Quality, Quantity and Invariance

Qualitative research assumes that obtaining text is enough to obtain the invariant meaning required for inference. This parallels the quantitative research that unjustifiably assumes that merely expressing data as numbers is enough to obtain the invariant mathematics required for inference.

Most qualitative researchers are unaware that the impetus for their movement stems from critiques of the misidentification of number with mathematical thinking. These researchers have not noticed that what sets their work apart from quantitative research is its requirement that the text of what is written, said, or done must be separable from the contingencies of its origins, so that it can take on a life of its own, and thus become invariant across respondents.

These issues make an interesting background for a conference on qualitative research methods, held by the Qualitative Interest Group (QUIG) at the University of Georgia-Athens on January 6-8, 1994.

Upon asserting that (quantitative) educational measurement can be productively approached from a (qualitative) phenomenological point of view, William Fisher was informed by the qualitative researchers that this cannot make sense because it would introduce into phenomenology the requirement that the test items remain invariant across respondents and examinees and collaborators. Yet this is just the requirement met by successful qualitative research! And it makes that research more mathematical in its spirit than the quantitative research that assumes it has mathematical status because it employs numbers.

What makes research mathematical? Kant asserts that "research is scientific to the extent that it is mathematical." But Heidegger shows this does not mean "to the extent that it is quantitative". "A study can be quantitative without being mathematical," and vice-versa (Thurstone, The Measurement of Values, 1959, pp. 9-10). A truly mathematical approach requires that test items be phenomenologically constituted - that is, constituted by and for the respondents according to their own sense of what the subject matter involves. Rasch's separability theorem specifies the criterion that must be met before quantitative studies become mathematical.

The requirement of separability for useful qualitative research is implied in Vivian Wilson Mott's paper "The Challenge of Phenomenological Research: From Philosophical Ideals to Practice." In outlining the principles of qualitative research, she discusses how structure simultaneously emerges from, and is imposed on, the phenomenological record. To the extent that the horizons of the thing observed and of the observer fuse, an invariant phenomenon becomes understood and enters into language and history.

A synthesis of qualitative and quantitative research based on the principle of invariance would lead to an explosion of useful knowledge in social science. This unrealized potential is evident in Mariana Enriquez-Olmos' paper "Educational Concerns of Foreign and Immigrant Parents." She interviewed five parents eliciting five recurring themes: discipline, respect for others, sense of family, religious education, and sex education. Her qualitative research emphasizes a point often ignored by quantitative research: it is essential to meaning that the voices of the people most concerned and most central be heard. The variables studied cannot be constructed purely out of a researcher's preconceptions. They must be constructed through overt collaboration with those participating in the research.

In order to make what she learned from her interviews generalizable, Enriquez-Olmos needs to show that her five recurring themes have some invariant structure to them, a structure that supersedes her five parents and her own perceptions. Here, sound quantitative research could aid her. Using her five parents' comments to guide the writing of a questionnaire would allow her to efficiently collect a large sample of data. This would enable here her to quantify and so generalize her findings beyond herself and her five collaborators.

A synthesis of qualitative and quantitative approaches would contribute to removing researchers' biases and jargon from their text. The findings of qualitative research would be exposed, through quantitative research, to a wide audience of respondents. Idiosyncrasies of particular respondents and researchers would be detected and sidelined for special investigation, while commonalities across respondents would be clarified.

William P. Fisher, Jr. 1994 RMT8:1 p. 341


Quality, quantity and invariance. Fisher WP Jr. … Rasch Measurement Transactions, 1994, 8:1 p.341



Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse Rasch Measurement Theory Analysis in R, Wind, Hua Applying the Rasch Model in Social Sciences Using R, Lamprianou El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Rasch Models for Measurement, David Andrich Constructing Measures, Mark Wilson Best Test Design - free, Wright & Stone
Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias Diseño de Mejores Pruebas - free, Spanish Best Test Design A Course in Rasch Measurement Theory, Andrich, Marais Rasch Models in Health, Christensen, Kreiner, Mesba Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen
Rasch Books and Publications: Winsteps and Facets
Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang Statistical Analyses for Language Testers (Facets), Rita Green Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind Rasch Measurement: Applications, Khine Winsteps Tutorials - free
Facets Tutorials - free
Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan

To be emailed about new material on www.rasch.org
please enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from Rasch.org

www.rasch.org welcomes your comments:

Your email address (if you want us to reply):

 

ForumRasch Measurement Forum to discuss any Rasch-related topic

Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement

Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.

Coming Rasch-related Events
Oct. 4 - Nov. 8, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 17 - Feb. 21, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
May 16 - June 20, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 20 - July 18, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Further Topics (E. Smith, Facets), www.statistics.com
Oct. 3 - Nov. 7, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com

 

The URL of this page is www.rasch.org/rmt/rmt81h.htm

Website: www.rasch.org/rmt/contents.htm