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0019-8501/99/$–see front matter
PII S0019-8501(98)00048-0
Industrial Marketing Management
28
, 215–229 (1999)
© 1999 Elsevier Science Inc. All rights reserved.
655 Avenue of the Americas, New York, NY 10010
Degrees-of-Freedom
Analysis of Case
Data in Business
Marketing Research
Elizabeth J. Wilson
Arch G. Woodside
A valuable, although little-used, case data analysis tech-
nique, Degrees of Freedom Analysis, is the subject of this arti-
cle. Given the richness of case data and its prevalence in busi-
ness marketing research, Degrees of Freedom Analysis has the
potential to become an important addition to one’s “research
workbench.” The technique, first proposed by Donald Camp-
bell (Campbell, Donald, T.: “Degrees of Freedom” and the
Case Study.
Comparative Political Studies,
8, 178–193
[1975]), is described. Three business marketing applications
are presented; the first two involve use of the technique to com-
pare the extent to which four theories of group decision making
are manifested in organizations. The third application illus-
trates how the technique can be used for theory development in
the context of manufacturer–distributor relationships. Our
contribution is in demonstrating how researchers can link
“traditional” (i.e., logical positivistic) hypothesis testing pro-
cedures to examine theoretical propositions in case study re-
search. This approach is one way of achieving a critical test
(Carlsmith, J. Merrill, Ellsworth, Phoebe C., and Aronson, El-
liot:
Methods of Research in Social Psychology.
Addison Wes-
ley Publishing Company, Reading, MA, 1976]), that is, testing
the relative empirical strengths of competing theories. Our ap-
plications highlight the value of generalizing case data to the-
ory versus the inappropriate attempt to generalize such data to
a population (Yin, Robert K.:
Case Study Research Design and
Methods,
second edition. Sage Publications, Thousand Oaks,
Address correspondence to E. Wilson, Louisiana State University, E.J.
Ourso College of Business, Department of Marketing, 3127 CEBA, Baton
Rouge, LA 70803.
The comments of the anonymous reviewers and special issue editor, Dr.
Karl O. Mann, are acknowledged with gratitude.
216
CA, 1994). The explication and demonstration of this tech-
nique is not available elsewhere to the degree provided here.
© 1999 Elsevier Science Inc. All rights reserved.
INTRODUCTION
Degrees of Freedom Analysis (DFA) was introduced
by the noted psychologist, experimental methodologist,
and philosopher of science, Donald Campbell, in the late
1960s. While it has been mentioned in passing by other
case methodologists [1, 2], there are few published exam-
ples of applications of this technique. One reason why
this technique is so interesting and unique is that DFA
employs a quantitative framework to gain insight and un-
derstanding about qualitative case data. The essence of
the technique is the idea of “pattern-matching” between
theoretical propositions and observations in a set of data.
A simple example to readily illustrate DFA is a doc-
tor–patient interaction. Upon examining a sick child, the
doctor, after a series of questions, determines symptoms
of fever, irritability, loss of appetite, nausea, and a dull
pain in the lower, right quadrant of the abdomen. The
pattern
of observed symptoms (quantitative data) leads
the doctor to diagnose her patient as suffering from ap-
pendicitis (the theoretical condition). In the same fash-
ion, case data collected in social science contexts can be
examined to note the degree of match to a pattern that is
set forth by theory.
Related to the medical diagnosis example, a key prob-
lem found in the literature is the tendency of medical
doctors to use only one or two points of observations and
their most easily retrieved knowledge [3]; this may not
represent sufficient coverage of issues to indicate a pat-
tern of responses. Consequently, too often the result is
jumping to inaccurate conclusions and misdiagnoses. In
short, the more patterns that can be “matched,” the more
confident one is that the diagnosis is accurate and not
subject to systematic bias.
Campbell [4] maintains that this pattern-matching ac-
tivity is analogous to having degrees-of-freedom in a sta-
tistical test:
In a case study done by an alert social scientist who has
thorough local acquaintance, the theory he uses to explain
the focal difference also generates predictions or expecta-
tions on dozens of other aspects of the culture, and he
does not retain the theory unless most of these are also
confirmed. In some sense, he has tested the theory with
degrees of freedom
[emphasis added] coming from the
multiple implications of one theory (pp. 181–182).
For such analysis, case data are considered quantita-
tively because the researcher notes the degree of match to
the theory in terms of “hits and misses.” How many hits
are needed to “confirm” the theory? Simple statistical
tests may be used to note whether the number of hits or
misses is greater than that expected by chance. Or, the re-
searcher may conduct DFA purely to note the absolute
number of confirmed predictions for the sake of basic
knowledge development (without worrying about whether
results are “statistically significant”). This aspect of de-
grees-of-freedom analysis is consistent with Denzin and
Lincoln’s observation [5, p. 3], as follows.
Nor does qualitative research have a distinct set of meth-
ods that are entirely its own. Qualitative researchers use
semiotics, narrative, content, discourse, archival, and pho-
nemic analysis,
even statistics
[emphasis added].
Our contribution is in demonstrating how researchers
can link “traditional” (i.e., logical positivistic) hypothesis
testing procedures to examine theoretical propositions in
case study research. This approach is one way of achiev-
ing a critical test [6], that is, testing the relative empirical
strengths of competing theories.
The contribution here is valuable for two reasons.
First, we provide detailed applications where case data
are generalized to theory versus the inappropriate attempt
to generalize such data to a population [2]. The explica-
tion and demonstration of this technique is not available
elsewhere to the degree provided here. Second, DFA uti-
lizes strong features from both the logical positivism and
critical relativism traditions in terms of its scientific
ELIZABETH J. WILSON is Associate Professor and Marjory B.
Ourso Excellence in Teaching Professor, E.J. Ourso College of
Business Administration, Louisiana State University, Baton
Rouge, LA. Liz received the Ph.D. in Business Administration
from Pennsylvania State University in 1989. Her research in
business marketing has been published in
Industrial Marketing
Management, Journal of Marketing Research, Journal of
Business-to-Business Marketing
, and elsewhere.
ARCH G. WOODSIDE is the Malcolm S. Woldenberg Professor
of Marketing, A.B. Freeman School of Business, Tulane
University, New Orleans, LA. Arch received the Ph.D. in
Business Administration from Pennsylvania State University in
1968. His research in business marketing has been published
in
Industrial Marketing Management, Journal of Marketing,
Journal of Business-to-Business Marketing
, and elsewhere.
217
method. That is, rich qualitative case data are used to ex-
amine whether theoretical propositions are supported or
not; thus, we can have some degree of objectivity and va-
lidity in the testing procedure.
By these examples, DFA is shown to be a very flexible
technique that can accommodate case research studies of
varying goals (e.g., theory development versus theory
comparison) and contexts (e.g., individual versus group
decisions, discrete transactions versus ongoing relation-
ships, etc.). In addition, DFA offers researchers some ad-
vances over existing techniques. For example, content
analysis [7] is a technique often associated with case
data. Results of content analysis are often expressed as
counts, means, or frequencies of the phenomenon of in-
terest. DFA takes the researcher a step further by subject-
ing the counts, or patterns, in a qualitative dataset to an
a
priori
set of predictions (i.e., hypotheses, propositions,
conjectures, etc.) so that theories can be compared, tested,
or constructed, according to the researcher’s purpose.
In the next section, a brief overview of the steps in-
volved in conducting DFA are reviewed.
DOING DEGREES-OF-FREEDOM ANALYSIS
The heart of DFA is the development and testing of a
“prediction matrix”. The prediction matrix sets up the
“pattern,” based on theory, to be either confirmed or dis-
confirmed by the case data. The statements in the predic-
tion matrix are analogous to hypotheses in the sense of
traditional statistical hypothesis testing. Campbell [4, p.
188] states that “one should keep a record of all the theo-
ries considered in the creative puzzle-solving process. To
represent the degrees of freedom from multiple implica-
tions, one should also keep a record of the implications
against which each was tested, and the box score of hits
and misses.”
Any research study, even the most exploratory, will
have some grounding in the extant literature. Research
may be motivated by an established theory or a “theory-
in-use.” A theory-in-use is the set of propositions guiding
the behavior of a decision maker, and theories-in-use are
usually stated implicitly rather than explicitly [8]. Other
examples of developing theories-in-use include script-
theory research [e.g., 9] and research on perceptual pro-
cessing and acquiring cognitive skills [10, 11]. Following
the development of such theories, the predictions made
explicit in the theories may be tested empirically after
collecting additional case data.
So, the first step in DFA is for the researcher to be fa-
miliar with the existing knowledge base about the phe-
nomenon of interest. If one or several theories on the
topic exist, the prediction matrix can be constructed with
relative ease. If no theory has been proposed in an area,
individual studies may generate rival explanations (via
theories-in-use) that may be incorporated into a predic-
tion matrix for testing. This use of DFA would then lead
toward the goal of theory development.
Upon careful development of one or more prediction
matrices, the researcher is ready for fieldwork. Data may
be in the form of personal interviews, document analysis,
participant or nonparticipant observation, or other case
data collection methods [2]. Care must be taken by the
researcher to conduct the data collection in such a way to
avoid introducing bias into the data. We discuss this
point in some detail later in this article and offer several
strategies for maintaining data integrity.
After the data are collected, trained judges then review
the information (interview transcripts, for example) to
note hits or misses to items in the prediction matrix. The
box-score of hits and misses can then be subjected to sta-
tistical tests to note the significance of the ratio of con-
firmed versus unconfirmed predictions found in the data.
Such tests might be a sign test [12], a chi-square test, or a
z-test for differences in proportions.
Testing rival theories, that is, doing a comparative the-
ory test [13] or critical test [6], via DFA deepens the
There are few published examples
illustrating degrees-of-freedom analysis,
first described by Donald Campbell.
218
value of case data. That is, when several theories exist,
the number of confirmed predictions can be noted to see
which theory tends to be supported relative to others. Or,
if theory development is the goal, the researcher can look
at the confirmed predictions to examine the variance in
findings across the original empirical studies. Construct-
ing a table of “benchmark” findings of confirmed predic-
tions may be the first step at formulating an initial theory.
Based on the discussion above, Figure 1 is a summary
diagram that provides an overview of DFA as a research
process. Upon completion of one DFA study, the re-
searcher may continue with additional programmatic in-
vestigations into the phenomenon of interest. This refin-
ing process is represented in Figure 1 by the feedback
loop. Depending on the outcome of one study, the re-
searcher may go back and repeat to some or all of the ac-
tivities in the process. In the remainder of this article
three DFA applications [14–16] are examined.
USING DEGREES-OF-FREEDOM ANALYSIS
FOR THEORY COMPARISON: GROUP
DECISION-MAKING IN
ORGANIZATIONAL BUYING
Dean [14] applied DFA to examine the degree of sup-
port for four theories of organizational decision making
in the context of adoption decisions of advanced manu-
facturing technology. Because Dean’s research is focused
on adopting and acquiring new manufacturing technolo-
gies, his empirical application of DFA may be of particu-
lar interest for industrial purchasing and marketing research-
ers. From the literature, the four theories include: (1) the
rational model of decision making [17]; (2) the bounded
rational model [18]; (3) the political model [19]; and (4)
the garbage can model [20]. Dean’s central finding was
that while no single theory was supported in all cases, one
theory, the bounded rationality model, tended to have more
of its predictions confirmed while the be garbage can
model tended to have the fewest confirmed predictions.
In a partial replication of Dean’s work, these four theo-
ries are examined in the context of organizational buying
decisions for copier equipment by Wilson and Wilson
[16]. Since they replicated Dean’s study in a marketing
context, the details of the Wilson and Wilson study are
presented here as an example of DFA as a comparative
theory test [6, 13].
FOUR MODELS OF ORGANIZATIONAL
DECISION MAKING
Briefly, each of the four models of decision making of-
fers different explanations for behavior in terms of out-
comes and processes. The rational model, derived from
microeconomics, posits that members of organizations
will make decisions that will provide maximum benefit
(i.e., utility) to the firm. The bounded rationality model
proposes that while decision makers try to be rational,
they are constrained by cognitive limitations, habits, and
biases (i.e., human nature). According to the political
model, decision makers are competing to satisfy their
own goals, and choice is a function of an individual’s
power. Finally, in the garbage can model, decisions are
the result of an unsystematic process. That is, problem
definitions can change, preferences are unclear, and peo-
ple may come and go from the decision group [14].
DEVELOPMENT OF A PREDICTION MATRIX
The four theories are a mixture of similar, complemen-
tary, competing, and orthogonal predictions about orga-
nizational decision-making behavior. The prediction ma-
DFA links traditional hypothesis testing
methods to examine theoretical propositions
in case study research to achieve
“critical tests.”
219
trix is developed based on seven basic decision activities
[14]. They are:
1. Problem definition—the conceptualization of the de-
cision problem or process by buying center members
2. Solution search—the existence, degree, and type of
search for alternative solutions to the problem(s)
3. Data collection, analysis, and use—the extensiveness,
type. and function of attempts to collect and use infor-
mation
4. Information exchange—the ways in which buying
center members share information during the decision
process
5. Individual preference formation—the existence, na-
ture, and resistance to change of buying center mem-
bers’ preferences
6. Evaluation criteria—how decision criteria are devel-
oped and used
7. Final choice—how when and why choices among al-
ternative products are made.
Thus, each theory or model of organizational decision-
making has predictions for buying center member behav-
ior in each of the seven facets. The following discussion
of these behaviors is adapted from Dean [14] for the
present business marketing context.
According to the rational model [17, 21], buying cen-
ter members would be expected to develop comprehen-
sive problem definitions, conduct an exhaustive informa-
tion search, develop
a priori
evaluation criteria, and
exchange information in an unbiased manner. Individual
preferences and final buying center choice should reflect
the alternative that offers the maximum benefit to the or-
ganization.
Under the bounded rationality model [18, 22], buying
center members simplify the problem definition, search is
sequential and limited to familiar areas, and information
exchange is biased by individual preferences. Preferences
originate from either personal or departmental sub-goals
for each buying center member. Evaluation of alterna-
tives follows a conjunctive decision rule where criteria
are expressed in terms of cutoff levels. Choice depends
on which alternative first exceeds the minimum cutoff
levels of the evaluative criteria.
The political model [19, 23] proposes that buying cen-
ter members will compete for decision outcomes to sat-
isfy personal and/or departmental interests. Preferences
are based on these interests and formed early in the deci-
sion process. Problem definition, search, data collection
and evaluation criteria are weapons used to tilt the deci-
sion outcome in one’s favor. Choice is a function of the
relative power of buying center members.
Finally, the garbage can model [20] suggests that deci-
sions are analogous to garbage cans into which problems,
solutions, choice opportunities, and buying center members
are dumped. Problem definitions are variable, changing as
new problems or people are attached to choice opportuni-
ties. Data are often collected and not used. Preferences
are unclear and may have little impact on choice. Evalua-
tion criteria are discovered during and after the process,
and choices are mostly made when problems are either
not noticed or are attached to other choices.
Given the propositions of each model across the seven
decision phases, a prediction matrix can be constructed.
Rather than have a general statement for each model and
decision phase, operational items may be developed to
make the data judging task clear. Such is the case for
buying copiers; two operational items for each decision
phase were developed. The resulting 56-cell table (2
statements
3
7 phases
3
4 models) contains the predic-
tions that a theory is either confirmed (Y), partially con-
firmed (P), or not confirmed (N). This prediction matrix
is shown in Table 1.
COLLECTION OF CASE DATA
The researcher must carefully design data collection
forms in order to avoid including items that favor one of
competing theories described in alternative predictive
matrices. Alternatively, to insure that the data have a
high degree of nomological validity, the research might
incorporate alternative questions that favor each theory
The heart of DFA is the development and
testing of a prediction matrix.
220
(e.g., several different scenarios illustrating alternative
theories could be evaluated by the respondent to see
which best matches his/her “reality”). The first ap-
proach—to achieve bias reduction in questioning—
would benefit by having independent experts check sev-
eral revisions of the open and closed-end questionnaire.
The same checking procedure may be used for the sec-
ond approach to insure that theory biases are built into
the scenarios accurately.
Possibly because DFA and the idea of formulating
competing prediction matrices are such new methods in
case study research, the issue of bias favoring one theory
over competing theories has not been addressed in the lit-
erature before. (This discussion reflects several thought-
ful comments by one of the anonymous reviewers of this
article.) To allow for objectivity and verifiability in data
collection and analysis, the actual survey forms used to
collect data for DFA should be available for independent
examination. In Wilson and Wilson’s study, the set of
questions is available in the original article and is not in-
cluded here for the sake of brevity [see 16 p. 590].
Wilson and Wilson collected data from members of
four buying centers regarding office copier decisions in
different departments across their university. Buying
centers typically consisted of two, and sometimes three,
persons. In-depth interviews were conducted by the first
Comparative theory testing via DFA
deepens the value of case data.
TABLE 1
Predictions of Four Models on Decision Process Activities in Organizational Buying
Decision Phase and Operating Mechanism
Rational
Model
Bounded
Rationality
Political
Model
Garbage Can
Model
1. Problem definition
Do the participants view the problem in the same way? Y P N P
Does the problem definition represent the goals of the organization? Y Y N Y
2. Search for alternative solutions
Is search limited to a few familiar alternatives? N Y P P
Are potential solutions considered simultaneously and compared with one another? Y P N N
3. Data collection, analysis, and use
Is information collected so that an optimal decision can be made? Y N N N
Is control over data collection and analysis used as a source of power? N N Y N
4. Information exchange
Is information biased so as to conform to the preference (position) of the person
transforming it? N Y Y N
Is information exchange negatively affected by people entering and leaving the decision
process and changing their focus of attention? N P N Y
5. Individual preferences
Do preferences change as problems become attached to or detached from the decision? N P N Y
Are individual preferences a function of personal goals and limited information about
the alternative? N Y P P
6. Evaluation criteria tradeoffs
Are criteria for a solution agreed on
a priori
?YPPN
Do tradeoffs across solution criteria occur? Y N P N
7. Final choice
Is the first alternative that exceeds the cutoff level(s) selected? N Y P N
Is the alternative chosen one that is expected to maximally benefit the organization,
compared with other alternatives? YPN P
Source:
Wilson and Wilson [16].
Y, yes (prediction confirmed); P, partial (prediction partially confirmed); N, no (prediction not confirmed).
221
author after the supplier choice decision had been made.
In addition, documents pertaining to each decision (i.e.,
purchase RFQs, supplier quotes, and purchase orders)
were analyzed.
The interviews were semistructured; similar questions
were asked of each respondent, but questions were open
ended. The questions were across broad areas of decision
activities and as such, the interviewer could ask for de-
tails on relevant points. In other words, the question or-
der and probes did not follow exactly the same route for
all interviews because of elaborations by respondents
when answering. The interview format and questions were
not designed to operationalize any one theory. The tran-
scripts and archival material were then reviewed by three
trained judges (the two authors plus an ABD graduate
student in business marketing) to note the extent to which
tenets of the four models were supported by the data.
The use of one interviewer only in the collection of
case data may increase the possibility of interviewer bias.
Several strategies are possible to reduce such bias. First,
in some cases two interviewers working alone, and some-
times as a team, can conduct multiple interviews in the
same case study and then, the two or more interviewers
can compare their mental and written notes. Second, ad-
ditional data from written documents and direct observa-
tions can be collected to verify or disconfirm the reported
reality presented by respondents to any one interviewer.
Third, a trusted informant within the organization may
act as a “consultant.” Interview notes may be reviewed
by the consulting informant to verify facts and eliminate
apparent paradoxes.
A criticism often leveled at studies using case data is
that generalization is difficult, if not impossible. Yin [2]
countered this argument by stating that each case should
be considered a study within itself—just like an experi-
ment. Thus, the buying decision data are viewed as an
initial case study with three replications. Yin makes the
point that multiple cases should not be considered as a
“sample” and external validity issues are not so problem-
atic as some logical positivists might argue.
Critics typically state that single cases offer a poor basis
for generalizing. However, such critics are implicitly con-
trasting the situation to survey research, in which a “sam-
ple” (if selected correctly) readily generalizes to a larger
universe.
This analogy to samples and universes is incor-
rect when dealing with case studies.
This is because sur-
vey research relies on
statistical
generalization [from a
sample to a population], whereas case studies (as with ex-
periments) rely on
analytic
generalization. In analytic
generalization, the investigator is striving to generalize a
particular set of results to some broader theory [2 p. 36].
INTERJUDGE RELIABILITY
An examination of the level of agreement among the
three judges offers information about the reliability of the
findings. Based on their review of the interview tran-
scripts and archival material, a judge could say that a the-
ory is confirmed (Y), partially confirmed (P) or not con-
firmed (N). Four levels of agreement exist for the three
judges—perfect (YYY, PPP, NNN), near perfect (YYP,
YPP, NNP, NPP), some (YYN, YNN), or none (YPN).
This scheme is adapted exactly from Dean [14].
The three judges did display a pattern of agreement
greater than one would expect by chance. Each judge
made 56 evaluations (7 phases
3
2 statements each
3
4
cases); see the prediction matrix in Table 1. Judges were
in perfect agreement for 55% of the evaluations and
nearly perfect agreement for 23%. Thus, near perfect to
perfect agreement occurred for 78% of the evaluations.
Judges were in some agreement for 20% of the evalua-
tions and in total disagreement in only 2% of the evalua-
tions. By chance, the distribution would be 11% total
agreement, 44% nearly perfect, 22% some agreement,
and 22% no agreement. By a chi-square test, these distri-
The researcher must carefully design data
collection forms to avoid including items
that favor one theory over another.
222
butions of agreement levels are significantly different
(
x
2
5
103.77, 3 d.f.,
P
,
0.001).
THEORY COMPARISON “BOX SCORES”
For brevity, results from one buying center case are
presented along with a summary of the results across the
four cases. These abbreviated findings serve our present
purpose of illustrating applications of DFA; the complete
set of tables are available [16].
Table 2 provides details about one copier buying deci-
sion case. For Judge A, 8 evaluations of a possible 14
confirmed the predictions of the rational model of orga-
nizational decision making. In other words, for the ratio-
nal model there were eight hits and six misses; a 57% hit
rate. Raw scores for the rows in Table 2 may not sum to
the same total because multiple hits were possible given
overlapping aspects of the theories, as indicated in the
prediction matrix.
Looking down the column for the rational model, 17
evaluations of 42 possible (3
3
14) confirmed the predic-
tions of the rational model. That is, the rational model
had 17 hits and 25 misses, a 40% hit rate. Similarly, the
bounded rationality model had a 62% hit rate while the
political and garbage can models had 31% hits, respec-
tively. On an absolute basis, the bounded rationality
model had more predictions supported by the case data
than the other decision-making models.
Even though care was taken by Wilson and Wilson to
insure that the survey questions did not favor one theory
over others, there is a possibility that respondents wanted
to appear rational to the interviewer. We speculate that
this may be, in part, an explanation of findings in support
of the bounded rationality model. Consequently, we rec-
ommend use of alternative survey methods, such as sce-
nario problem solving by respondents, to examine for the
contextual possibilities for applications of competing
theories.
To evaluate this result statistically, a chi-square test is
used to test whether there is a significant difference be-
tween the observed distribution of “hits” (i.e., confirmed
predictions) and the distribution one would expect by
chance. Use of the chi-square test in this manner is ap-
propriate since we are examining the extent to which two
distributions (observed and expected) are different from
each other [12].
Since the
a priori
assumption is that any model may be
as good as another, all four models have an equal chance
(25%) of having their predictions confirmed. The abso-
lute number of confirmed predictions across the models in
this case is 69. The expected distribution would be 69/4
5
17.25 hits per cell. The chi-square statistic is significant
at
P
,
0.10 which indicates that the two distributions are
significantly different and a systematic pattern occurs in
the data. The pattern is that the bounded rationality
model has more of its predictions confirmed compared to
the other models. See Table 2.
When the matches to the predictions are considered as
proportions, a z-test can be used to evaluate the results.
The highest proportion of matches is for the bounded ra-
tionality model (0.61) which is significantly larger than
that for the rational model (0.40); z
5
2.01,
P
,
0.05. It
follows that the number of matches for the bounded ra-
tionality model are also significantly greater than the po-
litical model and garbage can model.
Table 3 presents a meta-analytic summary of the re-
sults across all cases. Again, a chi-square test indicates
that the distribution of matches to the prediction matrix is
significantly different than that expected by chance (
x
2
5
15.9, 3 d.f.,
P
,
0.01). Specifically, the bounded ratio-
nality model tends to have more predictions confirmed
DFA may be used for theory development.
TABLE 2
Boxscore Results for Buying Case #1: Absolute and Percentage
Matches (Hits) to Predictions
Organizational Decision-Making Model
Rational
Model
Bounded
Rationality
Model
Political
Model
Garbage
Can
Model
Judge A 8 (0.57) 8 (0.57) 2 (0.14) 4 (0.29)
Judge B 2 (0.14) 9 (0.64) 8 (0.57) 3 (0.21)
Judge C 7 (0.50) 9 (0.64) 3 (0.21) 6 (0.43)
Total observed matches 17 (0.40) 26 (0.62) 13 (0.31) 13 (0.31)
Total expected matches 17.25 17.25 17.25 17.25
x
2
5
6.53, 3 d.f.,
P
,
0.10.
Numbers in parentheses are percentages of matches (hits).
223
from the case data compared to the other models of deci-
sion making. The proportion of matches for the bounded
rationality model is also significantly greater than the
proportion of matches for the political or garbage can
models (z
5
2.93,
P
,
0.05).
THEORY COMPARISON CONCLUSIONS
As depicted in Figure 1, the final step in DFA is to as-
sess the findings in light of the existing knowledge base.
Questions to ask at this point might be “how do our re-
sults compare to those of other studies?” and “how do our
results confirm or disconfirm rival theories?”.
Overall, the bounded rationality model has the greatest
number of predictions confirmed by the case data com-
pared with rival models. This conclusion supports Dean’s
contention that tenets of one theory may dominate while
rival theories may receive less support [14]. In the con-
text of a modified rebuy decision [24], a post-hoc look at
the findings indicates that the bounded rationality model
seems to provide the best framework for understanding
organizational decision making. This makes intuitive
sense given that modified rebuy decisions are character-
ized by limited problem solving behavior with buying
center members drawing on past buying experiences. We
can speculate that in other contexts, the results might be
different. The results of this comparative theory test
helps to clarify the context where one theory might apply
to a greater degree than others, but more research on
other contexts is necessary before more definitive con-
clusions can be made.
For example, if the decision had been for new technol-
ogy with little information available (a typical new task
situation), the political model may have had more predic-
tions confirmed since buying center members might be
motivated to “protect their turf” [25]. Similarly, the ratio-
nal model may have had more predictions confirmed in a
new task situation in order to reduce financial risk of
making a high dollar purchase. Thus, decision context is
proposed as strong moderator on the applicability of a
particular decision theory within a specific case study.
The following view may be best: decision-making re-
alities may reflect bits and pieces of competing theories.
No one theory may dominate. The issue becomes one of
learning the contingencies that generate the occurrence
of support for portions of each theory. Next, we illustrate
of the use of DFA for the purposes of theory develop-
ment in the area of relationship marketing.
USING DEGREES-OF-FREEDOM ANALYSIS
FOR THEORY DEVELOPMENT:
MANUFACTURER–DISTRIBUTOR
RELATIONSHIPS IN BUSINESS MARKETING
While there are a wealth of empirical studies on the
topic of relationship marketing [e.g., 26–29], there are no
established “middle-range” theories [30]; thus, this field
is ripe for the application of DFA.
Wilson and Vlosky and Wilson and Fontenot [15, 31]
conducted a large-scale case research project to gain
deeper understanding about partnering relationships be-
tween firms as opposed to typical (transactional and of-
ten adversarial) relationships. The context of their work
is in the area of manufacturer and distributor relation-
ships in the wood products industry. The motivation for
this work was to identify the activities that tend to be as-
sociated with the more beneficial (“win-win”) partnering
A major advantage of DFA is its flexibility.
TABLE 3
Meta-Analysis Across All Cases: Observed Matches to Predictions
Organizational
Decision-Making Model
Rational
Model
Bounded
Rationality
Model
Political
Model
Garbage
Can
Model
Case #1 17 26 13 13
Case #2 13 30 15 22
Case #3 27 15 6 20
Case #4 14 28 17 17
Total observed matches 71 (0.42) 99 (0.59) 51 (0.30) 72 (0.43)
Total expected matches 73.25 73.25 73.25 73.25
x
2
5
15.9, 3 d.f.,
P
,
0.01.
Numbers in parentheses are the percentage matches (hits).
224
relationships as opposed to short-term adversarial (“win-
lose”) relationships. In this section of the paper, a brief
review of their work is presented to illustrate a theory
building application of DFA.
GROUNDING IN THE EXTANT LITERATURE
Webster [32] proposes that business marketing rela-
tionships span a continuum from discrete transactions to
legal partnerships (vertical integration). In between these
two endpoints are relationships with varying degrees of
cooperation, trust, and dependence. Discrete transaction
relationships, historically the most common form in the
U.S. marketplace, are usually characterized as adversar-
ial with both the buyer and seller attempting to achieve
the best economic position at the expense of the other. As
one moves toward the opposite end of Webster’s contin-
uum, relationships are characterized as being more “part-
ner-oriented” with firms exhibiting higher degrees of co-
operation, trust, commitment, and communication [32].
Four models in the literature [26–29] offer a good base
for developing a prediction matrix. These studies include
some overlapping constructs (e.g., trust, functional con-
flict, communication) but also have their own unique
constructs and hypotheses. From these four studies, we
get an idea of the most often studied features of business-
to-business relationships, and based on the findings, we
can make predictions accordingly.
FIGURE 1. The research process for degrees-of-freedom analysis.
225
THE PREDICTION MATRIX
The prediction matrix for the relationship marketing
study is shown in Table 4. It includes predictions (most
in the form of “yes” or “no” answers to questions in the
matrix) for 11 relationship activities. Predictions are for
both partnering and typical relationships so that a con-
trast between these two forms can be observed. The 11
relationship activities (i.e., joint programs, pricing, logis-
tics, etc.) were distilled from the literature, and the indi-
cators shown in Table 4 are the operating mechanisms
used during the personal interview. These statements are
similar to those used in our previous example (see Table
1). Operating mechanisms in a prediction matrix are
helpful because they help the interviewer and respondent
to focus on issues rather than talk in generalities.
DATA COLLECTION
Members of research teams interviewed key informant
respondents at distributor organizations about activities
with partnering manufacturers and typical manufacturing
principals. A standard list of questions was provided to
each team for conducting semistructured interviews and
again, Dean’s [14] methodology was followed [15]. Spe-
TABLE 4
A Prediction Matrix of Relationship Activities
Relationship Activity Indicator Partnering Supplier Typical/Average Supplier
Programs Development of new product or service programs? Yes No
Joint programs to market manufacturers’ products? Yes No
Involvement in product deletion decisions? Yes No
Pricing Offer trade discounts? More generous than normal Industry norm only
Special pricing problems? No Yes
Claim policy? Better than industry norm Industry norm
Payment terms? Better than industry norm Industry norm
Logistics Typical shipment size? LTL accommodated Full truck load required
JIT Inventory management? Yes No
Method of transportation Truck or other options Truck only
FOB mill or FOB delivered? FOB mill FOB delivered
Dealer promotion Supplier featured in promotional literature? Yes No
Sharing of customer lists with supplier? Yes No
Sales volume incentives offered by supplier? Better than industry norm Industry norm
Advertising Co-op advertising? Yes No
Sales force activities Joint sales training? Yes Little to none
Joint sales calls to distributors customers? Yes No
Joint performance reviews of suppliers’ sales force? Yes No
Joint performance reviews of distributors sales force? Yes No
Joint customer lead development for distributor? Yes No
Marketing planning Conduct joint marketing planning with supplier? Yes No
Does supplier request a written marketing plan? Yes No
Performance reviews Conduct annual performance reviews with the supplier? Yes No
Manufacturing Does supplier configure shipments to your specs? Yes No
Does supplier use/offer UPC bar coding? Yes No
Does supplier manufacture products to your specs? Yes No
Does supplier offer special packaging services? Yes No
Communication Does distributor visit supplier? Yes No
Does supplier visit distributor? Yes No
Seek out supplier at trade shows or association meetings? Yes No
Information exchange Does supplier have access to distributor’s computer files Yes No
Does distributor have access to supplier’s computer files Yes No
Face-to-face communication frequency Multiple times per week Less than once per week
Telephone communication frequency Multiple times per day Once per day or less
Electronic communication frequency Multiple times per day Once per day or less
Which department mostly communicates with supplier? Multiple departments Purchasing
Other departments that communicate with supplier? Multiple departments Senior management
Use of EDI between supplier and distributor? Yes No
Source:
Wilson and Vlosky 1997 [15].
226
cifically, questions were asked about the activities firms
engage in (or don’t engage in) with what the respondent
considers a “partnering” supplier and a “typical” sup-
plier. Wilson and Vlosky’s complete questionnaire is in-
cluded in their original article [15 p. 69–70], and while
questions may seem to require simple yes or no re-
sponses from participants, the research teams were in-
structed to use the specific questions to get respondents
talking about their business relationships. Interviewers
were expected to, and did, use their own probes with re-
spondents in order to get fine detail and nuance in order
to write up their final cases.
The research teams were used since informants were
spread across the United States and Canada. Team mem-
bers were identified as being active academic researchers
in either marketing or wood science and in the general
geographic area of the potential distributor respondents.
After conducting the interviews, team members worked
to transcribe their field notes and write cases on the com-
panies they studied. Based on the complete set of field
notes, the team members made judgements to complete
the prediction matrix for their particular case. While most
teams interviewed only one distributor, some [e.g., 33],
compiled data from multiple cases. The cases written by
the research teams have additional in-depth nuance on man-
ufacturer-distributor relationships that is beyond the scope
of our reporting for the present article. Interested readers
are urged to consult the May 1997 issue of
Journal of
Business Research
to view the cases in their entirety.
DEGREES-OF-FREEDOM ANALYSIS RESULTS
Table 5 contains the DFA results for the partnering
suppliers to the wood products distributor informants.
For most cells of the prediction matrix, 10 cases could be
evaluated. In some cases, though, particular questions did
not apply to the distributor respondent; thus, the number
of observations ranges between 5 and 10 cases. From Ta-
ble 5, the specific activities present for partnering firms
(e.g., joint marketing programs, trade discounts, joint
sales force performance reviews, specially configured
shipments, etc.) can be observed.
Wilson and Vlosky used a combination of statistical
tests used to evaluate the compiled results of prediction
matrices completed by the research teams. First, a sign test
[12] is done for each row/prediction. “The sign test gets its
name from the fact that it uses plus and minus signs [or
“yes” “no” responses] . . . as its data” [12, p. 68]. We can
evaluate each row of the prediction matrix by assessing
the number of cases where the partnering prediction is
confirmed (yes) or not confirmed (no). The resulting ratio
can be evaluated in terms of an associated p-level for a bi-
nomial test [12, pp. 68–75 and Table D, p. 250].
So, in Table 5 we see that in 7 of 10 cases, partnering
suppliers participate in development of product/service
programs. While this result is in the expected direction
proposed by Wilson and Vlosky,
P
5
0.17 (from Table D
in Siegel); thus, it is only marginally significant, at best.
This is noted in the explanation of Table 5. For the next
row of the prediction matrix, 8 of 10 firms reported they
did participate in joint programs to market the partnering
manufacturer’s products. This result is statistically sig-
nificant (
P
,
0.05) and is so noted in the explanation at
the bottom of Table 5. Results for the remaining rows are
interpreted similarly.
To evaluate the results over the entire table, a weighted
average of the proportion of matches to the prediction
matrix is calculated (53%). A z-test is used to determine
whether this proportion is not significantly different from
chance (50%). The computational formula for this test is
available in Bruning and Kintz [34]. The difference be-
tween 53 and 50% is not statistically significant for the
table as a whole.
Even so, we do gain interesting insights about partner-
ing behavior by examining the rows of Table 5. In so do-
ing, a post-hoc profile of partnering relationship activi-
ties emerges. For example, in the context of one specific
industry (wood products), partnering activities with man-
ufacturing principals are manifested in terms of joint
marketing programs, superior pricing arrangements, co-
operation between the sales forces, and joint planning ac-
tivities, to name a few. There was relatively little partner-
ing activity between manufacturers and distributors in
more “sensitive” areas such as information exchange
(e.g., use of EDI and having computerized access to in-
formation in the partner’s organization).
The detailed insights such as those described above al-
low for industry specific refinements in thinking about
business-to-business relationships. Wilson and Vlosky’s
findings corroborate work of earlier studies. For exam-
ple, in the wood products industry, manufacturers and
distributors still have some progress to make in terms of
investments in technology before partnering activity in
communication will occur. Vlosky [35] notes that the in-
dustry is fraught with distrust between firms; this would
contribute to an unwillingness to share information and
communicate freely.
227
In this narrow industry example, several studies have
been conducted as initial explorations [35, 36]; subse-
quent corroboration of such findings in Wilson and
Vlosky [15] provides an initial step in the inductive the-
ory building process for a research area [37]. The next
step in the research program of Wilson and Vlosky
would be to test their posterior (i.e., post-hoc) profile of
partnering relationship activities for additional verifica-
tion. The partnering activity statements/predictions in the
posterior profile [14, p. 67] would become new hypothe-
ses for an additional study that may use DFA or other
analysis techniques, as needed.
DFA AS A RESEARCH TOOL
As evident from the two examples of DFA reviewed
here, the technique has a lot to offer to researchers in
business marketing. Many phenomena in this field are
very complex and a case methodology is needed to un-
cover and confirm nuances of organizational and/or indi-
TABLE 5
Boxscore Results for Partnering Supplier Relationships
Relationship Activity Indicator Prediction Hits (%) N of Cases Significance*
Programs Development of new product or service programs? Yes 70 10
1
Joint programs to market principal’s products? Yes 80 10
11
Involvement in product deletion decisions? Yes 30 10
2
Pricing Offer trade discounts? Yes 80 10 11
Special pricing problems? No 80 10 11
Claim policy? Better than industry norm 60 10 1
Payment terms? Better than industry norm 20 10 22
Logistics JIT Inventory management? Yes 10 10 22
FOB mill or FOB delivered? FOB Mill 20 10 22
Dealer promotion Supplier featured in promotional literature? Yes 20 10 22
Sharing of customer lists with supplier? Yes 20 10 22
Sales volume incentives offered by supplier? Better than industry norm 50 10 0
Advertising Co-op advertising? Yes 50 10 0
Sales force activities Joint sales training? Yes 70 10 1
Joint sales calls to distributors customers? Yes 70 10 1
Joint performance reviews of suppliers sales force? Yes 20 10 22
Joint performance reviews of distributors sales force? Yes 10 10 22
Joint customer lead development for distributor? Yes 100 10 11
Marketing planning Conduct joint marketing planning with supplier? Yes 60 10 1
Does supplier request a written marketing plan? Yes 0 10 22
Performance reviews Conduct annual performance reviews with the supplier? Yes 70 10 1
Manufacturing Does supplier configure shipments to your specs? Yes 100 5 **
Does supplier use/offer UPC bar coding? Yes 20 5 **
Does supplier manufacture products to your specs? Yes 100 5 **
Does supplier offer special packaging services? Yes 40 5 **
Communication Does distributor visit supplier? Yes 100 10 11
Does supplier visit distributor? Yes 100 10 11
Seek out supplier at tradeshows or association meetings? Yes 100 10 11
Information exchange Does supplier have access to distributor’s computer files Yes 20 10 22
Does distributor have access to supplier’s computer files Yes 20 10 22
Face-to-face communication frequency Multiple times per week 20 5 **
Telephone communication frequency Multiple times per day 90 10 11
Electronic communication frequency Multiple times per day 40 5 **
Which department mostly communicates with supplier? Multiple departments 40 5 **
Other departments that communicate with supplier? Multiple departments 40 5 **
Use of EDI between supplier and distributor? Yes 30 10 2
*The test of statistical significance is a sign test (Siegel [31]) by using the following indicators: 11, the partnering relationship prediction is supported both direc-
tionally and statistically (P , 0.05); 1, the partnering relationship prediction is supported directionally; 2, the partnering relationship prediction is not supported
directionally; 22, the partnering relationship opposite to that predicted is supported statistically (P , 0.05); and **, no statistical testing inferences are made in
these cells due to the small number of cases.
The weighted average hit rate of predictions to observations is 53%; that is, our predictions for partnering relationship activities are confirmed approximately half
the time. By a z-test, this proportion of hits to misses is not significant. Source: Wilson and Vlosky [15].
228
vidual behavior. Case studies are also more feasible lo-
gistically in terms of data collection, compared with
experiments or even surveys, given the time demands on
respondents in the business-to-business context. With
multiple case observations, the researcher can use DFA
to meta-analyze his/her data for purposes of theory build-
ing, theory comparison, or theory testing.
A major advantage of DFA is its flexibility. Data from
one case or many cases may be used. While case research
methodologists [i.e., 2] maintain that studies with n 5 1
can be perfectly valid in terms of analytical generaliza-
tion, researchers need multiple data points for any sort of
“statistical” generalization. However, multiple cases in a
DFA should not be considered as data points/observa-
tions in a sample, but separate “replications”, in the same
way that multiple experiments about a common phenom-
enon are considered.
DFA is flexible in how results are evaluated. One or
several judges may evaluate the data to tally the theory
box-score results. When multiple judges are used, inter-
judge reliability computations offer additional evidence
of the reliability of the evaluations and the validity of this
approach.
The purpose of the researcher’s study (theory building
or theory comparison) is a third dimension on which
DFA demonstrates flexibility. In theory building, dispar-
ate findings from studies in the literature can be explored,
propositions can be formulated and assessed, and the de-
veloping theory can be refined through post-hoc exami-
nation of DFA findings. On the theory comparison side,
Campbell [4] and Sternthal et al. [13] both noted the need
for considering rival explanations against each other to
note which theory offers a better explanation for phe-
nomena. DFA is a way to conduct such comparative the-
ory tests.
RESEARCH LIMITATION CONSIDERATIONS
In our examples of studies employing DFA, several
limitations should be noted and avoided where possible.
For example, in Wilson and Wilson [16], respondents
were not contacted for a follow-up review of the decision
that the interviewer had recorded. Thus, replication of
this research is needed to determine if the results obtained
are stable. This correction was made in case data collec-
tion as reported in Wilson and Vlosky [15]; in writing the
case reports, researchers often had multiple visits with re-
spondents to verify and clarify information obtained at
earlier visits. In addition, the case data analyzed by Wil-
son and Vlosky were collected in a semistructured depth
interview, as described earlier. Case writers were asked
post-hoc to complete the prediction matrix based on the
information gathered from wood products distributors. In
other words, the case writers did not have the prediction
matrix until all data had been gathered in order to mini-
mize data contamination and theory confirmation bias.
As we have noted throughout this tutorial on DFA,
strategies to reduce the potential for bias in data collec-
tion should be given consideration by researchers plan-
ning to use this technique. Wilson and Wilson [16] em-
ployed both personal interviews and document analysis
in an effort to achieve triangulation. However, assur-
ances about data reliability and validity would be in-
creased if post-hoc interviews had been done or by em-
ploying some of the other strategies mentioned earlier
(use interview teams, present respondents with alterna-
tive decision scenarios, use a “consultant” respondent for
verification).
Similarly, more data integrity checks would benefit
Wilson and Vlosky’s [15] work since multiple interviews
were the only source of data. However, in their defense,
most of the cases were written by teams of academic pro-
fessionals who have a relatively high degree of knowl-
edge about and experience with validity issues. We
would have less confidence in their conclusions if a “stu-
dent worker” or other novice individual had been em-
ployed to collect the data. The bottom line, though, is that
more formal controls on data collection (as suggested ear-
lier) would only improve DFA studies and should be
given serious consideration.
CONCLUSION: CONTRIBUTIONS AND
FUTURE RESEARCH
The contribution of this article is to illustrate and ad-
vocate the use of DFA in business marketing research.
Detailed examples [15, 16] are presented as a tutorial to
illustrate the technique in theory comparison and theory
building applications. This explication of the technique is
important because although the approach was originally
described by Campbell [4], he never, in any of his writ-
ings, provided a field study application of the method.
Similarly, other case methodologists [1, 2] mention DFA
briefly but provide no examples.
Much potential exists for DFA in business market re-
search. For example, a DFA examination of the major
paradigms used to frame relationship marketing studies
would be interesting. Research in relationship marketing
229
has been grounded in overarching, global paradigms such
as exchange theory, transaction cost analysis, game the-
ory, and organizational governance theory. When are
these models applicable and in which contexts in rela-
tionship marketing? By developing a prediction matrix
from these paradigms, theory comparison studies (similar
to those described in this article) are possible.
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