Learning Objectives

•  Survey the triangulation strategies listed in Norman Denzin’s taxonomy (Table 2)
• Identify which of the strategies are the more commonly used and contemplate the reasons for their frequency.
• Take note of the difficulty (and risks) inherent in theory triangulation and between-method triangulation – two of the hardest strategies. Reflect on what sort of plans could be installed to overcome this difficulty.
•  Become familiar with Martyn Hammersley’s four types of triangulation logics. 
•  Understand why case units are called “units of analysis” even though the initial analytic steps do not necessarily involve unit-frameworks directly.  

Research Rigor through Triangulation

As the history in Module 2 previewed, the systematic rigor of case studies has been greatly enhanced by the introduction triangulation strategies in the latter half of the 20^th century. Norman Denzin provided the taxonomy for these strategies in his second edition of The Research Act (1978), differentiating between “data triangulation,” “investigator triangulation,” “theory triangulation,” “within method triangulation,” “between method triangulation,” and “multiple triangulation” (see Table 2 below). Robert Yin, the scientist generally credited with reviving the case study tradition, suggested in the 1980s to enhance the data analysis through pattern-matching and time-series strategies (Yin, 1989, 1984, 1981[a], 1981[b]), but has since relocated these approaches within the larger discussion of “data triangulation” and “methods triangulation” (Yin, 1994, 2003). 

TABLE 2: Denzin’s Taxonomy for Triangulation Strategies  

Data Source Triangulation

Probably the most common form of triangulation is data source triangulation since the case study approach assumes multiple access points to the social system. The researcher could identify two or more geographical settings (space bracketing), two or more historical processes (time bracketing), or two or more institutions, organizations, or programs (institution/program bracketing). Additionally, the researcher could choose to triangulate between multiple individuals or groups (individual bracketing, group bracketing), which is sometimes also called “perspective” triangulation given that the cross-referencing takes place between the perspectives of individuals or grouping. Lastly, the researcher could triangulate between two or more material holdings of data (such as the records collected from Archive A and Archive B), which constitute a single method of collection but distinct sources. Each of these pre-identified “sources” is expected to yield sufficient data for analysis, such that a thorough cross-referencing can take place at the end, whether through qualitative coding, pattern matching, descriptive statistics, or some other analytic format. In short, the study’s research questions can only be sufficiently answered by drawing meaning (codes/themes or patterns) from each pre-identified source (e.g., Place A and Place B, or Group A and Group B), and then synthesizing this meaning into a holistic narrative.  

Data sources chosen for triangulation often align with the case units for study, but this is not always necessary. For example, a researcher could examine two community college systems in a metropolitan area, assigning each system as a separate case unit, and then triangulate the data for multiple campus satellites in each college system. The resulting strategy would be a “within case” analysis that also triangulates between multiple settings (a “space bracketed” data triangulation). It might go so far as to conduct both “within case” and “cross case” analyses, using the results of initial triangulations to perform an additional round of analysis between the case units themselves (if the two college systems are expected to be sufficiently similar).   

FIGURE 11 – Example of Data Source Triangulation, Bracketed by Space

Investigator Triangulation

The use of multiple researchers (or teams) would be extremely rare at the doctoral dissertation level, since most academic departments expect their doctoral candidates to demonstrate independent scholarship, and hence avoid issues of co-authorship and divisions-of-labor. Beyond the doctoral level, however, there could be a variety of reasons to employ investigator triangulation. Perhaps the case study is of an interdisciplinary nature and will therefore triangulate between a sociologist and anthropologist’s data collection. Or perhaps the study is of international in scope and will therefore triangulate between a domestic research team and overseas research team. The case study could also be tied to a “Community-Based Participatory Research” (CBPR) project that has multiple stakeholders or partners, and therefore involves multiple research teams in the field. Whatever the strategy, the plan would require that each researcher (or team) generate sufficient data to allow for cross-check analysis in the end. In other words, the study’s primary research questions must be sufficiently answered by drawing meaning (codes/themes or patterns) from each researcher or team’s dataset. 

Theory Triangulation 

Theory triangulation became popular in the 1980s and 90s as a result of federally funded research on policy issues and programs, especially in education and human services (Fielding, 2005; Yin, 2000; Smith & Kleine, 1986; Yin, 1981[b]). In this strategy, the researcher pre-identifies a set of theories pertaining to the phenomenon and designs the sampling/data collection in such a way that produces data with strong theoretical relevance. For example, the researcher might design two sets of screening questionnaires and corresponding interview instruments, each meant to yield data for a distinct theoretical foundation. After the data collection, the researcher would need to analyze across the datasets to establish the relevance for each theory. The logic of the triangulation would depend entirely on the study’s aim: some theory triangulations seek to capture realism/objectivity, while other theory triangulations seek to assess points of contact/synthesis or points of divergence/conflict. The word “theory” should not be taken too literally here, as researchers may pursue a triangulation of conceptual models, or even social/cultural narratives (if postmodern in design). 

Studies with theory triangulation are notoriously difficult to execute and carry a high risk for the novice researcher. They tend to place significant pressure on the researcher to operationalize each theory in the sampling and data collection. Moreover, even if the researcher succeeds in operationalizing the theories, there could still be unforeseen factors that diminish the theoretical relevance of the data (e.g., the sample may be knowledgeable of the theories, but feel institutional pressure to provide terse responses or negatively characterize the theories). The absence of theory-richness in the dataset could mean research failure since a theory triangulation would not be possible. 

Methodological Triangulation 

Most case studies involve some form of methodological triangulation. Using “within method” triangulation, for example, the researcher would pursue a single methodological paradigm – e.g., qualitative research only – and administer different methods of qualitative data collection: interviews, field observations, archival records collection, focus group sessions, questionnaires, and so forth. Remember that epistemology plays a significant role in determining which methods are “qualitative”; a Likert-scaled questionnaire could be “qualitative” if the epistemic value of the questionnaire is to help complete a holistic narrative (rather than produce statistically valid data for a population-level). The triangulation would then be carried out between the resulting datasets in each method.   

Conversely, for “between method” triangulation, the researcher would need to incorporate data collection methods from both qualitative and quantitative paradigms. For instance, a researcher who plans to conduct a program evaluation might select a pre-test, a post-test, and qualitative interviews during the program’s implementation. The pre/post-tests both align to a quantitative paradigm because they require the use of statistical analyses to arrive at objective snapshots of the “pre” and “post” situation. The interviews, on the other hand, align to a qualitative paradigm because they imply the use of coding and thematic analysis to arrive at an inter-subjective account of participants’ views during the program. The researcher will then have to triangulate across the epistemic divide, comparing statistical results (and objectivist claims) with thematic results (and subjectivist claims). This is the challenge of what is now called “Mixed-Methods Research” (or MMR), in that researchers have to formulate strategies for how to bridge across epistemic differences within the data and results (Denzin, 2012; Teddlie & Tashakkori, 2011; Bergman, 2008). 

Triangulation Logic 

Martyn Hammersley identified four main kinds of logic to support triangulation in qualitative or mixed-methods research (2008, pp. 22-36). The first is a “validation” logic, which seeks to perform a cross-check of some kind to achieve realism or objectivity in the results. The second is a “complementarity” logic, which seeks to perform a cross-check to identify complementary raw data or complementary analytic results (codes/themes or patterns). The third is an “epistemic dialogue” logic, which seeks to perform a cross-check to achieve points of contact between contrasting epistemologies (such as the positivism of quantitative studies and interpretivism of qualitative studies – see Module 3 for details). This sort of logic is common to the MMR genre, and hence “between methods” triangulation. The fourth is a “contingency” logic and is actually a restatement of Aaron Cicourel’s “indefinite triangulation” strategy (Cicourel, 1974). According to this logic, the temporal dimension of the data collection cannot be trusted because of the many contingencies that occur in naturalistic inquiry (e.g., on a given day, a sample of nurses may work longer hours and feel less enthusiastic about their interviews, and thus offer unfavorable views of their jobs). To understand these contingencies, the researcher is encouraged to conduct iterative data collection at varying points in time, and then cross-check between these datasets. Contrary to the “validation” logic, the goal of this “contingency” logic is not to establish realism; but rather, to understand why the participants expressed differing views at distinct moments in time (even after being presented with the same protocols for data collection).   

Confusion about “Unit of Analysis”

There are authors who, in rare instances, distinguish between the “case unit” and “unit of analysis,” but this far from a common practice, as methodologists generally try to avoid sowing confusion (Thomas, 2011, p. 513; VanWynsberghe & Khan, 2007, p. 87). Wieviorka (1992, p. 160) and others confirm that the case unit is indeed the final unit of analysis. Once all the data have been subjected to a triangulation style analysis (whether by sources, methods, or such), the resulting codes/themes or patterns still have to be analyzed for their relationship to the case units themselves. This analysis usually takes place during the answering of the main research questions. Novice researchers and graduate students sometimes get confused by the phrase “unit of analysis” because, in their eyes, the most immediate analytic steps do not involve the case units; they instead involve the forms of triangulation described above. To be clear, though, the final step is always to connect the analytic results (codes/themes or patterns) back to the cases themselves and use those connections to answer the questions that guided the study. 

References

Bergman, M. (Ed.) (2008). Advances in Mixed Methods Research: Theories and Applications. Thousand Oaks: SAGE.

Cicourel, A. V. (1974). Cognitive Sociology. New York: Free Press.

Denzin, N. K. (1978). The Research Act: A Theoretical Introduction to Sociological Methods (2^nd ed.). Chicago: Aldine.

Denzin, N. K. (2012). Triangulation 2.0. Journal of Mixed Methods Research 6 (2): 80-88.

Fielding, N. G. (2005). The resurgence, legitimation, and institutionalization of qualitative methods. Forum: Qualitative Social Research 6 (2). Retrieved from: 

 http://www.qualitative-research.net/index.php/fqs/article/view/455

Hammersley, M. (2008). Troubles with triangulation. In M. Bergman (Ed.), Advances in Mixed Methods Research: Theories and Applications (pp. 22-36). Thousand Oaks: SAGE.

Smith, L. R., & Kleine, P. F. (1986). Qualitative research and evaluation: triangulation and multimethods reconsidered. New Directions for Evaluation 30 (2): 55-71

Teddlie, C., & Tashakkori, A. (2011). Mixed methods research contemporary issues in an emerging field. In N. K. Denzin & Y. S. Lincoln (Eds.), Handbook of Qualitative Research (4^th ed., 285-300). Thousand Oaks: SAGE.

Thomas, G. (2011). A typology for the case study in social science following a review of definition, discourse, and structure. Qualitative Inquiry 17 (6): 511-21. 

Wieviorka, M. (1992). Case studies: history or sociology? In C. C. Ragin & H. S. Becker (Eds.), What is a Case? Exploring the Foundations of Social Inquiry (pp. 159-72). Cambridge, UK: Cambridge Univ. Press.

VanWynsberghe, R., & Khan, S. (2007). Redefining case study. International Journal of Qualitative Methods 6 (2): 80-94.

Yin, R. K. (1981[a]). The case study crisis: some answers. Administrative Science Quarterly 26 (1): 58-65.

Yin, R. K. (1981[b]). The case study as a serious research strategy. Science Communication 3 (1): 97-114.

Yin, R. K. (1984). Case Study Research: Design and Methods (1^st ed.). Thousand Oaks: SAGE.

Yin, R. K. (1989). Case Study Research: Design and Methods (1^st ed., Revised). Thousand Oaks: SAGE.

Yin, R. K. (1994). Case Study Research: Design and Methods (2^nd ed.). Thousand Oaks: SAGE.

Yin, R. K. (2000). Case study evaluations: a decade of progress. In D. L. Stufflebeam, G. F. Madaus, & T. Kellaghan (Eds.), Evaluation Models: Viewpoints on Education and Human Services Evaluation (pp. 185-94). Dordrecht: Kluwer Academic. 

Yin, R. K. (2002). Case Study Research: Design and Methods (3^rd ed.). Thousand Oaks: SAGE.