Lack of hypothesis or a priori basis for analysis...name of concept and references? In contrast to an a priori approach with a testable hypothesis, what is it called when a study examines data in search of a possible relationship in a more exploratory and unfounded way?
For example, if a researcher tries multiple combinations or variations of data (different lags, intervals, time periods, methods, and so on) before finding a "statistically significant" result ... is there a formal name for this and are there any references about this type of practice? (including, importantly, what type of statistical testing would be appropriate in such cases...)
 A: To your first question, I think it is just called: "feasibility study", "pilot study/experiment", "exploratory study/research", "(experimental) parameter optimization", etc.
The purpose of such experiments is to get an idea of whether such an experiment is feasible, how the data look like (scale, distribution, variation), what may be the factors of interest and confounding factors. Most importantly, exploratory data can help to guide an a-priori power-analysis for a following hypothesis-driven experiment when no good reference data are available.
In exploratory research you mainly will use descriptive methods to get a feeling for the data. Of course you can use any statistical test, too. However, you must be very careful about the conclusions drawn. What you describe above sounds like there is a real risk for running into a multiple comparison problem.
Exploratory research is legitimate (and often necessary) before advancing towards hypothesis-driven approaches in which you estimate the factors at play with precision and try to draw conclusions (at some degree of certainty) on them.
