Fisher’s dilemma

One of my projects has been at an impasse for a long time, and one of the project team members came up with a little fable that captures it neatly:

A fisherman named Fisher makes a living by fishing. He goes out every day and always comes back with some fish. The number of fish he gets each day follows a uniform distribution (the probability of catching 1 fish is 10%, 2 fish 10%, and so on through 10 fish). The average caught per day is 5.5. On a day when his statistician friend came to visit, he came back with 8 fish. The statistician calculated the 95% CI of a ratio of a random variable with uniform distribution over the mean (5.5) and found a portion of the CI was less than 1. The statistician thereby concluded that there is not enough evidence to suggest that this was a good day. His wife thought he had a good day because 8 is more than 5.5. Fisher was confused.

The author and myself are with Fisher’s wife. The rest of the team, including the client, sides with the statistician. These are such different ways of perceiving reality that I cannot imagine ever finding a resolution. But far from feeling despondent, I feel unburdened, at liberty to wrap this project up and move on to something else.

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