Why do we refute the null hypothesis rather than prove a primary hypothesis?

In a clinical trial we are testing to see if a new treatment is more effective than existing treatments. You’d think therefore that we’d create a hypothesis like “my new treatment will be 40% better than the current leading treatment for headaches” and then we’d go out and run a trial to prove this hypothesis. We don’t though…we create a “null hypothesis” that states that nothing is going to change i.e. “my new compound is no better than the current leading treatment for headaches” and then we try to reject this.

This seems counter-intuitive and seems to unnecessarily create a double-negative. If you use Google to find out why we take this convoluted approach you will get a lot of academic mathematical justification but non written in common sense terms so I decided that I’d give it a go.

Why do we start with the null hypothesis? It could be that saying “reject the null hypothesis” makes you feel really smart and a little bit rebellious. The internet's combined wisdom suggests that mathematically, the principle of disconfirmation states that you cannot prove something is 100% true but you can prove that it is false…this may be true but I struggle to marry this up to the objective of a clinical trial using common sense. Surely, I *could* prove that my compound is better than the current treatments, no?

So here’s my theory and it really comes down to the inability to quantify, not the ability to ‘prove/reject’.

• Let’s start with trying to prove a primary hypothesis:
  • My new compound will be 40% better than the current leading treatment for headaches.
  • To prove this I need to be able to quantify the improvement. Could you tell me whether your headache is x% better than it was an hour ago?
  • What if I could measure its effectiveness but it appears to be just 38% better? Does my trial fail?
  • Bottom line, it is incredibly difficult to set the standard for ‘better’ in a hypothesis for a drug’s efficacy because 'better' needs to be demonstrable and with drugs, that's really hard, 
• Now consider rejecting a null hypothesis:
  • My new compound is no better than the current leading treatment for headaches.
  • Could you tell me whether your headache has improved? I am sure that you could.
  • Could you give me a general indication before the drug was taken and an hour after (on a scale of 0-10 for example)? I'd think so. 
  • Using control groups and with a large enough sample size, it is relatively easy to show that a drug is ‘better than’ or ‘not better than’ an alternative without having to set a threshold of how much better. It is not having to deal with "how much better" that makes this more realistic.
  • So the bar to reject the null hypothesis is much lower than to demonstrate a specific improvement
• In the primary hypothesis example, I have to set thresholds for my expectations as the primary goal. In the second example, I just need to show that it is better. Once you’ve shown that then you can focus on trying to show how much better…or even what “better” means in this context. Don’t get me wrong, the trial will want to show a demonstrable improvement but that can be secondary to just showing this it is indeed an improvement.
• So why not just have a primary hypothesis that says "my compound is generally better than the current treatment"? Effectively, that is what refuting the null hypothesis is saying but with the added benefit of sounding super smart when you say it...IMHO.

As a final thought, in the UK there was an advertising slogan for a pain reliever that claimed, “Nothing works faster than Anadin”. I was pondering whether this would be a null hypothesis for the first ever pain killer or an alternative hypothesis claiming that Anadin was the fastest in class…or just terrible marketing.

Feel free to comment but the feedback needs to stay in the common-sense realm. The first person to write H₀ gets abused.