Discovering power laws is an important thing in physics.
Often people claim they have evidence for one.
My question is:
Over how many orders of magnitude must the data follow the apparent power law for you to believe it?
Often I read papers or hear speakers showing just one decade (or less!).
Is this convincing? Is it important?
Personally, I find that my prejudice is that I need to see at least 1.5 decades before I even take notice. Two decades is convincing and three or more is impressive.
What do other people think?
Some of the most important power laws are those associated with critical phenomena (and scaling). The most impressive experiments see thermodynamic quantities which depend on a power of the deviation from the critical temperature by many orders of magnitude. My favourite experiment involved superfluid helium on the space shuttle and observed scaling over 7 decades!