I am not sure about quasi-normal distribution but Q methodology does not need to use a forced distribution at all. You can even ask participants to rank items one-by-one at a time instead of using a distribution. It is just that it would make it easier for them to use a distribution rather than asking them to rank 80 items from 1 to 80. Basically, the main point in Q methodology is not a distribution but the pattern of the sorted items. At least, this is how I understand about Q methodology anyway.

I know about one attempt to mix Q methodology with discourse analysis, in a study on environmental justice in Brazil (here: http://d-nb.info/1029850070/34).

Hi Philipp, thanks for the link to that interesting thesis. As I understand the thesis DA and Q are combined, not compared. What I am looking for is a comparison of those methods.

My temporally conclusion is that the Q method is suitable to get individual views for problem situations which are well discussed. Hence, the individual view is somehow informed, structured and reflected. I would call this a complicated problem situation (rather short-term, local problems). For new, not well discussed, long-term, wicked problems (I call them complex), qualitative interviews with DA seams for me more suitable. They are more open and gives the interviewee more opportunity for opinion building and discourse forming.

Would you agree?

Another option is to combine DA with Q. The DA can be done on the interview data (which is used to generate statements for the Q-sort) and on any discussion done with participants during and after the Q sort. So the Q serves to focus on accessing the 'attitudes' of participants on specific topics, and the DA is done on a wider ranging discussion. This is more or less how I'm organising my PhD studies. As Christopher mentioned - the listserv is a great and very helpful community.

I know of no specific article that compares and contrasts Q methodology with discourse analysis, but several that utilize Q as a method of discourse analysis. The following might be places to start:

Addams, H. & Proops, J. (Eds.), Social discourse and environmental policy: An application of Q methodology. Cheltenham, UK: Edward Elgar.

de Graaf, G. (2005). Veterinarians’ discourses on animals and clients. Journal of Agricultural and Environmental Ethics, 18, 557-578.

Dryzek, J.S. (1990). Discursive democracy: Politics, policy and science. London: Cambridge University Press. (Chapter 9, "The Measure of Political Man—and Woman," pp. 173 189.)

Dryzek, J.S. (1994). Australian discourses of democracy. Australian Journal of Political Science, 29, 221 23.

Dryzek, J., & Holmes, L.T. (2002). Post-communist democratization: Political discourses across thirteen countries. Cambridge, U.K.: Cambridge University Press.

Kanra, B., & Ercan, S.A. (2012). Negotiating difference in a Muslim society: A longitudinal study of Islamic and secular discourses in Turkey. Digest of Middle East Studies, 21(1), 69-88.

Peng, Y. (1998). Democracy and Chinese political discourses. Modern China, 24, 408-444.

Stainton-Rogers, W. (Ed.) (1997-1998). Using Q as a form of discourse analysis. Operant Subjectivity, 21, 1-72 (entire issue):

Stenner, P. (Ed.) (2008-2009). Special Issue: Q and constructivism: Between discursive practice and subjective process. Operant Subjectivity, 32, entire issue.

Woolley, J.T., & McGinnis, M.V. (2000). The conflicting discourses of restoration. Society and Natural Resources, 13, 339-357.

Dryzek has been the most assiduous in applying a conceptual framework of discourse analysis within Q methodology. I would be inclined to say that Q's concept of concourse is more general than discourse, the latter being a special case of the former.

The essential difference for me is that the Q method is oriented to subjectivity and uses a statistical model whereas discourse analysis focuses on text products and processes by using linguistic analysis. Consequently they are in a way opposed approaches, the one stressing individualism, the other stressing communicative systems. In a radical form discourse analysis could be seen as a anti-humanist approach. Q-method on the other hand does just the opposite overemphasizing subjective elements. Under a disciplinary regard, q-method would belong to clinical psychology, discourse analysis to cultural sociology.

This response is a bit late, but I did wish to correct the record that discourse  analysis is cultural while Q methodology is clinical.  I have listed several publications below--and there are many others of the same kind--that show Q being applied in both clinical and cultural contexts:

Ajani, M. (2015). Citizenship, the self and the other: Critical discussions on citizenship and how to approach religious and cultural difference. Newcastle upon Tyne, UK: Cambridge Scholars Publishing.

Andrews, C.S. (2011). Defining and exploring modesty in Jewish American women. Journal of Religion and Health, 50, 818-834.

Barr, K., J. Ormrod, & R. Dudley (in press). An exploration of what service users value about early intervention in psychosis services. Psychology and Psychotherapy: Theory, Research and Practice. ePublication in advance of print (2015, January 8). doi: 10.1111/papt.12051

Brown, S.R. (1984). Values, development, and character: Appraising Korean experience. Korea Fulbright Forum, No. 1, 33‑66.

Fairweather, J. & T. Rinne (2012). Clarifying a basis for qualitative generalization using approaches that identify shared culture. Qualitative Research, 12, 473-485.

Franz, A., M. Worrell, & C. Vögele (2013). Integrating mixed method data in psychological research: Combining Q methodology and questionnaires in a study investigating cultural and psychological influences on adolescent sexual behavior. Journal of Mixed Methods Research, 7, 370-389.

Stephenson, W. (1962). “Ideal” types. Psychological Record, 12, 9-16.

Stephenson, W. (1980). Consciring: A general theory for subjective communicability. In Dan Nimmo (Ed.), Communication yearbook 4 (pp. 7-36). New Brunswick, NJ: Transaction Books.

Stephenson, W. (1985). Perspectives in psychology: Integration in clinical psychology. Psychological Record, 35, 41-48.

Wallis, J., J. Burns, & R. Capdevila (2011). What is narrative therapy and what is it not? The usefulness of Q methodology to explore accounts of White and Epston's (1990) approach to narrative therapy. Clinical Psychology & Psychotherapy, 18, 486-497.

Subjectivity is ubiquitous, in the culture as well as on the couch, and only the words 'clinical' and 'cultural' (backed by the authority of their disciplines) create the impression that there is a boundary between them.  It is not the case that Q methodology overemphasizes subjectivity, any more than that chemistry overemphasizes elements.  Subjectivity is everywhere, and Q is its science.

I will suggest you look up :

St. Pierre, E. A. (2013). Post qualitative research: The critique and the coming after. In N.K. Denzin & Y.S. Lincoln (Eds.), Collecting and interpreting qualitative materials (4th Ed.) (pp.447-480). Los Angeles/London/New Delhi: Sage Publications INC.