I just returned from a fishing trip to Canada and, to my surprise (not really), a statistical issue came to mind. Can you use statistics to determine when to change your lure?
I was sitting in a boat with another person and fishing. We had our choice of different lures, different colors, and a choice of casting or trolling. It sounds like a story problem, but it is not. The question was to determine when the other person was catching more fish than I was, to a significant level, so that I would then change to match his lure/color/speed.
So what did I do? I changed if my partner caught four without my catching any. It seemed right at the time. Now back home I decided to see if my intuition was good. So here is an analysis of the catching count compared to a 50% (random) chance to catch a fish.
If you look at the table, it was not until my partner caught 6 fish that could I be sure that I was not doing as well as he. When I changed at four to 0, I was deciding with a 87.5% confidence. I should know better.
So what if I compared his catch to mine, when I had caught one fish.
In this case, he needed to catch nine to my one before we had shown a significant difference (from 50% chance). I know that binomial probabilities are difficult to estimate, and the sample sizes required for significance are nearly always greater than I guess. In this case I re-proved it to myself.
All is well and good, if catching a fish is really a random event, that each person has a 50% chance. I do not believe it is true, so is this a wasted analysis? No, it is just fun.
On my last day, we fished all day switching lures every 15 minutes or so with only one fish every hour or so, and then I went to a gold red-eye spoon on a slow troll. I started catching a fish every five minutes. When my partner changed to a lure like mine, we had a great day. It was hard to get up to a trolling speed without one of us catching a fish. So there is more to it than random dumb luck. Although that is my only hope!
But I did catch a lot of fish, and here is the big one.
It was 39″ long and about 19 pounds.