Realistic scientific studies of productivity are often not feasible. For example, people often claim that programming language X makes them more productive than language Y. How could you conduct a study where you randomly assign someone a programming language to use for a career? You could do some rinky-dink study where you have 30 CS students do an artificial assignment using language X and 30 using Y. But that’s not the same thing, not by a long shot.
If someone, for example Rich Hickey, says that he’s three times more productive using one language than another, you can’t test that assertion scientifically. But what you can do is ask whether you think you are similar to that person and whether you work on similar problems. If so, maybe you should give their recommended language a try.
Suppose you wanted to test whether people are more productive when they concentrate intensely for two hours in the morning and two hours in the afternoon. You couldn’t just randomize people to such a schedule. That would be like randomizing some people to run a four-minute mile. Many people are not capable of such concentration. They either lack the mental stamina or the opportunity to choose how they work. So you’d have to start with people who have the stamina and opportunity to work the way you want to test. Then you’d randomize some of these people to working longer, fractured work days. Is that even possible? How would you keep people from concentrating? Harrison Bergeron anyone? And if it’s possible, would it be ethical?
Real anecdotal evidence is sometimes more valuable than artificial scientific data. As Tukey said, it’s better to solve the right problem the wrong way than to solve the wrong problem the right way.