How to overcome the unequal sample size problem in convergent parallel design? e.g. using snowballing technique quantitative samples reached 160, and only 25 of 160 samples agreed to participate in qualitative interviews. (subject is HIV patients)
I'm not sure there is any problem to overcome, given your case. Indeed, it would be ideal to have a same number of people in both Qual and Quant phase. In reality, however, it tends to be impossible because there are a lot of reasons people would decline an interview... plus, think about the logistics of interviewing 160-individuals. Unless you have a lot of time, it is quite impossible to get in-depth with 160-individuals.
Anyway, my suggestion for you is to do in-depth interviews on those available interview participants and worry less about your unequal sampling size. Depending on the variables you're studying, these individuals might have good insights on the general populations. Based on my experience, if things done right, we can get more data from a willing small sample pool than a less willing large sample pool.
To echo and build on what's been said already by others, there's no reason you should need equal sample size across your qualitative and quantitative strands. Presumably you are using qualitative and quantitative approaches for a reason, and they serve different purposes within your overall design. Chances are, the qualitative strand is giving you a different type of information at a different level of depth, and it's reasonable for that to come from a smaller number of individuals.
If you recruited for both strands at the same time from the same population, though, you might want to think carefully about what sort of relative bias might have been introduced in this process (i.e. the characteristics of the group that agreed to participate in interviews might be systematically different than the whole group that agreed to participate in the study or the population of interest. You will need to consider that in interpreting your findings and drawing conclusions).
I've never liked the terminology "convergent parallel" designs because things that are parallel never converge. To me, convergence by itself summarizes the goal in such designs, but so be it.
With convergence, the key goal is to show the equivalence of the results from a qualitative and a quantitative study of the same research question. Each method should be 'self-sufficient' in the sense of meeting the appropriate standards for that type of method. Hence, there is no need to generate an overly large sample for the qualitative portion of your study.
I think there are at least three issues you should consider before you undertake a convergent design. First, what you do actually achieve if you answer the same question twice? Unless you have a strong interest in validity, this is not a very interesting finding.
Second, what will you do if your results diverge rather than converge? Do you have a plan for handing results that do not agree?
Third, how will you assess convergence? Determining the similarity between statistical results and qualitative analyses can be quite difficult. For one approach, see my suggestions in:
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