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Quantitative & Qualitative research methods

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In the social sciences, quantitative research refers to the systematic empirical investigation of social phenomena via statistical, mathematical or computational techniques.[1] The objective of quantitative research is to develop and employ mathematical models, theories and/or hypotheses pertaining to phenomena. The process of measurementis central to quantitative research because it provides the fundamental connection between empirical observationand mathematical expression of quantitative relationships. Quantitative data is any data that is in numerical form such as statistics, percentages, etc.[1] In layman's terms, this means that the quantitative researcher asks a specific, narrow question and collects numerical data from participants to answer the question. The researcher analyzes the data with the help of statistics. The researcher is hoping the numbers will yield an unbiased result that can be generalized to some larger population. Qualitative research, on the other hand, asks broad questions and collects word data from participants. The researcher looks for themes and describes the information in themes and patterns exclusive to that set of participants.
Quantitative research is used widely in social sciences such as psychology, economics, sociology, and political science, and less frequently in anthropology and history. Research in mathematical sciences such as physics is also 'quantitative' by definition, though this use of the term differs in context. In the social sciences, the term relates to empirical methods, originating in both philosophical positivism and the history of statistics, which contrastqualitative research methods.
Qualitative methods produce information only on the particular cases studied, and any more general conclusions are only hypotheses. Quantitative methods can be used to verify which of such hypotheses are true.
A comprehensive analysis of 1274 articles published in the top two American sociology journals between 1935 and 2005 found that roughly two thirds of these articles used quantitative methods.[2]

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[edit]Over and over view

Quantitative research is generally made using scientific methods, which can include:
  • The generation of models, theories and hypotheses
  • The development of instruments and methods for measurement
  • Experimental control and manipulation of variables
  • Collection of empirical data
  • Modeling and analysis of data
In the social sciences particularly, quantitative research is often contrasted with qualitative research which is the examination, analysis and interpretation of observations for the purpose of discovering underlying meanings and patterns of relationships, including classifications of types of phenomena and entities, in a manner that does not involve mathematical models. Approaches to quantitative psychology were first modeled on quantitative approaches in the physical sciences by Gustav Fechner in his work on psychophysics, which built on the work of Ernst Heinrich Weber. Although a distinction is commonly drawn between qualitative and quantitative aspects of scientific investigation, it has been argued that the two go hand in hand. For example, based on analysis of the history of science, Kuhn (1961, p. 162) concludes that “large amounts of qualitative work have usually been prerequisite to fruitful quantification in the physical sciences”.[3] Qualitative research is often used to gain a general sense of phenomena and to form theories that can be tested using further quantitative research. For instance, in the social sciences qualitative research methods are often used to gain better understanding of such things as intentionality (from the speech response of the researchee) and meaning (why did this person/group say something and what did it mean to them?) (Kieron Yeoman).
Although quantitative investigation of the world has existed since people first began to record events or objects that had been counted, the modern idea of quantitative processes have their roots in Auguste Comte's positivist framework.[4] Positivism emphasized the use of the scientific method through observation to empirically test hypotheses explaining and predicting what, where, why, how, and when phenomena occurred. Positivist scholars like Comte believed only scientific methods rather than previous spiritual explanations for human behavior could advance science.

[edit]Use of statistics

Statistics is the most widely used branch of mathematics in quantitative research outside of the physical sciences, and also finds applications within the physical sciences, such as in statistical mechanics. Statistical methods are used extensively within fields such as economics, social sciences and biology. Quantitative research using statistical methods starts with the collection of data, based on the hypothesis or theory. Usually a big sample of data is collected - this would require verification, validation and recording before the analysis can take place. Software packages such as SPSS and R are typically used for this purpose. Causal relationships are studied by manipulating factors thought to influence the phenomena of interest while controlling other variables relevant to the experimental outcomes. In the field of health, for example, researchers might measure and study the relationship between dietary intake and measurable physiological effects such as weight loss, controlling for other key variables such as exercise. Quantitatively based opinion surveysare widely used in the media, with statistics such as the proportion of respondents in favor of a position commonly reported. In opinion surveys, respondents are asked a set of structured questions and their responses are tabulated. In the field of climate science, researchers compile and compare statistics such as temperature or atmospheric concentrations of carbon dioxide.
Empirical relationships and associations are also frequently studied by using some form of General linear model, non-linear model, or by using factor analysis. A fundamental principle in quantitative research is that correlation does not imply causation, although some such as Clive Granger suggest that a series of correlations can imply a degree of causality. This principle follows from the fact that it is always possible a spurious relationship exists for variables between which covariance is found in some degree. Associations may be examined between any combination of continuous and categorical variables using methods of statistics.

[edit]Measurement

Views regarding the role of measurement in quantitative research are somewhat divergent. Measurement is often regarded as being only a means by which observations are expressed numerically in order to investigate causal relations or associations. However, it has been argued that measurement often plays a more important role in quantitative research.[5] For example, Kuhn argued that within quantitative research, the results that are shown can prove to be strange. This is because accepting a theory based on results of quantitative data could prove to be a natural phenomenon. He argued that such abnormalities are interesting when done during the process of obtaining data, as seen below:
When measurement departs from theory, it is likely to yield mere numbers, and their very neutrality makes them particularly sterile as a source of remedial suggestions. But numbers register the departure from theory with an authority and finesse that no qualitative technique can duplicate, and that departure is often enough to start a search (Kuhn, 1961, p. 180).
In classical physics, the theory and definitions which underpin measurement are generally deterministic in nature. In contrast, probabilistic measurement models known as the Rasch model and Item response theory models are generally employed in the social sciences. Psychometrics is the field of study concerned with the theory and technique for measuring social and psychological attributes and phenomena. This field is central to much quantitative research that is undertaken within the social sciences.
Quantitative research may involve the use of proxies as stand-ins for other quantities that cannot be directly measured. Tree-ring width, for example, is considered a reliable proxy of ambient environmental conditions such as the warmth of growing seasons or amount of rainfall. Although scientists cannot directly measure the temperature of past years, tree-ring width and other climate proxies have been used to provide a semi-quantitative record of average temperature in the Northern Hemisphere back to 1000 A.D. When used in this way, the proxy record (tree ring width, say) only reconstructs a certain amount of the variance of the original record. The proxy may be calibrated (for example, during the period of the instrumental record) to determine how much variation is captured, including whether both short and long term variation is revealed. In the case of tree-ring width, different species in different places may show more or less sensitivity to, say, rainfall or temperature: when reconstructing a temperature record there is considerable skill in selecting proxies that are well correlated with the desired variable.[6]

[edit]Relationship with qualitative methods

In most physical and biological sciences, the use of either quantitative or qualitative methods is uncontroversial, and each is used when appropriate. In the social sciences, particularly in sociology, social anthropology and psychology, the use of one or other type of method can be a matter of controversy and even ideology, with particular schools of thought within each discipline favouring one type of method and pouring scorn on to the other. The majority tendency throughout the history of social science, however, is to use eclectic approaches-by combining both methods. Qualitative methods might be used to understand the meaning of the conclusions produced by quantitative methods. Using quantitative methods, it is possible to give precise and testable expression to qualitative ideas. This combination of quantitative and qualitative data gathering is often referred to as mixed-methods research.[7]

[edit]Examples

  • Research that consists of the percentage amounts of all the elements that make up Earth's atmosphere.
  • Survey that concludes that the average patient has to wait two hours in the waiting room of a certain doctor before being selected.
  • An experiment in which group x was given two tablets of Aspirin a day and Group y was given two tablets of a placebo a day where each participant israndomly assigned to one or other of the groups. The numerical factors such as two tablets, percent of elements and the time of waiting make the situations and results quantitative.
  • In finance, quantitative research into the stock markets is used to develop models to price complex trades, and develop algorithms to exploit investment hypotheses, as seen in quantitative Hedge Funds and Trading Strategy Indices.

[edit]See also

[edit]References

  1. ^ a b Given, Lisa M. (2008). The Sage encyclopedia of qualitative research methods. Los Angeles, Calif.: Sage Publications. ISBN 1412941636.
  2. ^ Hunter, Laura and Erin Leahey. 2008. "Collaborative Research in Sociology: Trends and Contributing Factors". American Sociologist 39:290–306
  3. ^ Thomas S. Kuhn, The Function of Measurement in Modern Physical Science
  4. ^ Kasim, R., Alexander, K. and Hudson, J. A CHOICE OF RESEARCH STRATEGY FOR IDENTIFYING COMMUNITY-BASED ACTION SKILL REQUIREMENTS IN THE PROCESS OF DELIVERING HOUSING MARKET RENEWAL.Research Institute for the Built and Human Environment, University of Salford,United Kingdom
  5. ^ Moballeghi, M. & Moghaddam, G.G. How Do We Measure Use of Scientific Journals? A Note on Research Methodologies. Shahed University and Razi Metallurgical Research Center, Tehran, IRAN.
  6. ^ Briffa, K.R., T.J. Osborn, F.H. Schweingruber, I.C. Harris, P.D. Jones, S.G. Shiyatov and E. A.Vaganov, 2001. Low-frequency temperature variations from a northern tree ring density network. Journal of Geophysical Research, 106(D3):2929–2941.
  7. ^ Diriwächter, R. & Valsiner, J. Qualitative Developmental Research Methods in Their Historical and Epistemological Contexts. FQS. Vol 7, No. 1, Art. 8 – January 2006
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Not to be confused with qualitative data.
For the journal, see Qualitative Research.
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Qualitative research is a method of inquiry employed in many different academic disciplines, traditionally in the social sciences, but also in market research and further contexts.[1] Qualitative researchers aim to gather an in-depth understanding of human behavior and the reasons that govern such behavior. The qualitative method investigates the why and how of decision making, not just what, where, when. Hence, smaller but focused samplesare more often needed than large samples.
In the conventional view, qualitative methods produce information only on the particular cases studied, and any more general conclusions are only propositions (informed assertions). Quantitative methods can then be used to seek empirical support for such research hypotheses. This view has been disputed by Oxford University professor Bent Flyvbjerg, who argues that qualitative methods and case study research may be used both for hypotheses-testing and for generalizing beyond the particular cases studied.[2]



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[edit]History

In the early 1900s, some researchers rejected positivism, the theoretical idea that there is an objective world about which we can gather data 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. In the 70s and 80s, 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, and gender, 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. 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” and what can count as “scientific” research in scholarship, a current, ongoing debate in the academy.

[edit]Data collection

Qualitative researchers may use different approaches in collecting data, such as the grounded theory practice, narratology, storytelling, classical ethnography, or shadowing. Qualitative methods are also loosely present in other methodological approaches, such as action research or actor-network theory. Forms of the data collected can include interviews and group discussions, observation and reflection field notes, various texts, pictures, and other materials.
Qualitative research often categorizes data into patterns as the primary basis for organizing and reporting results.[citation needed] Qualitative researchers 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.[3]
The ways of participating and observing can vary widely from setting to setting. Participant observation is a strategy of reflexive learning, not a single method of observing.[4] In participant observation[5] 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[citation needed].
Some distinctive qualitative methods are the use of focus groups and key informant interviews. The focus group technique involves a moderator facilitating a small group discussion between selected individuals on a particular topic. This is a particularly popular method in market research and testing new initiatives with users/workers.
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.
In the academic social sciences the most frequently used qualitative research approaches include the following:
  1. Ethnographic Research, used for investigating cultures by collecting and describing data that is intended to help in the development of a theory. This method is also called “ethnomethodology” or "methodology of the people". 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.
  2. Critical Social Research, used by a researcher to understand how people communicate and develop symbolic meanings.
  3. 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.
  4. 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.
  5. 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?
  6. 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.
  7. Phenomenology describes the “subjective reality” of an event, as perceived by the study population; it is the study of a phenomenon.
  8. 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.

[edit]Data analysis

Question book-new.svgThis unreferenced section requires citations to ensureverifiability.

[edit]Interpretive techniques

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.

[edit]Coding

Main article: Coding (social sciences)
Coding 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. 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-end 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.
Contemporary qualitative data analyses are sometimes supported by computer programs, termed Computer Assisted Qualitative Data Analysis Software. 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.
A frequent criticism of coding method is that it seeks to transform qualitative data into quantitative data, 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.

[edit]Recursive abstraction

Some qualitative datasets are analyzed without coding. A common method here is recursive abstraction, where datasets are summarized; those summaries are then further summarized 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.

[edit]Mechanical techniques

Some techniques rely on leveraging computers to scan and sort large sets of qualitative data. At their most basic level, mechanical techniques rely on counting words, phrases, or coincidences of tokens within the data. Often referred to as content analysis, the output from these techniques is amenable to many advanced statistical analyses.
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).
A frequent criticism of mechanical techniques is the absence of a human interpreter. And while masters of these methods are able to write sophisticated software to mimic some human decisions, the bulk of the “analysis” is 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) letting the data go untouched, leaving any actionable nuggets undiscovered.

[edit]Paradigmatic differences

Contemporary qualitative research has been conducted from a large number of various paradigms that influence conceptual and metatheoretical concerns of legitimacy, control, data analysis, ontology, and epistemology, among others. Research conducted in the last 10 years has been characterized by a distinct turn toward more interpretive, postmodern, and criticalpractices.[6] Guba and Lincoln (2005) identify five main paradigms of contemporary qualitative research: positivism, postpositivism, critical theories, constructivism, and participatory/cooperative paradigms.[6] 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”.[7] 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).

[edit]Validation

A central issue in qualitative research is validity (also known as credibility and/or dependability). There are many different ways of establishing validity, including: member check, interviewer corroboration, peer debriefing, prolonged engagement, negative case analysis, auditability, confirmability, bracketing, and balance. Most of these methods were coined, or at least extensively described by Lincoln and Guba (1985)[8]

[edit]Academic research

By the end of the 1970s many leading journals began to publish qualitative research articles[9] and several new journals emerged which published only qualitative research studies and articles about qualitative research methods.[10]
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.[10]
The new millennium saw a dramatic increase in the number of journals specializing in qualitative research with at least one new qualitative research journal being launched each year.

[edit]See also

[edit]Notes

  1. ^ 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
  2. ^ Bent Flyvbjerg, 2006, "Five Misunderstandings About Case Study Research." Qualitative Inquiry, vol. 12, no. 2, April, pp. 219-245.; Bent Flyvbjerg, 2011, "Case Study," in Norman K. Denzin and Yvonna S. Lincoln, eds., The Sage Handbook of Qualitative Research, 4th Edition (Thousand Oaks, CA: Sage), pp. 301-316.
  3. ^ Marshall, Catherine & Rossman, Gretchen B. (1998). Designing Qualitative Research. Thousand Oaks, CA: Sage. ISBN 0-7619-1340-8
  4. ^ Lindlof, T. R., & Taylor, B. C. (2002) Qualitative communication research methods: Second edition. Thousand Oaks, CA: Sage Publications, Inc. ISBN 0-7619-2493-0
  5. ^ "Qualitative Research Methods: A Data Collector’s Field Guide". techsociety.com. Retrieved 7 October 2010.
  6. ^ a b Guba, 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
  7. ^ 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
  8. ^ Lincoln Y and Guba EG (1985) Naturalistic Inquiry, Sage Publications, Newbury Park, CA.
  9. ^ 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 978-1-76194-776-9
  10. ^ a b Denzin, 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

[edit]References

  • Adler, P. A. & Adler, P. (1987). : context and meaning in social inquiry / edited by Richard Jessor, Anne Colby, and Richard A. Shweder] OCLC 46597302
  • Boas, Franz (1943). Recent anthropology. Science, 98, 311-314, 334-337.
  • 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.
  • Flyvbjerg, B. (2006). "Five Misunderstandings About Case Study Research." Qualitative Inquiry, vol. 12, no. 2, April 2006, pp. 219–245.
  • Flyvbjerg, B. (2011). "Case Study," in Norman K. Denzin and Yvonna S. Lincoln, eds., The Sage Handbook of Qualitative Research, 4th Edition (Thousand Oaks, CA: Sage), pp. 301–316.
  • Giddens, A. (1990). The consequences of modernity. Stanford, CA: Stanford University Press.
  • Holliday, A. R. (2007). Doing and Writing Qualitative Research, 2nd Edition. London: Sage Publications
  • Kaminski, Marek M. (2004). Games Prisoners Play. Princeton University Press. ISBN 0-691-11721-7.
  • Mahoney, J & Goertz, G. (2006) A Tale of Two Cultures: Contrasting Quantitative and Qualitative Research, Political Analysis, 14, 227–249. doi:10.1093/pan/mpj017
  • Malinowski, B. (1922/1961). Argonauts of the Western Pacific. New York: E. P. Dutton.
  • Miles, M. B. & Huberman, A. M. (1994). Qualitative Data Analysis. Thousand Oaks, CA: Sage.
  • Pamela Maykut, Richard Morehouse. 1994 Beginning Qualitative Research. Falmer Press.
  • Patton, M. Q. (2002). Qualitative research & evaluation methods ( 3rd ed.). Thousand Oaks, CA: Sage Publications.
  • Pawluch D. & Shaffir W. & Miall C. (2005). Doing Ethnography: Studying Everyday Life. Toronto, ON Canada: Canadian Scholars' Press.
  • Ragin, C. C. (1994). Constructing Social Research: The Unity and Diversity of Method, Pine Forge Press, ISBN 0-8039-9021-9
  • Stebbins, Robert A. (2001) Exploratory Research in the Social Sciences. Thousand Oaks, CA: Sage.
  • Taylor, Steven J., Bogdan, Robert, Introduction to Qualitative Research Methods, Wiley, 1998, ISBN 0-471-16868-8
  • Van Maanen, J. (1988) Tales of the field: on writing ethnography, Chicago: University of Chicago Press.
  • Wolcott, H. F. (1995). The art of fieldwork. Walnut Creek, CA: AltaMira Press.
  • Wolcott, H. F. (1999). Ethnography: A way of seeing. Walnut Creek, CA: AltaMira Press.
  • Ziman, John (2000). Real Science: what it is, and what it means. Cambridge, Uk: Cambridge University Press.

[edit]External links

[edit]Videos

reference : http://en.wikipedia.org/wiki/Quantitative_methods





Multivariate statistics is a form of statistics encompassing the simultaneous observation and analysis of more than one statistical variable. The application of multivariate statistics ismultivariate analysis. Methods of bivariate statistics, for example simple linear regression and correlation, are special cases of multivariate statistics in which two variables are involved.
Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical implementation of multivariate statistics to a particular problem may involve several types of univariate and multivariate analysis in order to understand the relationships between variables and their relevance to the actual problem being studied.
In addition, multivariate statistics is concerned with multivariate probability distributions, in terms of both:
  • how these can be used to represent the distributions of observed data;
  • how they can be used as part of statistical inference, particularly where several different quantities are of interest to the same analysis.

Contents

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[edit]Types of analysis

There are many different models, each with its own type of analysis:
  1. Multivariate analysis of variance (MANOVA) extends the analysis of variance to cover cases where there is more than one dependent variable to be analyzed simultaneously: see alsoMANCOVA.
  2. Multivariate regression analysis attempts to determine a formula that can describe how elements in a vector of variables respond simultaneously to changes in others. For linear relations, regression analyses here are based on forms of the general linear model.
  3. Principal components analysis (PCA) creates a new set of orthogonal variables that contain the same information as the original set. It rotates the axes of variation to give a new set of orthogonal axes, ordered so that they summarize decreasing proportions of the variation.
  4. Factor analysis is similar to PCA but allows the user to extract a specified number of synthetic variables, fewer than the original set, leaving the remaining unexplained variation as error. The extracted variables are known as latent variables or factors; each one may be supposed to account for covariation in a group of observed variables.
  5. Canonical correlation analysis finds linear relationships among two sets of variables; it is the generalised (i.e. canonical) version of bivariate correlation.
  6. Redundancy analysis is similar to canonical correlation analysis but allows the user to derive a specified number of synthetic variables from one set of (independent) variables that explain as much variance as possible in another (independent) set. It is a multivariate analogue of regression.
  7. Correspondence analysis (CA), or reciprocal averaging, finds (like PCA) a set of synthetic variables that summarise the original set. The underlying model assumes chi-squared dissimilarities among records (cases). There is also canonical (or "constrained") correspondence analysis (CCA) for summarising the joint variation in two sets of variables (like canonical correlation analysis).
  8. Multidimensional scaling comprises various algorithms to determine a set of synthetic variables that best represent the pairwise distances between records. The original method isprincipal coordinates analysis (based on PCA).
  9. Discriminant analysis, or canonical variate analysis, attempts to establish whether a set of variables can be used to distinguish between two or more groups of cases.
  10. Linear discriminant analysis (LDA) computes a linear predictor from two sets of normally distributed data to allow for classification of new observations.
  11. Clustering systems assign objects into groups (called clusters) so that objects (cases) from the same cluster are more similar to each other than objects from different clusters.
  12. Recursive partitioning creates a decision tree that attempts to correctly classify members of the population based on a dichotomous dependent variable.
  13. Artificial neural networks extend regression and clustering methods to non-linear multivariate models.

[edit]Important probability distributions

There is a set of probability distributions used in multivariate analyses that play a similar role to the corresponding set of distributions that are used in univariate analysis when the normal distribution is appropriate to a dataset. These multivariate distributions are:
The Inverse-Wishart distribution is important in Bayesian inference, for example in Bayesian multivariate linear regression. Additionally, Hotelling's T-squared distribution is a univariate distribution, generalising Student's t-distribution, that is used in multivariate hypothesis testing.

[edit]History

Anderson's 1958 textbook, An Introduction to Multivariate Analysis, educated a generation of theorists and applied statisticians; Anderson's book emphasizes hypothesis testing vialikelihood ratio tests and the properties of power functions: Admissibility, unbiasedness and monotonicity.[1][2]

[edit]Software & Tools

There are an enormous number of software packages and other tools for multivariate analysis, including:

[edit]See also

[edit]References

  1. ^ Sen, Pranab Kumar; Anderson, T. W.; Arnold, S. F.; Eaton, M. L.; Giri, N. C.; Gnanadesikan, R.; Kendall, M. G.; Kshirsagar, A. M. et al. (June 1986). "Review: Contemporary Textbooks on Multivariate Statistical Analysis: A Panoramic Appraisal and Critique". Journal of the American Statistical Association 81 (394): 560–564. DOI:10.2307/2289251. ISSN 0162-1459.JSTOR 2289251.(Pages 560–561)
  2. ^ Schervish, Mark J. (November 1987). "A Review of Multivariate Analysis". Statistical Science 2 (4): 396–413. DOI:10.1214/ss/1177013111. ISSN 0883-4237. JSTOR 2245530.

[edit]Further reading

[edit]External links

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