German literature would typically list the following categories (I am trying to make a meaningful translation):

- reconstruction of subjective meanings. e.g., oral history or biographical research.

- description of social action and social environment. e.g. ethnographical or phenomenological research.

- reconstruction of structures. "Objective Hermeneutics" - a classic. see Oevermann, or Hermeneutics. https://en.wikipedia.org/wiki/Hermeneutics

- reconstruction of interpretation. see Reichertz: https://www.uni-due.de/kowi/R_engl.shtml

The last item is really an extension of the first three.

Hope this helps.

The sequence of questions in a qualitative research study could be in the following order-

1. Factual Information

2. Opinion Questions

3. Probing Questions

4. Interpretative & Conclusive queries 

The following books and papers should be helpful to your topic: 

• Crescentini, A. and Mainardi, G. (2009) Qualitative research articles: guidelines, suggestions and needs, Journal of Workplace Learning, 21, 5, pp. 431-439.
• Mack, N., Woodsong, C., MacQueen, K. M., Guest, G. and Namey, E. (2005) Qualitative Research Methods: A Data Collector's Field Guide, Family Health International, North Carolina, US.
• Sampson, J. P. J. (2012). A Guide to Quantitative and Qualitative Dissertation Research from Educational Psychology and Learning Systems Faculty Publications, Paper 1: http://diginole.lib.fsu.edu/edpsy_faculty_publications/1/?utm_source=diginole.lib.fsu.edu%2Fedpsy_faculty_publications%2F1&utm_medium=PDF&utm_campaign=PDFCoverPages
• Yin, R. K. (2011) Qualitative Research from Start to Finish, The Guilford Press, New York: USA. 

Hello Arif,

You have a very interesting question here.  I am keenly aware that human beings like to categorise things because doing so brings cognitive comfort.

Unfortunately, I'm not sure that this comfort can be easily achieved in many contexts.  Let me take your categories about quantitative research (the ones you propose in your question) as an example.  What you have done - used three categories - is immediately meaningful and works a lot of the time.  However, it is arguable that there are only two main categories of research questions, namely those that are addressed with descriptive statistics and those that are addressed with inferential statistics, and that the inferential category subdivides into questions with an associational focus versus questions with a difference focus.

But even that categorisation doesn't really work.  For example, some people categorise correlation (including Pearson's and Spearman's correlation coefficients, intraclass correlation coefficients, and other measures of association - even, perhaps factor analysis?) as descriptive, I guess often because, unlike inferential statistics, they (or some of them) are not based on probability theory. At the same time, I'm pretty sure that many people would regard Pearson's and Spearman's correlations as inferential in nature because they are usually presented with p values. So, it is not easy to determine whether correlations are descriptive or inferential in nature.

Furthermore, depending on the way a research question is couched, it could be conceived of as being associational or difference in nature. This often becomes evident when chi-square is the most appropriate statistic for analysing a particular research issue.  With chi-square, the ball can often bounce either way.

So!  - sorry, but rather than answering your question, I've messed it up.  I hope the outcome is not destructive, however.  In essence, I am trying to indicate that making categories, attractive as it might seem, is sometimes not an easy matter - which is, of course, why you asked your question in the first place.

As far as qualitative research is concerned, I suspect the landscape is more difficult to categorise than it is for quantitative research and therefore you perhaps should not beat your head against a wall until clarity emerges.  Complete clarity might be unattainable, so it might be necessary to make the best of what is possible, or perhaps even reframe the question / issue that is troubling you.

Maybe one solution is to draw up the best set of categories that is attainable, and then be clear about why it does not fully resolve into neatness. Working along those lines might be the most effective and satisfying way to indulge in an intellectual workout.

One thing that interests me is whether there is a difference between the nature of research questions and the nature of the methods, or even frameworks, that are used to address them.  I suspect that these things might become confused with each other at times and therefore make the task of categorisation more complicated than it might otherwise be.

I know that when we were teaching qualitative methods, we used to divide qual studies into phenomenology, ethnography, grounded theory, case studies, and action research - and then look at the kinds of activities and analyses that could be used under each of them.  I don't know whether that was the best way to go about things, but at least it gave us some meaningful structure to work within rather than working within a swamp of blubber.  Ah, and we also acknowledged that there were other things that could fall under the umbrella of qualitative research that might not have fitted within our proposed categories.

Happy thinking!

Robt.