Clinical trials are the standard way to produce new evidence. A new book reminds us that this is quite new. It starts explaining the scurby case and how it took 50 years to apply its results (lemon) to avoid death among sailors. There is aplenty of details and experiments among medicine, social and policy domains. You'll find a reference to the Rand Health Insurance Experiment and nudge examples.
If you want a good review of the book, check this one or Diane Coyle.
The more we ask the question ‘What’s your evidence?’, the more likely we are to find out what works – and what does not. Scepticism isn’t the enemy of optimism: it’s the channel through which our desire to solve big problems translates into real results. If we let our curiosity roam free, we might be surprised how much we can learn about the world, one coin toss at a time.