A rose by any other name would smell as sweet.
— Shakespeare, Romeo and Juliet, Act II Scene II
Shakespeare is making the claim that an object’s characteristics are immutable and that any description of the object leaves the original unaltered. I wonder what he would have made of the notion that the perceiver brings connotations and significances that interplay and interfere with the object. Calling a rose a ‘stench blossom’ (Keeler & Moore, 1997) may not impact on the chemicals released from the rose, but it will affect reception of those chemicals, and thus the derived meaning of the rose. In a similar vein, the technique of mathematical modelling reinterprets and subjugates an entity into highly differing representations of existence. It is this relationship between the model and its claims to validity in the representations that I will look at in this essay before distinguishing between quantitative and qualitative methods using that relationship as a distinguishing factor.
A statistical model is a symbolic representation in mathematical code of an entity that is not numeric. It is perhaps too easy to ‘trust’ the numerical precision of a statistical model and to fail to see weaknesses in ontological conceptions that lie between the various elements of the model. We need to ask what role a model has in relation to its object. Gavrilova and Leshcheva present a taxonomy for ontology of six components, each comprising many elements; relationships, domains, owner, formalisation, purpose, and methodology (2015). A number of relations are possible including, description, explanation, and categorisation. With a mutually understood relation among researchers, the ontology allows for tools that enable “coherent and cohesive reasoning purposes” (Chandraksekaran et al., 1999, p. 21) that include the formulating of research hypotheses. Taking just one component as an example, within ‘formalisation’ lies the degree to which the model is described formally (i.e. mathematically) or informally (e.g. with loose descriptor terms). The statistical model at the base of any quantitative analysis is a formal, mathematical description of a construct, and the language used to present the research hypotheses is natural language. Thus there are two representations whose similarity in meaning may be questioned to satisfy the requirement of internal validity.
The notion of construct is objectified and as an object has its own set of ontologies. A construct is invisible and “is the actual characteristic or ability that [a variable] represents in a human being” (Brown, 1988, p. 8). Constructs, too, need to have their elements made explicit, and care is required to avoid circular or nested definitions within constructs (MacKenzie, 2003). As a reviewer of research articles for potential publication, MacKenzie laments that a “common mistake [in the definition of constructs] is to define a construct as the result of … some other construct” (MacKenzie, 2003, p. 325). Doing so invalidates the research, i.e. “makes it impossible to empirically test the proposed theoretical linkages”, because the variables chosen to epitomise the construct return values for the surface construct and not the underlying construct (MacKenzie, 2003, p. 325).
Quantitative methods address research questions where constructs can be operationalised using variables that allow for the building of a statistical or mathematic model of the construct. Qualitative methods, however, do not mathematicize constructs, relying instead on “demonstrat[ing] that the categories [i.e. ontologies] that the researchers are using are meaningful to the participants themselves” (Cohen et al., 2007, p. 110).
Brown, J. D. (1988). Understanding research in second language learning. Cambridge: CUP.
Chandrasekaran, B., Josephson, J. R., & Benjamins, V. R. (1999). What are ontologies, and why do we need them?. IEEE Intelligent systems, 14(1), 20-26.
Cohen, L., Manion, L. & Morrison, K. (2007). Research methods in education (5th ed). London: Routledge.
Gavrilova, T. A., & Leshcheva, I. A. (2015). Ontology Design and Individual Cognitive Peculiarities: A Pilot Study. Expert Systems with Applications, 42, 3883-3892.
Keeler, K. (Writer), & Moore, S. D. (Director). (1997). The Principal and the Pauper. Episode 180. In B. Oakley & J. Weinstein. (Producer), The Simpsons. Los Angeles, California: Fox Network.
MacKenzie, S. B. (2003). The dangers of poor construct conceptualisation. Journal of the Academy of Marketing Sciences, 31(3), 323-326.