I've found a similar topic related to "via the Internet", but I'm still wondering if you can use the phrase without a preposition - "via survey."
I conducted primary research via survey.
I conducted primary research via a survey.
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Yes, you are correct: "via survey" refers to the method of research, whereas "via a survey" is a specific instance of that method.
Extending your example to highlight that "via survey" refers to the method used, your report might have read as follows.
"Primary research on patient preferences was conducted via survey. In addition, statistical analysis was used to assess dose responses, while a literature review assessed comparative death rates after 12 months in a range of countries."
There is also another subtle but important difference between "via a survey" and "via survey": the way the two phrases sound when spoken or read aloud. The article "a" is difficult to pronounce nicely after the word "via". Therefore, a sentence referring to a single survey ought to be restructured to avoid the "via a" construct.
It looks like both are correct. One can find relevant results for both cases - by survey and by a survey in Corpus of Global Web-Based English
Below are usages of both cases starting with conduct research via ....
If you search for this phrase in Google, you get several relevant results.
For instance, from Annals of Family Medicine
It provides infrastructure, researcher consultation, and facilitated collaboration to conduct research via survey
These professionals conduct research via survey, focus groups and polls, and identify consumer habits and market trends.
Here, you also get relevant results. For example, from Chronic cough: An exploration of impact and an evaluation of non-pharmacological management in adults
There are a number of different strategies to conduct research via a survey including mailed surveys, group-administered surveys, telephone surveys, internet surveys or mixed model surveys (Check and Schutt, 2012).
So, in my case, I should write: "Next, I conducted primary research via survey. I prepared two types of surveys: one for doctors to determine the necessary features and another one for patients to better understand their needs." instead of "Next, I conducted primary research via a survey." The first one would be the type of research method, then the next sentence would refer to particular surveys.
is correct in its analysis, which I emphasised.
"via survey" is a method, and "via a survey" is with a particular instance of a survey.
Both are grammatically correct and easily understood. If there are multiple surveys you can also say "via surveys" or "via three different surveys", etc. None are better than the others, it's your choice which one to use.
This n-gram shows that "via survey" and "via a survey" are nearly equal in usage in books.