Thank you for your comment. The issue of construct validity and sample size is made complex by the acceptability of single case research and Yin’s argument for analytic generalisation (Yin, 2008). Without such an argument, the purely statistical probabilistic calculations are well established in social research (e.g. see many of the chapters in Alasuutari, Bickman, & Brannen, 2008). When sample sizes are robust enough to be are considered adequate representations of the target population, parametric statistics may be conducted, and even with smaller sizes, there are non-parametric tools available (Cohen, Manion, & Morrison, 2011; Flick, 2014). In these instances, a research is able to make claims about the evidence supporting a construct when the relevant statistic figures are validated as being likely within a given level of confidence, error and p-value. In other words, the issue of the existence of the construct is intimately tied to strength of the evidence used to argue for it: and this strength, in parametric and non-parametric quantitative statistics, is ultimately related to the sample size.
However, for qualitative research, the notion of existence takes on a different meaning. The example of cancer may be an illustrative one. Without doubt (because I had it and know directly) non-Hodgkin’s lymphoma (NHL) exists (or more accurately, the medico-biological phenomena that results in altered cellular biomechanisms that has the associated socio-medico label of NHL exists). The condition affects about 20 people in 100,000. If I were to take a random sample of 1,000 individuals and investigate the existence of that cancer, there would be a 0.2% chance that a patient is in that sample. Non- and parametric tools would not be available to the researcher to argue for the existence of NHL. Similarly, if a quantitative research plan was set up to investigate the existence of a construct (i.e. NHL) in a random population, only very lucky samples would help the research.
However, the existence of a single case of NHL is enough to show that NHL exists. The famous black swan example(Popper, 1959) and the associated notions of falsifiability and verifiability, point to a different kind of search, an investigation that gains validation upon the discovery of a single case. When a phenomenon can be argued to exist, a la Yin’s (2008) analytical generalisation, work can begin into understanding that phenomenon more accurately.
These examples do not discuss the concept of a construct directly. These are hidden ideas that “that have to be inferred from observable indicators” (Williams & Vogt, 2011). A wider question is that of interpretation. If an observable phenomenon is interpreted as pointing to an occluded phenomenon, how stable is that interpretation when only one instance can be observed? The black swan, for example, may be a single genetic mutation and not really be sufficient evidence to disprove the white swan theory. Or it may point to the existence of a new type of swan. Sato (2016) notes the importance of theoretical sampling, the deliberate choice of, for example, selecting other black swans to improve the robustness of the theoretical category.
With these issues in mind, I progress to the task of attempting to delineate the possible constructs from the myriad of possibilities thrown up by the literature on epistemic cognition. But the question becomes if I use a limited number of cases, how stable are the claims of existence and non-existence?
Alasuutari, P., Bickman, L., & Brannen, J. (2008). The SAGE Handbook of Social Research Methods. Los Angeles: Sage Publications.
Cohen, L., Manion, L., & Morrison, K. (2011). Research Methods in Education. Professional Development in Education (7th ed.). Abingdon: Routledge.
Flick, U. (2014). The SAGE Handbook of Qualitative Data Analysis. Los Angeles: Sage Publications. http://doi.org/10.4135/9781446282243.n33
Popper, K. (1959). The Logic of Scientific Discovery. London and New York: Routledge.
Sato, H. (2016). Generalization Is Everything, or Is It?: Effectiveness of Case Study Research for Theory Construction. Annals of Business Administrative Science, 15(1), 49–58. http://doi.org/10.7880/abas.0151203a
Williams, M., & Vogt, W. P. (2011). Innovation in Social Research Methods. Los Angeles: Sage Publications.
Yin, R. (2008). The case study as a research method. Case study research: Design and methods.