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

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Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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