Eq. (10) above], where Y=a.o. Performance; X
1
=Budget
style; X
2
=Task Interdependence; and X
3
=Task Uncertainty.
The author is interested in the coecients
4
and
5
. Their
interpretation is hindered because of, among others, the use of
raw scores instead of centred variables. The results therefore do
not provide support for, nor allow rejection, of the hypothesis.
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 303
therefore does not lie in its mathematics or statis-
tics, but in the interpretation of its meaning. Cohen
and Cohen (1983, p. 306) note in this respect:
The fact that the mathematics can rigorously
support the analysis of interactions of high
order, however, does not mean that they
should necessarily be constructed and used:
interactions greater than three-way are most
dicult to conceptualize, not likely to exist,
and are costly in statistical inference (. . .)
However, even for a three-way interaction the
problems noted by Cohen and Cohen (1983) exist.
First, Schmidt and Hunter (1978) and Champoux
and Peters (1987), for example, note that the sam-
ple sizes typical in (organizational) research lack
the power to ®nd the hypothesized interactions of
a high-order. Budgetary studies are no exception,
with sample sizes often far below 100 (cf. Young,
1996). Second, the diculty of conceptualizing
three-way interactions becomes clear if one con-
siders that a three-way interaction means that a
two-way interaction is a function of a third vari-
able. In terms of Eq. (10), this means that a sig-
ni®cant coecient of the three-way interaction
term (
7
) indicates that the interaction e?ect of X
1
and X
2
on Y is a function of X
3
. However, because
of the symmetry mentioned earlier, a three-way
interaction therefore simultaneously expresses:
(a) the moderating e?ect of X
3
on the X
1
 X
2
interaction a?ecting Y;
(b) the moderating e?ect of X
2
on the X
1
 X
3
interaction a?ecting Y; and,
(c) the moderating e?ect of X
1
on the X
2
 X
3
interaction a?ecting Y.
The complexity is evident if it is further con-
sidered that (a) implies that X
3
is `moderating the
moderating e?ect' that X
2
has on the relationship
between X
1
and Y, and that also here the sym-
metry applies that was mentioned earlier. Because
of the complexity, it seems even more important
here that theory should dictate which variables are
labeled the moderators.
A three-way interaction is graphically illustrated
in Fig. 4, which depicts a three-way interaction for
one continuous and two dichotomous independent
variables. Panel A and B both show a two-way
interaction, and illustrate how the relationship
between X
1
and Y is di?erent for high and low
values of X
2
. Panel A shows the two-way interac-
tion for low values of X
3
. Panel B shows the two-
way interaction for high values of X
3
. The three-
way interaction signi®es the di?erence between the
two changes in slope for high and low values of
X
3
. A signi®cant three-way interaction does not
indicate that a two-way interaction is signi®cant
for some values of X
3
, and not for others. Indeed,
a three-way interaction can be signi®cant, both
when the `underlying' two-way interactions are
signi®cant, and when they are not.
20
Note that
here and in many (graphical) examples in this
paper, the analysis is simpli®ed by using dichoto-
mic variables. For three continuous variables, the
graphical depiction and explanation of three-way
interactions are far more complex. In sum, Cohen
and Cohen (1983, pp. 347±348) therefore advocate
a restricted use of higher-order interactions, and
state:
No interaction set should be included in the
IV's (independent variables) unless it is ser-
iously entertained on substantive grounds
(. . .). This requires as a minimum condition
that it be understood by the investigator and
on practical grounds that it can be clearly
explicable to his audience.
Of the 28 papers analyzed, six papers speci®-
cally study three-way interactions (Brownell &
Dunk, 1991; Brownell & Hirst, 1986; Dunk, 1993;
Gul & Chia, 1994; Harrison, 1993; Lau et al.,
1995). Three of these six papers decompose the
three-way interaction into two-way interactions
(Brownell & Dunk, 1991, pp. 700±701; Brownell &
Hirst, 1986, pp. 247±248; Lau et al., 1995, p. 372).
In this way the authors can ascertain that the sig-
ni®cant three-way interaction is indeed a `real'
20
Thus, a signi®cant universal relationship may exist
between the independent and dependent variables, while the
three-way interaction is also signi®cant. An example of (hypo-
thetical) data that exhibit this relationship is available from the
authors upon request.
304 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
relationship and not fallacious.
21
As stated before,
a signi®cant three-way interaction does not con-
tain any information about the signi®cance of the
underlying two-way interactions. To establish the
latter, the additional analysis is required.
22
The
other three papers mentioned (Dunk, 1993; Gul &
Chia, 1994; Harrison, 1993) do not check the sig-
ni®cance of the two-way interaction e?ects under-
lying the three-way interactions found. Solely
based on the signi®cance of the three-way interac-
tion, the authors draw conclusions with respect to
the underlying relationship at the level of two-way
interactions (Dunk, 1993, p. 407; Harrison, 1993,
p. 333) and even at the level of main e?ects (Gul &
Chia, 1994, p. 422), Gul &Chia (1994), for example,
measure the three-way interaction of Management
Accounting System Scope, Perceived Environmental
Uncertainty and Decentralization on Managerial
Performance. They use the partial derivative of the
three-way interaction Eq. (10) to analyze two-way
interactions and main e?ects. The result of their
analysis is theoretically uninterpretable, since they
do not establish whether two-way interactions
exist at all. The same conclusion holds for the
papers of Dunk (1993) and Harrison (1993).
It seems clear that Cohen and Cohen's (1983)
warning concerning higher-order interactions is
not heard in the budgetary research paradigm. A
reviewer of Gul and Chia's paper suggested the use
of a four-way interaction (1994, footnote 10). It is
easy to consider the problems and complexities
associated with this format.
4.5. Interaction, e?ect size, and the Johnson±
Neyman technique
A further issue related to the interpretation of
the outcomes of MRA is that a (signi®cant) coef-
®cient of the interaction only contains information
about changes in the relationship between vari-
ables, and does not contain information about the
optimal value of the dependent variable (i.e. e?ect
size, see Champoux & Peters, 1987). This is illu-
strated in Fig. 5. In panel A, Y has the highest
(lowest) value when both X
1
and X
2
are high (low).
In contrast, in panel B, Y has the highest (lowest)
value when X
1
is high (low) and X
2
is low (high).
Note that in both cases the interactions (X
1
 X
2
)
are equal with respect to both direction and size.
This means that in both cases, an increase in the
value of X
2
has an equal positive e?ect on the
form of the relationship between X
1
and Y. The
di?erence between the cases is due to a main e?ect
of the moderating variable on the dependent vari-
able (cf. Kren & Kerr, 1993). The proper inter-
pretation of a positive interaction therefore is not
that Y achieves the highest values for the highest
values of X
1
and X
2
, but that for higher values of
X
1
; X
2
has a more positive e?ect on Y. Hence,
MRA cannot be used to test expectations about
Fig. 4. Three-way interactions for two dichotomous moderators.
21
Lau et al. (1995) provide a clear example of such a
decomposition. A ¯aw in their analysis, however, is that they
de®ne a null hypothesis and alternative hypotheses (pp. 363±
364), which are not mutually exclusive. This means that the
statistical results could have supported both the null hypothesis
and the alternative hypotheses.
22
Brownell and Dunk (1991) do the additional analysis to
con®rm the expected form and sign of the two-way interactions
(p. 701). Finding a signi®cant three-way interaction does not
warrant such speci®c expectations.
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 305
the values of X
1
and X
2
for which Y will have the
highest value. This is the consequence of MRA
testing the signi®cance of the interaction e?ect,
and not testing for a combined e?ect of the main
e?ects and the interaction e?ect on the dependent
variable.
The di?erence between a signi®cant interaction
and e?ect size is not always recognized in the
papers examined. For example, Dunk (1992)
hypothesizes that:
(. . .) the higher (lower) the level of manu-
facturing process automation and the higher
(lower) the reliance on budgetary control, the
higher will be production subunit perfor-
mance (p. 198; emphasis added).
This hypothesis states that high/high and low/low
combinations of the independent variables max-
imize the dependent variable. Dunk (1992) uses
MRA to test this hypothesis and thus incorrectly
assumes that the signi®cant interaction contains
information about e?ect size. Further, Brownell
(1983), Brownell and Hirst (1986), Mia (1989),
Dunk (1989, 1990, 1993) and Brownell and Dunk
(1991) also assume that a signi®cant interaction
means that a certain combination of variables
maximizes the dependent variable. For example,
Dunk (1993) states the following about the sig-
ni®cance of the coecient of the three-way inter-
action term (b
7
):
As b-(. . .) is signi®cant and negative, it
appears that slack is low when participation,
information asymmetry, and budget emphasis
are all high (pp. 405±406; emphasis added).
Such a statement is not only incorrect, the ques-
tion of the `highest Y' is likely to be irrelevant in
testing contingency models, especially when the
main e?ects are due to uncontrollable, exogenous
contingency factors.
Two papers apply a formal analysis of e?ect
sizes by using the so-called Johnson±Neyman
technique (Brownell, 1982a; Lau et al., 1995). This
technique can be used to ®nd the `region of sig-
ni®cance' for the di?erence between the e?ects of
di?erent values of the moderator at a given value
of the independent variable (Pedhazur & Pedha-
zur-Schmelkin, 1991). In other words, the techni-
que provides a measure to establish whether the
e?ect of the moderator is `large enough' to lead to
signi®cant di?erent values of the dependent vari-
able. The Johnson±Neyman technique can be illu-
strated more clearly by returning to Fig. 5. The
question is whether for a given value of X
1
, there
is a signi®cant di?erence between the value of Y
for subgroup 1 and 2 (i.e. for X
2
=low and
X
2
=high). In panel A, the `region of signi®cance'
will relate to higher values of X
1
, since the di?er-
ence between the two regression lines increases
with increases in X
1
. In panel B, on the other
hand, the `region of signi®cance' will relate to
lower values of X
1
. Despite this di?erence in
`region of signi®cance', the interactions are equal
with respect to both direction and size, as stated
before. The use of the Johnson±Neyman technique
in MRA is therefore questionable, since it plays no
Fig. 5. Interaction contains no information on value independent variable.
306 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
role in the test of hypotheses of the interaction
format. Since the interaction contains no infor-
mation on e?ect sizes (i.e. values of the dependent
variable), the results of this technique are of no
relevance to the interpretation of the interaction
e?ect. The formula used to ®nd the `region of sig-
ni®cance' is not only determined by the moderating
e?ect (i.e. e?ect on slope) of the contingency vari-
able, but also by its e?ect on the intercept. The
region of signi®cance could be very large even if the
interaction e?ect is very small and insigni®cant,
because of a large di?erence in the intercept (and
vice versa). Further, looking at Eqs. (2a) and (2b),
one sees that the di?erence between intercepts is
in¯uenced by the `main e?ect of the moderator' (cf.
Kren & Kerr, 1993). As a result, the Johnson±Ney-
man technique mixes main e?ects and moderating
e?ects, and thus seems of little value to explore the
nature of the interaction e?ect alone, as stated and
done by Brownell (1982a) and Lau et al. (1995).
4.6. Interaction and (non-)monotonicity
Both in formulating and in testing contingency
hypotheses of the interaction format, it is impor-
tant to consider the (non-)monotonicity of the
hypothesized relationship. A statistically sig-
ni®cant coecient of the interaction term does not
contain information about whether the relation-
ship found is monotonic or non-monotonic, nor
does contingency theory have an a priori `pre-
ference' for monotonic or non-monotonic rela-
tionships. Since, however, the substantive
implications are di?erent for monotonic and non-
monotonic relationships, studies should explicitly
state whether the aim is to investigate and test
(non-)monotonicity.
23,24
Six of the 28 papers use
the method of the partial derivative to analyze
the (non-)monotonicity of relationships found
(Govindarajan & Gupta, 1985; Gul & Chia, 1994;
Harrison, 1993; Lau et al., 1995
25
; Mia, 1988,
1989). For example, Govindarajan and Gupta
(1985) measure the partial derivative of two two-
way interactions and provide graphs of these
equations. The resulting two graphs are examples
of an almost perfect non-monotonic relationship
in which the line crosses the X-axis near zero. The
conclusion is that for one extreme value of the mod-
erator (i.e. Strategy) the organization will be e?ective
if, here, accounting information is used in perfor-
mance evaluation, while being ine?ective for the
other extreme value of the moderator. Harrison
(1993) and Gul and Chia (1994) both measure the
partial derivative of the three-way interaction Eq.
(10). However, as the above analysis shows that their
results are uninterpretable because of a misspeci®ed
model, the conclusions about non-monotonicity are
invalid as well.
The graph of the partial derivative is one test for
non-monotonic e?ects but non-monotonicity can
also be measured by a regression per subgroup.
Four of the 28 papers use subgroup regression
analysis and all indicate that a non-monotonic
relationship exists (Brownell, 1983, 1985; Brownell
& Merchant, 1990; Mia & Chenhall, 1994). A fur-
ther strong point of these studies is that, except for
Brownell and Merchant (1990), they all measure
the statistical signi®cance for the di?erent sub-
groups, which allows a better understanding of the
higher-order interaction. In the majority of
papers, however, the issue of (non-)monotonicity
is not addressed.
5. Summary of ®ndings, conclusions and
implications
The evidence in the previous sections leads to
the initial conclusion that the use of MRA in the
papers reviewed is seriously ¯awed, caused by the
uncritical application of this statistical technique
and too little knowledge of its speci®c require-
ments and underlying assumptions. Table 2 pre-
sents an overview of the ®ndings. Generally, it
appears that six major types of errors in MRA use
23
Only Mia (1988, 1989) explicitly states a non-monotonic
form hypothesis.
24
Recall that an important reason for budgetary research to
adopt a contingency perspective were the opposite results of
Hopwood (1972) and Otley (1978). Hopwood (1972) found a
positive e?ect of budget emphasis, whereas Otley (1978) found a
negative e?ect. A contingency hypothesis that attempts to
explain these opposite e?ects of budget emphasis can only do so
by predicting a non-monotonic interaction e?ect.
25
Lau et al. (1995) only mention the result of the non-
monotonic test in a footnote (p. 374).
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 307
frequently occur in budgetary studies. These are:
(1) format of statistical test not in conformity with
hypothesis; (2) faulty use of tests for interactions of
the `strength' type when hypothesizing interactions
of the `form' type; (3) incorrect interpretation of
main e?ects; (4) incorrect speci®cation of the
MRA equation; (5) incorrect use of higher-order
interactions equations to test lower-order interac-
tions; and, (6) incorrect conclusions about e?ect
sizes from MRA. Overall, 27 of the 28 papers
(96%) exhibit at least one of the above errors.
26
Although the summary of ®ndings reveals that
only one paper appears free from errors, this does
not imply that the statistical results presented in
all other papers are meaningless, nor that the
conclusions drawn and presented in these papers
are not supported by the data. Regarding the for-
mer, although researchers may have applied MRA
incorrectly, and may have interpreted the MRA
results incorrectly, it may be that the statistical
results presented in these studies are interpretable
and useful. Therefore, an additional analysis was
done to evaluate the interpretability of the statis-
tical results as presented. This further analysis
reveals that the statistical results of 12 of the 28
papers (43%) can still not be interpreted. For
these papers, the uninterpretability of statistical
results is due to: (a) the use of subgroup correla-
tion analysis instead of the required MRA
(Govindarajan, 1984; Merchant, 1981, 1984,
1990); (b) the incorrect speci®cation of the MRA
equation (Brownell, 1982b; Frucot & Shearon,
1991; Harrison, 1992, 1993; Hirst, 1983; Imoisili,
1989); and (c) the de®cient analysis of a three-way
interaction (Dunk, 1993; Gul & Chia, 1994).
Regarding the latter, the analysis in the present
paper does also not prove that the conclusions
drawn and presented in the reviewed papers are
incorrect and unsupported by the data. It may be
that the statistical results presented in these papers
are robust and insensitive to the analytical ¯aws
and model misspeci®cations found. To check the
robustness of the results, another additional ana-
lysis would be required. Such an analysis would
imply the re-analysis of the original data using
MRA in conformity with the methodology and a
subsequent comparison of the results with those
presented in the original papers. Thus far, the
authors have not been able to conduct this test.
27
Table 2
Summary and overview of ®ndings
Major types of errors in MRA use Number of articles
1. Format of statistical test not in conformity with hypothesis 21 (75%)
2. Faulty use of tests for interactions of the `strength' type 4 (14%)
3. Incorrect interpretation of main e?ects 8 (29%)
4. Incorrect speci®cation of the MRA equation 4 (14%)
5. Incorrect use of higher-order interactions 3 (11%)
6. Incorrect conclusions about e?ect sizes from MRA 10 (36%)
Number of articles containing at least one of the above errors 27 (96%)
26
The paper of Govindarajan and Gupta (1985) does not
contain any errors with respect to the application and inter-
pretation of MRA.
27
To conduct such an analysis, the authors asked, at the
outset of the paper, for the data from two recent papers in the
sample. These two papers explicitly stated that the data `were
available upon request'. The authors of the two papers were
approached by both regular mail and e-mail. The letter and e-
mail stated the subject of the present paper and the purpose of
the request, which was to analyze the data for strictly methodo-
logical reasons. The results of this request were disappointing.
The author(s) of one paper replied that the data were lost due to
a move to a new university. The author(s) of the second paper
did not reply at all. After these two `answers', data were asked
from a third budgetary control paper. This was not included in
the sample (since it did not test `interaction'), but was compar-
able and deemed useful for the additional data-analysis. Also
here it said that the data were available. In this case the author
quickly replied but stated that the data were lost due to a `com-
puter crash'. Overall, this raises suspicion about the actual data
availability and, consequently, of the value of a `data avail-
ability policy'. Although the aim of this paper is not to investi-
gate the e?ectiveness of data availability policy proposed by
some journals, such an investigation does seem in order.
308 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
In sum, the ®ndings in this paper provide clear
evidence that the use of statistics in the budgetary
contingency literature does not indicate a high
level of technical quality. Many studies show too
little knowledge of the characteristics and pitfalls
of MRA, and do not display the expertise and
care required in the interpretation of its out-
comes. Moreover, budgetary studies contain little
rigor in their use of contingency theory, since it is
also found that many studies do not provide a
good link between the verbal (substantive) format
of the hypothesis and the statistical format sub-
sequently used to test the hypothesis. The reason
for this apparent negligence is not obvious, but it
may be an additional ground to be critical at
theoretical advancement in this area of the litera-
ture (cf. Chapman, 1997; Lindsay & Ehrenberg,
1993; Hartmann, in press; Young, 1996). Earlier
Briers and Hirst (1990, p. 385) have sharply criti-
cized the underdevelopment of contingency the-
ory in many budgetary and RAPM studies. They
stated:
Of particular concern is the inclusion of vari-
ables in hypothesis with little supporting
explanation. For example, some studies use
box diagrams with arrows indicating causally
related variables. Although this is a parsimo-
nious way of communicating connections, the
supporting argument in some studies is only
suggestive (. . .).
This apparent lack of ambition to develop a true
contingency theory of management accounting
was noted before by Otley, who suggested that in
many studies:
. . .[t]he contingency approach is invoked, so it
seems, in order to cover up some of the
embarrassing ambiguities that exist in the
universalistic approach (Otley, 1980, p. 414).
Indeed, many of the papers that have appeared
since then still su?er from the defects at which
Otley was hinting. These two main conclusions
provide ample reason to be worried about the
current state of budgetary contingency research
for at least three reasons. First, the analysis only
included papers from high-quality accounting
journals. Second, the analysis referred to an area
of research considered to be of great importance
to the broad area of management accounting
research. Third, the analysis examined a research
methodology which has become typical for this
and related research ®elds. The dangers of the
impact and persistence of errors in MRA found
for the state of knowledge in this speci®c ®eld of
research are large given the lack of successful
replication studies here (cf. Lindsay & Ehrenberg,
1993), and the lack of large sample studies
(Lindsay, 1995).
The main implication for future research is that
major advancements in this ®eld can be made.
Regarding the technical failures in MRA, the
®ndings in this study provide strong support for
earlier pleas for the improvement of the methodo-
logical quality of management accounting
research (cf. Lindsay & Ehrenberg, 1993; Lindsay,
1995; Young, 1996). In itself, MRA is a method
that is well-regarded and well-described in the lit-
erature. Regarding the ¯aws that a?ect both MRA
and contingency theory, authors should strive for
better and more explicit articulations of con-
tingency hypotheses. Moreover, additional care is
required in linking the form of the theoretical
proposition with the format of the statistical test.
This could also mean an increased focus on other
than simply `interaction' types of contingency ®t
(see e.g. Venkatraman, 1989). Such more con-
sciously matched theories, hypotheses and tests
are the necessary ingredients to develop a `true'
contingency theory of management accounting (cf.
Chapman, 1997). Since it is the theory that dic-
tates the format of `contingency ®t', it should also
be theory that dictates the appropriate way of
testing `contingency ®t'.
Appendix A
Selected forms and types of contingency ®t
Appendix B
Overview of reviewed articles
F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315 309
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310 F.G.H. Hartmann, F. Moers / Accounting, Organizations and Society 24 (1999) 291±315
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