In computational geometry, polygon triangulation is the decomposition of a polygonal area (simple polygon) P into a set of triangles, i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P.
Triangulations may be viewed as special cases of planar straight-line graphs. When there are no holes or added points, triangulations form maximal outerplanar graphs.
Over time a number of algorithms have been proposed to triangulate a polygon.
It is trivial to triangulate any convex polygon in linear time into a fan triangulation, by adding diagonals from one vertex to all other vertices.
The total number of ways to triangulate a convex n-gon by non-intersecting diagonals is the (n − 2)-th Catalan number, which equals , a solution found by Leonhard Euler.
A monotone polygon can be triangulated in linear time with either the algorithm of A. Fournier and D.Y. Montuno, or the algorithm of Godfried Toussaint.
Ear clipping method
One way to triangulate a simple polygon is based on the two ears theorem, the fact that any simple polygon with at least 4 vertices without holes has at least two 'ears', which are triangles with two sides being the edges of the polygon and the third one completely inside it. The algorithm then consists of finding such an ear, removing it from the polygon (which results in a new polygon that still meets the conditions) and repeating until there is only one triangle left.
This algorithm is easy to implement, but slower than some other algorithms, and it only works on polygons without holes. An implementation that keeps separate lists of convex and concave vertices will run in O(n2) time. This method is known as ear clipping and sometimes ear trimming. An efficient algorithm for cutting off ears was discovered by Hossam ElGindy, Hazel Everett, and Godfried Toussaint.
Using monotone polygons
A simple polygon may be decomposed into monotone polygons as follows.
For each point, check if the neighboring points are both on the same side of the 'sweep line', a horizontal or vertical line on which the point being iterated lies. If they are, check the next sweep line on the other side. Break the polygon on the line between the original point and one of the points on this one.
Note that if you are moving downwards, the points where both of the vertices are below the sweep line are 'split points'. They mark a split in the polygon. From there you have to consider both sides separately.
Using this algorithm to triangulate a simple polygon takes O(n log n) time.
Dual graph of a triangulation
A useful graph that is often associated with a triangulation of a polygon is the dual graph. Given a triangulation of , one defines the graph () as the graph whose vertex set are the triangles of , two vertices (triangles) being adjacent if and only if they share a diagonal. It is easy to observe that () is a tree with maximum degree 3.
Until 1988, whether a simple polygon can be triangulated faster than O( log ) time was an open problem in computational geometry. Then, Tarjan & Van Wyk (1988) discovered an O( log log )-time algorithm for triangulation, later simplified by Kirkpatrick, Klawe & Tarjan (1992). Several improved methods with complexity O( log*) (in practice, indistinguishable from linear time) followed.
Bernard Chazelle showed in 1991 that any simple polygon can be triangulated in linear time, though the proposed algorithm is very complex. A simpler randomized algorithm with linear expected time is also known.
Seidel's decomposition algorithm and Chazelle's triangulation method are discussed in detail in Li & Klette (2011). 
The time complexity of triangulation of an -vertex polygon with holes has an Ω( log )lower bound.
Minimum-weight triangulation is a triangulation in which the goal is to minimize the total edge length, rather than the number of triangles.
Both triangulation problems are a special case of triangulation (geometry) and a special case of polygon partition.
A point set triangulation is a polygon triangulation of the convex hull of a set of points. A Delaunay triangulation is another way to create a triangulation based on a set of points.
A related problem is polygon triangle covering, in which the triangles may overlap. Another related problem is tiling by polygons, where the goal is to cover the entire plane with polygons of pre-specified shapes.
- ^ abcdMark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf (2000), Computational Geometry (2nd revised ed.), Springer-Verlag, ISBN 3-540-65620-0 Chapter 3: Polygon Triangulation: pp.45–61.
- ^Pickover, Clifford A., The Math Book, Sterling, 2009: p. 184.
- ^Fournier, A.; Montuno, D. Y. (1984), "Triangulating simple polygons and equivalent problems", ACM Transactions on Graphics, 3 (2): 153–174, doi:10.1145/357337.357341, ISSN 0730-0301
- ^Toussaint, Godfried T. (1984), "A new linear algorithm for triangulating monotone polygons," Pattern Recognition Letters, 2 (March):155–158.
- ^Meisters, G. H., "Polygons have ears." American Mathematical Monthly 82 (1975). 648–651
- ^ElGindy, H.; Everett, H.; Toussaint, G. T. (1993). "Slicing an ear using prune-and-search". Pattern Recognition Letters. 14 (9): 719–722. doi:10.1016/0167-8655(93)90141-y.
- ^Tarjan, Robert E.; Van Wyk, Christopher J. (1988), "An O(n log log n)-time algorithm for triangulating a simple polygon", SIAM Journal on Computing, 17 (1): 143–178, doi:10.1137/0217010, MR 0925194 .
- ^Kirkpatrick, David G.; Klawe, Maria M.; Tarjan, Robert E. (1992), "Polygon triangulation in O(n log log n) time with simple data structures", Discrete and Computational Geometry, 7 (4): 329–346, doi:10.1007/BF02187846, MR 1148949 .
- ^Clarkson, Kenneth L.; Tarjan, Robert; van Wyk, Christopher J. (1989), "A fast Las Vegas algorithm for triangulating a simple polygon", Discrete and Computational Geometry, 4: 423–432, doi:10.1007/BF02187741 .
- ^Seidel, Raimund (1991), "A Simple and Fast Incremental Randomized Algorithm for Computing Trapezoidal Decompositions and for Triangulating Polygons", Computational Geometry: Theory and Applications, 1: 51–64, doi:10.1016/0925-7721(91)90012-4
- ^Clarkson, Kenneth L.; Cole, Richard; Tarjan, Robert E. (1992), "Randomized parallel algorithms for trapezoidal diagrams", International Journal of Computational Geometry & Applications, 2 (2): 117–133, doi:10.1142/S0218195992000081, MR 1168952 .
- ^Chazelle, Bernard (1991), "Triangulating a Simple Polygon in Linear Time", Discrete & Computational Geometry, 6: 485–524, doi:10.1007/BF02574703, ISSN 0179-5376
- ^Amato, Nancy M.; Goodrich, Michael T.; Ramos, Edgar A. (2001), "A Randomized Algorithm for Triangulating a Simple Polygon in Linear Time", Discrete & Computational Geometry, 26 (2): 245–265, doi:10.1007/s00454-001-0027-x, ISSN 0179-5376
- ^Li, Fajie; Klette, Reinhard (2011), Euclidean Shortest Paths, Springer, doi:10.1007/978-1-4471-2256-2, ISBN 978-1-4471-2255-5 .
Not to be confused with qualitative data.
For the journal, see Qualitative Research (journal).
Qualitative research is a method of inquiry employed in many different academic disciplines, including in the social sciences and natural sciences, but also in non-academic contexts including market research, business, and service demonstrations by non-profits.
Qualitative research is a broad methodological approach that encompasses many research methods. The aim of qualitative research may vary with the disciplinary background, such as a psychologist seeking to gather an in-depth understanding of human behavior and the reasons that govern such behavior. Qualitative methods examine the why and how of decision making, not just what, where, when, or "who", and have a strong basis in the field of sociology to understand government and social programs. Qualitative research is popular among political science, social work, and special education and education researchers.
In the conventional view of statisticians, qualitative methods produce information only on the particular cases studied (e.g., ethnographies paid for by governmental funds which may involve research teams), and any more general conclusions are considered propositions (informed assertions).Quantitative methods can then be used to seek empirical support for such research hypotheses.
In contrast, a qualitative researcher holds that understanding of a phenomenon or situation or event comes from exploring the totality of the situation (e.g., phenomenology, symbolic interactionism), often with access to large amounts of "hard data". It may begin as a grounded theory approach with the researcher having no previous understanding of the phenomenon; or the study may commence with propositions and proceed in a scientific and empirical way throughout the research process (e.g., Bogdan & Taylor, 1990).
A popular method of qualitative research is the case study (e.g., Stake, 1995)  or (Yin, 1989) which examines in depth "purposive samples" to better understand a phenomenon (e.g., support to families; Racino, 1999); hence, smaller but focused samples are more often used than large samples which may also be conducted by the same or related researchers or research centers (e.g., Braddock, et al., 1995).
Qualitative methods are an integral component of the five angles of analysis fostered by the data percolation methodology, which also includes quantitative methods, reviews of the literature (including scholarly), interviews with experts and computer simulation, and which forms an extension of data triangulation.
To help navigate the heterogeneous landscape of qualitative research, one can further think of qualitative inquiry in terms of 'means' and 'orientation' (Pernecky, 2016).
Robert Bogdan in his advanced courses on qualitative research traces the history of the development of the fields, and their particular relevance to disability and including the work of his colleague Robert Edgerton and a founder of participant observation, Howard S. Becker. As Robert Bogdan and Sari Biklen describe in their education text, "historians of qualitative research have never, for instance, included Freud or Piaget as developers of the qualitative approach, yet both relied on case studies, observations and indepth interviewing".
In the early 1900s, some researchers rejected positivism, the theoretical idea that there is an objective world which we can gather data from and "verify" this data through empiricism. These researchers embraced a qualitative research paradigm, attempting to make qualitative research as "rigorous" as quantitative research and creating myriad methods for qualitative research. Of course, such developments were necessary as qualitative researchers won national center awards, in collaboration with their research colleagues at other universities and departments; and university administrations funded Ph.D.s in both arenas through the ensuing decades. Most theoretical constructs involve a process of qualitative analysis and understanding, and construction of these concepts (e.g., Wolfensberger's social role valorization theories).
In the 1970s and 1980s, the increasing ubiquity of computers aided in qualitative analyses, several journals with a qualitative focus emerged, and postpositivism gained recognition in the academy. In the late 1980s, questions of identity emerged, including issues of race, class, gender, and discourse communities, leading to research and writing becoming more reflexive. Throughout the 1990s, the concept of a passive observer/researcher was rejected, and qualitative research became more participatory and activist-oriented with support from the federal branches, such as the National Institute on Disability Research and Rehabilitation (NIDRR) of the US Department of Education (e.g., Rehabilitation Research and Training Centers for Family and Community Living, 1990). Also, during this time, researchers began to use mixed-method approaches, indicating a shift in thinking of qualitative and quantitative methods as intrinsically incompatible. However, this history is not apolitical, as this has ushered in a politics of "evidence" (e.g., evidence-based practices in health and human services) and what can count as "scientific" research in scholarship, a current, ongoing debate in the academy.
Data collection, analysis and field research design
Qualitative researchers face many choices for techniques to generate data ranging from grounded theory development and practice, narratology, storytelling, transcript poetry, classical ethnography, state or governmental studies, research and service demonstrations, focus groups, case studies, participant observation, qualitative review of statistics in order to predict future happenings, or shadowing, among many others. Qualitative methods are used in various methodological approaches, such as action research which has sociological basis, or actor-network theory.
The most common method used to generate data in qualitative research is an interview which may be structured, semi-structured or unstructured. Other ways to generate data include group discussions or focus groups, observations, reflective field notes, texts, pictures, and other materials. Very popular among qualitative researchers are the studies of photographs, public and official documents, personal documents, and historical items in addition to images in the media and literature fields.
To analyse qualitative data, the researcher seeks meaning from all of the data that is available. The data may be categorized and sorted into patterns (i.e., pattern or thematic analyses) as the primary basis for organizing and reporting the study findings (e.g., activities in the home; interactions with government). Qualitative researchers, often associated with the education field, typically rely on the following methods for gathering information: Participant Observation, Non-participant Observation, Field Notes, Reflexive Journals, Structured Interview, Semi-structured Interview, Unstructured Interview, and Analysis of documents and materials.
The ways of participating and observing can vary widely from setting to setting as exemplified by Helen Schwartzman's primer on Ethnography in Organizations (1993). or Anne Copeland and Kathleen White's "Studying Families" (1991). Participant observation is a strategy of reflexive learning, not a single method of observing. and has been described as a continuum of between participation and observation. In participant observation researchers typically become members of a culture, group, or setting, and adopt roles to conform to that setting. In doing so, the aim is for the researcher to gain a closer insight into the culture's practices, motivations, and emotions. It is argued that the researchers' ability to understand the experiences of the culture may be inhibited if they observe without participating.
The data that is obtained is streamlined (texts of thousands of pages in length) to a definite theme or pattern, or representation of a theory or systemic issue or approach. This step in a theoretical analysis or data analytic technique is further worked on (e.g., gender analysis may be conducted; comparative policy analysis may be developed). An alternative research hypothesis is generated which finally provides the basis of the research statement for continuing work in the fields.
Some distinctive qualitative methods are the use of focus groups and key informant interviews, the latter often identified through sophisticated and sometimes, elitist, snowballing techniques. The focus group technique (e.g., Morgan, 1988) involves a moderator facilitating a small group discussion between selected individuals on a particular topic, with video and handscribed data recorded, and is useful in a coordinated research approach studying phenomenon in diverse ways in different environments with distinct stakeholders often excluded from traditional processes. This method is a particularly popular in market research and testing new initiatives with users/workers.
The research then must be "written up" into a report, book chapter, journal paper, thesis or dissertation, using descriptions, quotes from participants, charts and tables to demonstrate the trustworthiness of the study findings.
Specialized uses of qualitative research
Qualitative methods are often part of survey methodology, including telephone surveys and consumer satisfaction surveys.
In fields that study households, a much debated topic is whether interviews should be conducted individually or collectively (e.g. as couple interviews).
One traditional and specialized form of qualitative research is called cognitive testing or pilot testing which is used in the development of quantitative survey items. Survey items are piloted on study participants to test the reliability and validity of the items. This approach is similar to psychological testing using an intelligence test like the WAIS (Wechsler Adult Intelligence Survey) in which the interviewer records "qualitative" (i.e., clinical observations)throughout the testing process. Qualitative research is often useful in a sociological lens. Although often ignored, qualitative research is of great value to sociological studies that can shed light on the intricacies in the functionality of society and human interaction.
There are several different research approaches, or research designs, that qualitative researchers use. In the academic social sciences, the most frequently used qualitative research approaches include the following points:
- Basic/generic/pragmatic qualitative research, which involves using an eclectic approach taken up to best match the research question at hand. This is often called the mixed-method approach.
- Ethnographic Research. An example of applied ethnographic research is the study of a particular culture and their understanding of the role of a particular disease in their cultural framework.
- Grounded Theory is an inductive type of research, based or "grounded" in the observations or data from which it was developed; it uses a variety of data sources, including quantitative data, review of records, interviews, observation and surveys.
- Phenomenology describes the "subjective reality" of an event, as perceived by the study population; it is the study of a phenomenon.
- Philosophical Research is conducted by field experts within the boundaries of a specific field of study or profession, the best qualified individual in any field of study to use an intellectual analysis, in order to clarify definitions, identify ethics, or make a value judgment concerning an issue in their field of study their lives.
- Critical Social Research, used by a researcher to understand how people communicate and develop symbolic meanings.
- Ethical Inquiry, an intellectual analysis of ethical problems. It includes the study of ethics as related to obligation, rights, duty, right and wrong, choice etc.
- Social Science and Governmental Research to understand social services, government operations, and recommendations (or not) regarding future developments and programs, including whether or not government should be involved.
- Activist Research which aims to raise the views of the underprivileged or "underdogs" to prominence to the elite or master classes, the latter who often control the public view or positions.
- Foundational Research, examines the foundations for a science, analyzes the beliefs, and develops ways to specify how a knowledge base should change in light of new information.
- Historical Research allows one to discuss past and present events in the context of the present condition, and allows one to reflect and provide possible answers to current issues and problems. Historical research helps us in answering questions such as: Where have we come from, where are we, who are we now and where are we going?
- Visual Ethnography. It uses visual methods of data collection, including photo, voice, photo elicitation, collaging, drawing, and mapping. These techniques have been used extensively as a participatory qualitative technique and to make the familiar strange.
- Autoethnography, the study of self, is a method of qualitative research in which the researcher uses their personal experience to address an issue.
The most common analysis of qualitative data is observer impression. That is, expert or bystander observers examine the data, interpret it via forming an impression and report their impression in a structured and sometimes quantitative form.
Main article: Coding (social sciences)
Coding is an interpretive technique that both organizes the data and provides a means to introduce the interpretations of it into certain quantitative methods. Most coding requires the analyst to read the data and demarcate segments within it, which may be done at different times throughout the process. Each segment is labeled with a "code" – usually a word or short phrase that suggests how the associated data segments inform the research objectives. When coding is complete, the analyst prepares reports via a mix of: summarizing the prevalence of codes, discussing similarities and differences in related codes across distinct original sources/contexts, or comparing the relationship between one or more codes.
Some qualitative data that is highly structured (e.g., open-ended responses from surveys or tightly defined interview questions) is typically coded without additional segmenting of the content. In these cases, codes are often applied as a layer on top of the data. Quantitative analysis of these codes is typically the capstone analytical step for this type of qualitative data. The most common form of coding is open-ended coding, while other more structured techniques such as axial coding or integration are described (Strauss & Corbin, 1990). However, more important than coding are qualities such as the "theoretical sensitivity" of the researcher.
Contemporary qualitative data analyses are sometimes supported by computer programs, termed Computer Assisted Qualitative Data Analysis Software which has replaced the detailed hand coding and labeling of the past decades. These programs do not supplant the interpretive nature of coding but rather are aimed at enhancing the analyst’s efficiency at data storage/retrieval and at applying the codes to the data. Many programs offer efficiencies in editing and revising coding, which allow for work sharing, peer review, and recursive examination of data. The university goals were to place such programs on computer mainframes and analyze large data sets which is not easily conducted past 1,000 to 2,000 pages of text.
Common Qualitative Data Analysis Software includes:
A frequent criticism of coding method by individuals from other research tracks is that it seeks to transform qualitative data into empirically valid data, which contain: actual value range, structural proportion, contrast ratios, and scientific objective properties; thereby draining the data of its variety, richness, and individual character. Analysts respond to this criticism by thoroughly expositing their definitions of codes and linking those codes soundly to the underlying data, therein bringing back some of the richness that might be absent from a mere list of codes.
Some qualitative datasets are analyzed without coding. A common method here is recursive abstraction, where datasets are summarized; those summaries are therefore furthered into summary and so on. The end result is a more compact summary that would have been difficult to accurately discern without the preceding steps of distillation.
A frequent criticism of recursive abstraction is that the final conclusions are several times removed from the underlying data. While it is true that poor initial summaries will certainly yield an inaccurate final report, qualitative analysts can respond to this criticism. They do so, like those using coding method, by documenting the reasoning behind each summary step, citing examples from the data where statements were included and where statements were excluded from the intermediate summary.
Coding and "thinking"
Some data analysis techniques, often referred to as the tedious, hard work of research studies similar to field notes, rely on using computers to scan and reduce large sets of qualitative data. At their most basic level, numerical coding relies on counting words, phrases, or coincidences of tokens within the data; other similar techniques are the analyses of phrases and exchanges in conversational analyses. Often referred to as content analysis, a basic structural building block to conceptual analysis, the technique utilizes mixed methodology to unpack both small and large corpuses. Content analysis is frequently used in sociology to explore relationships, such as the change in perceptions of race over time (Morning 2008), or the lifestyles of temporal contractors (Evans, et al. 2004). Content analysis techniques thus help to provide broader output for a larger, more accurate conceptual analysis.
Mechanical techniques are particularly well-suited for a few scenarios. One such scenario is for datasets that are simply too large for a human to effectively analyze, or where analysis of them would be cost prohibitive relative to the value of information they contain. Another scenario is when the chief value of a dataset is the extent to which it contains "red flags" (e.g., searching for reports of certain adverse events within a lengthy journal dataset from patients in a clinical trial) or "green flags" (e.g., searching for mentions of your brand in positive reviews of marketplace products). Many researchers would consider these procedures on their data sets to be misuse of their data collection and purposes.
A frequent criticism of mechanical techniques is the absence of a human interpreter; computer analysis is relatively new having arrived in the late 1980s to the university sectors. And while masters of these methods are able to write sophisticated software to mimic some human decisions, the bulk of the "analysis" is still nonhuman. Analysts respond by proving the value of their methods relative to either a) hiring and training a human team to analyze the data or b) by letting the data go untouched, leaving any actionable nuggets undiscovered; almost all coding schemes indicate probably studies for further research.
Data sets and their analyses must also be written up, reviewed by other researchers, circulated for comments, and finalized for public review. Numerical coding must be available in the published articles, if the methodology and findings are to be compared across research studies in traditional literature review and recommendation formats.
Distinct qualitative paradigms
Contemporary qualitative research has been conducted using a large number of paradigms that influence conceptual and metatheoretical concerns of legitimacy, control, data analysis, ontology, and epistemology, among others. Research conducted in the twenty-first century has been characterized by a distinct turn toward more interpretive, postmodern, and critical practices. Guba and Lincoln (2005) identify five main paradigms of contemporary qualitative research: positivism, postpositivism, critical theories, constructivism, and participatory/cooperative paradigms. Each of the paradigms listed by Guba and Lincoln are characterized by axiomatic differences in axiology, intended action of research, control of research process/outcomes, relationship to foundations of truth and knowledge, validity (see below), textual representation and voice of the researcher/participants, and commensurability with other paradigms. In particular, commensurability involves the extent to which paradigmatic concerns "can be retrofitted to each other in ways that make the simultaneous practice of both possible". Positivist and post positivist paradigms share commensurable assumptions but are largely incommensurable with critical, constructivist, and participatory paradigms. Likewise, critical, constructivist, and participatory paradigms are commensurable on certain issues (e.g., intended action and textual representation).
Qualitative research in the 2000s also has been characterized by concern with everyday categorization and ordinary storytelling. This "narrative turn" is producing an enormous literature as researchers present sensitizing concepts and perspectives that bear especially on narrative practice, which centers on the circumstances and communicative actions of storytelling. Catherine Riessman (1993) and Gubrium and Holstein (2009) provide analytic strategies, and Holstein and Gubrium (2012) present the variety of approaches in recent comprehensive texts. Relatedly, narrative practice increasingly takes up the institutional conditioning of narrative practice (see Gubrium and Holstein 2000).
A central issue in qualitative research is trustworthiness (also known as credibility, or in quantitative studies, validity). There are many different ways of establishing trustworthiness, including: member check, interviewer corroboration, peer debriefing, prolonged engagement, negative case analysis, auditability, confirmability, bracketing, and balance. Most of these methods are described in Lincoln and Guba (1985). As exemplified by researchers Preston Teeter and Jorgen Sandberg, data triangulation and eliciting examples of interviewee accounts are two of the most commonly used methods of establishing trustworthiness in qualitative studies. Dependability is equivalent to the notion of reliability in quantitative methods and is the extent to which two or more people are likely to come to the same conclusions by examining the same evidence. Again, Lincoln and Guba (1985) is the salient reference.
Qualitative research journals
By the end of the 1970s many leading journals began to publish qualitative research articles and several new journals emerged which published only qualitative research studies and articles about qualitative research methods. In the 1980s and 1990s, the new qualitative research journals became more multidisciplinary in focus moving beyond qualitative research’s traditional disciplinary roots of anthropology, sociology, and philosophy. In the late 1980s to 1990s, early academic articles emerged beginning the transformation from institutional studies (e.g., Taylor's "Let them eat programs") to studies of community, community services and community life reviewed and cited in professional journals. These studies ranged from extremely controversial concerns involving the death penalty and disability (Bogdan, 1995) to the efforts of families with service providers (O'Connor, 1995)  to the government divisions which regulate families by "coming to take" the children away (Taylor, 1995).
Qualitative research in psychology
Wilhelm Wundt, the founder of scientific psychology, was one of the first psychologists to conduct qualitative research. Early examples of his qualitative research were published in 1900 through 1920, in his 10-volume study, Völkerpsychologie (translated to: Social Psychology). Wundt advocated the strong relation between psychology and philosophy. He believed that there was a gap between psychology and quantitative research that could only be filled by conducting qualitative research. Qualitative research dove into aspects of human life that could not adequately be covered by quantitative research; aspects such as culture, expression, beliefs, morality and imagination.
There are records of qualitative research being used in psychology before World War II, but prior to the 1950s, these methods were viewed as invalid. Owing to this, many of the psychologists who practiced qualitative research denied the usage of such methods or apologized for doing so. It was not until the late 20th century when qualitative research was accepted in elements of psychology though it remains controversial. The excitement about the groundbreaking form of research was short-lived as few novel findings emerged which gained attention. Community psychologists felt they didn't get the recognition they deserved. A selection of autobiographical narratives of community psychologists can be found in "Six Community Psychologists Tell Their Stories: History, Contexts and Narratives" (Kelly & Song, 2004), including the well known Julian Rappaport.
- ^Denzin, Norman K.; Lincoln, Yvonna S., eds. (2005). The Sage Handbook of Qualitative Research (3rd ed.). Thousand Oaks, CA: Sage. ISBN 0-7619-2757-3.
- ^"The rise and relevance of qualitative research". International Journal of Social Research Methodology. 13: 139–155. doi:10.1080/13645570902966056.
- ^Bogdan, R.; Taylor, S. (1987). "Looking at the bright side: A positive approach to qualitative policy and evaluation research". Qualitative Sociology. 13 (2): 183–192. doi:10.1007/BF00989686.
- ^Stake, R. (1995). The art of case study research. Thousand Oaks, CA: Sage.
- ^Yin, R. (1989). Case Study Research: Design and Methods. Newbury Park, CA: Sage. ISBN 0-8039-3470-X.
- ^Racino, J. (1999). Policy, Program Evaluation and Research in Disability: Community Support for All. London: Haworth Press. ISBN 0-7890-0597-2.
- ^Braddock, D.; Bachelder, L.; Hemp, R.; Fujiura, G. (1995). The State of the States in Developmental Disabilities (4th ed.). Washington, DC: American Association on Mental Retardation.
- ^Mesly, Olivier (2015). Creating Models in Psychological Research. United States: Springer Psychology: 126 pages. ISBN 978-3-319-15752-8
- ^PERNECKY, T. (2016). Epistemology and Metaphysics for Qualitative Research. London, UK: SAGE Publication
- ^Becker, H. S. (1970). "Whose Side Are We On?". Sociological Work: Method and Substance. Chicago: Aldine. pp. 123–134. ISBN 0-87855-630-3.
- ^Bogdan, R. C.; Biklen, S. (1982). Qualitative Research for Education: An Introduction to Theory and Methods. Boston: Allyn & Bacon. p. 14. ISBN 0-205-07695-5.
- ^Wolfensberger, W. (1994). "A Brief Introduction to Social Role Valorization as High-Order Concept for Structuring Human Services" (2nd Edition). Syracuse, NY: Training Institute for Human Service Planning, Leadership and Change Agentry, Syracuse University.
- ^Glaser, B.G. & Strauss, A.I. (1967). "The Discovery of Grounded Theory: Strategies for Qualitative Research". NY, NY: Aldine DeGruyter.
- ^Savin-Baden, M.; Major, C. (2013). Qualitative Research: The Essential Guide to Theory and Practice. London: Routledge.
- ^Taylor, S. J.; Bogdan, R. (1984). Introduction to Qualitative Research Methods: The Search for Meanings (2nd ed.). Singapore: John Wiley and Sons.
- ^Racino, J.; O'Connor, S. (1994). "'A home of my own': Homes, neighborhoods and personal connections". In Hayden, M.; Abery, B. Challenges for a Service System in Transition: Ensuring Quality Community Experiences for Persons with Developmental Disabilities. Baltimore, MD: Paul H. Brookes. pp. 381–403. ISBN 1-55766-125-1.
- ^Marshall, Catherine & Rossman, Gretchen B. (1998). Designing Qualitative Research. Thousand Oaks, CA: Sage. ISBN 0-7619-1340-8
- ^Bogdan, R.; Ksander, M. (1980). "Policy data as a social process: A qualitative approach to quantitative data". Human Organization. 39 (4): 302–309. doi:10.17730/humo.39.4.x42432981487k54q.
- ^Schwartzman, H.B. (1993). "Ethnography in Organizations". Qualitative Research Methods Series 27. Thousand Oaks, CA: SAGE.
- ^Copeland, A.P. (1991). "Studying Families". Applied Social Research Methods Series, Volume 27. Thousand Oaks, CA: SAGE.
- ^Lindlof, T. R., & Taylor, B. C. (2002) Qualitative communication research methods: Second edition. Thousand Oaks, CA: Sage Publications, Inc. ISBN 0-7619-2493-0
- ^"Qualitative Research Methods: A Data Collector's Field Guide"(PDF). techsociety.com. Retrieved 7 October 2010.
- ^Morgan, D. (1988). Focus Groups as Qualitative Research. Qualitative Research Methods Series. 16. Thousand Oaks, CA: Sage. ISBN 0-8039-3208-1.
- ^Valentine, G (1999). "Doing household research: Interviewing couples together and apart". Area. 31 (1): 67–74. doi:10.1111/j.1475-4762.1999.tb00172.x.
- ^Bjørnholt, M; Farstad, G.R. (2012). "'Am I rambling?' On the advantages of interviewing couples together"(PDF). Qualitative Research. 14 (1): 3–19. doi:10.1177/1468794112459671.
- ^Creswell, John (2006). Qualitative Inquiry and Research Design: Choosing among Five Approaches. Sage.
- ^Creswell, John (2008). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches. Sage.
- ^Ralph, N.; Birks, M.; Chapman, Y. (29 September 2014). "Contextual Positioning: Using Documents as Extant Data in Grounded Theory Research". SAGE Open. 4 (3). doi:10.1177/2158244014552425.
- ^Gill, M. J. (2014). The Possibilities of Phenomenology for Organizational Research. Organizational Research Methods, 17:2, 118-137.
- ^Mannay, D. 2013. ‘Who put that on there... why why why?:’ Power games and participatory techniques of visual data production. Visual Studies, 28 (2), pp.136-146
- ^Mannay, D. (2010). "Making the familiar strange: Can visual research methods render the familiar setting more perceptible?". Qualitative Research. 10 (1): 91–111. doi:10.1177/1468794109348684.
- ^MIT study on the scope of observer impression in qualitative research(MIT qualitative research)
- ^Saladana, Johnny (2012). The Coding Manual for Qualitative Researchers. Sage. ISBN 1446247376.
- ^Strauss, A. & Corbin, J. (1990). Basics of Qualitative Research: Grounded Theory Procedures and Techniques. New Delhi: Sage.
- ^Morning, Ann (2008). "Reconstructing Race in Science and Society: Biology Textbooks, 1952-2002". American Journal of Sociology.
- ^Evans, James (2004). "Beach Time, Bridge Time and Billable Hours: The Temporal Structure of Temporal Contracting"(PDF). Administrative Science Quarterly. 49: 1–38. JSTOR 4131454.
- ^ abGuba, E. G., & Lincoln, Y. S. (2005). "Paradigmatic controversies, contradictions, and emerging influences" In N. K. Denzin & Y. S. Lincoln (Eds.), The Sage Handbook of Qualitative Research (3rd ed.), pp. 191-215. Thousand Oaks, CA: Sage. ISBN 0-7619-2757-3
- ^Guba, E. G., & Lincoln, Y. S. (2005). "Paradigmatic controversies, contradictions, and emerging influences" (p. 200). In N. K. Denzin & Y. S. Lincoln (Eds.), The Sage Handbook of Qualitative Research (3rd ed.), pp. 191-215. Thousand Oaks, CA: Sage. ISBN 0-7619-2757-3
- ^Lincoln Y and Guba EG (1985) Naturalistic Inquiry, Sage Publications, Newbury Park, CA.
- ^Teeter, Preston; Sandberg, Jorgen (2016). "Constraining or Enabling Green Capability Development? How Policy Uncertainty Affects Organizational Responses to Flexible Environmental Regulations". British Journal of Management. doi:10.1111/1467-8551.12188.
- ^Loseke, Donileen R. & Cahil, Spencer E. (2007). "Publishing qualitative manuscripts: Lessons learned". In C. Seale, G. Gobo, J. F. Gubrium, & D. Silverman (Eds.), Qualitative Research Practice: Concise Paperback Edition, pp. 491-506. London: Sage. ISBN 978-1-4129-3420-6
- ^ abDenzin, Norman K. & Lincoln, Yvonna S. (2005). "Introduction: The discipline and practice of qualitative research". In N. K. Denzin & Y. S. Lincoln (Eds.), The Sage Handbook of Qualitative Research (3rd ed.), pp. 1-33. Thousand Oaks, CA: Sage. ISBN 0-7619-2757-3
- ^Taylor, S.J., Bogdan, R., & Racino, J. (1991). Life in the Community: Case Studies of Organizations Serving People with Developmental Disabilities in the Community. Baltimore, ND: Paul H. Brookes.
- ^Taylor, S.J.,Bogdan, R., & Lutfiyya, Z.M. (1995). The Variety of Community Experiences: Qualitative Studies of Family and Community Life. Baltimore, MD: Paul H. Brookes.
- ^Bogdan, R. (1995). "A simple farmer accused of murder: The case of Delbert Ward. In. S.J.Taylor, R. Bogdan, & Z.M. Lutfiyya, The Variety of Community Experience: Qualitative Studies of Family and Community Life(pp.79-100). Baltimore, MD: Paul H. Brookes.
- ^O'Connor, S. (1995). More than they bargained for: The meaning of support to families. In: S.J. Taylor, R. Bogdan & Z.M. Lutfiyya, The Variety of Community Experiences: Qualitative Studies of Family and Community Life. (pp.193-210). Baltimore, MD: Paul H. Brookes.
- ^Taylor, S.J. (1995). "Children's division is coming to take pictures: Family life and parenting in a family with disabilities. In: S.Taylor, R. Bogdan, & Z.M. Lutfiyya, The Variety of Community Experiences: Qualitative Studies of Family and Community Life. (pp.23-46). Baltimore, MD: Paul H. Brookes.
- ^ abWertz, Charmaz, McMullen. "Five Ways of Doing Qualitative Analysis: Phenomenological Psychology, Grounded Theory, Discourse Analysis, Narrative Research, and Intuitive Inquiry". 16-18. The Guilford Press: March 30, 2011. 1st ed. Print.
- ^Kelly, J.G. & Song, A.V. (2004). "Six Community Psychologists Tell Their Story." Binghamton, NY: The Haworth Press.
- Adler, P. A. & Adler, P. (1987). : context and meaning in social inquiry / edited by Richard Jessor, Anne Colby, and Richard A. Shweder] OCLC 46597302
- Baškarada, S. (2014) "Qualitative Case Study Guidelines", in The Qualitative Report, 19(40): 1-25. Available from 
- Boas, Franz (1943). "Recent anthropology". Science. 98: 311–314, 334–337. doi:10.1126/science.98.2546.334.
- Creswell, J. W. (2003). Research design: Qualitative, quantitative, and mixed method approaches. Thousand Oaks, CA: Sage Publications.
- Denzin, N. K., & Lincoln, Y. S. (2000). Handbook of qualitative research ( 2nd ed.). Thousand Oaks, CA: Sage Publications.
- Denzin, N. K., & Lincoln, Y. S. (2011). The SAGE Handbook of qualitative research ( 4th ed.). Los Angeles: Sage Publications.
- DeWalt, K. M. & DeWalt, B. R. (2002). Participant observation. Walnut Creek, CA: AltaMira Press.
- Fischer, C.T. (Ed.) (2005). Qualitative research methods for psychologists: Introduction through empirical studies. Academic Press. ISBN 0-12-088470-4.
- Franklin, M. I. (2012), "Understanding Research: Coping with the Quantitative-Qualitative Divide". London/New York. Routledge
- Giddens, A. (1990). The consequences of modernity. Stanford, CA: Stanford University Press.
- Gubrium, J. F. and J. A. Holstein. (2000). "The New Language of Qualitative Method." New York: Oxford University Press.
- Gubrium, J. F. and J. A. Holstein (2009). "Analyzing Narrative Reality." Thousand Oaks, CA: Sage.
- Gubrium, J. F. and J. A. Holstein, eds. (2000). "Institutional Selves: Troubled Identities in a Postmodern World." New York: Oxford University Press.
- Hammersley, M. (2008) Questioning Qualitative Inquiry, London, Sage.
- Hammersley, M. (2013) What is qualitative research?, London, Bloomsbury.
- Holliday, A. R. (2007). Doing and Writing Qualitative Research, 2nd Edition. London: Sage Publications
- Holstein, J. A. and J. F. Gubrium, eds. (2012). "Varieties of Narrative Analysis." Thousand Oaks, CA: Sage.