Is cognitive science hypothesis-based or bound to strict experiments involving statistics? When I look at medical journal articles on Google Scholar I see a lot of stuff based on double blind placebo tests. From this, I've gathered that medicine often performs experiments. 

I've been in touch with cognitive behavioral psychological therapy, but not enough to say whether psychology is more "philosophical", in being hypothesis based, or instead bound to strict experiments using statistics.
You may want to have a look at our 40 questions to date that use the statistics tag. These may demonstrate the complexity of our applications in statistics. Wikipedia also has an entire psychological statistics page that seems intended to index other pages on specific applications. Psychological experiments commonly test null hypotheses (e.g., $H_0$: the experimental treatment and placebo control conditions will not differ in measures of an outcome variable), so experimental methods and hypothesis testing methods do not exclude one another. Moreover, concern for placebo effects implies a study may be at least loosely related to cognitive-psychology itself, as placebo effects involve cognitive-neuroscience, neurobiology, psychopharmacology, and experimental-psychology, maybe among others. Plenty to read!