Hypothesis testing is like a court of law: You aim to disprove the null hypothesis. The hypothesis of a court: The person in the dock is innocent. The aim is to gather evidence that is inconsistent with this hypothesis. We reject the hypothesis (and decide the person is guilty) if the evidence makes the hypothesis unlikely (beyond all reasonable doubt) .
Observational studies could feed into inductive reasoning. Pilot studies have a place in forming hypotheses. Some disciplines (e.g. psychology) seem to disapprove of observational studies. Presumably such studies are written up as if the hypotheses were decided before gathering the data. (A dangerous practice!)
In a controlled experiment where the quantity of interest is a measurement, forty or so independent observations will typically enable modest-sized differences to be identified.
With observational data and questionnaire data, gathering 150 data or more should typically be the aim: you want 25 observations in each category of interest.
More data is needed with counts than measurements.
More data is needed with binary quantities (yes/no; cured/not cured; success/failure) than with Likert scores.
Questionnaires Likert scales are good: strongly weakly indifferent/ disagree/ strongly agree/ agree/ disagree. Having five points on a Likert scale is often about right. Code the values as 1, 2, 3, 4, 5 and it is usually OK to treat them as measurements. Open-ended questions are hard to analyse.
Turning data into information: First produce summary statistics (means percentages, standard deviations), graphs, bar-charts, cross-tabulations.
Try to get a feel for your data – what does it tell you? (If you feel you are non-numerate, work at becoming numerate.)
Try to form quantitative hypotheses that you think the data will refute. (e.g. “The proportions in the ‘strongly agree’ category are the same in these two sub-populations” or “As this quantity changes, the average value of this other quantity does not change”.)