Science is awesome!
My brother, who is a scientist, just posted a really interesting post on his infrequently updated blog that is related to the work he is doing in researching the dietary habits of skates. I am definitely not a scientist, but I will try to explain here why I think his work is interesting and important.
A lot of Simon’s research is analyzing the stomach contents of skates he pulls out of the ocean. He cuts the stomachs open and pulls out all the little bits, and then using a microscope, categorizes everything that the skate has recently consumed. Most of the time this involves identifying different species of shrimp by the shape of the tiny prongs on their noses.
So, say he cuts open 100 skates, and in 80 of them, he finds 5 shrimp with three pointy nose prongs, and in 20 of them he finds no shrimp with three pointy nose prongs. Current practices dictate that when he calculates the average number of this type of shrimp consumed by skates, he includes twenty zeros in the average - ((5×80) + (20×0)) / 100 - meaning the estimate would be that on average, skates eat 4 three-prong-shrimp.
But, my brother says, that isn’t true or accurate! This method discounts the fact that 20% of the skates just don’t eat shrimp and in fact implies that they DO eat a significant amount of shrimp - a meaningful difference! Some skates do not like shrimp, and no amount of math is going to make them eat shrimp. If you are trying to properly model their eating habits, you should not ignore this fact!
His proposal is that the zero values should not be included in the calculation of the average, and instead two terms should be calculated: 80% of skates consume an average of 5 shrimp, and 20% of skates do not consume shrimp at all. This gives a much more accurate description of the dietary habits.
Thus, my brother is a genius.
Here is my brother’s original post, where he talks about apples instead of three-nose-prong shrimp. He talks a little bit more about the conceptual math behind his idea, so reading his original post may make the nonsense that I just spewed a bit more understandable. Like I said, me ain’t no scientist, me just some guy who likes to eat a non-zero amount of shrimp.
Update - See comments for my brother’s corrections to my bastardized version of his originally correct blog post.
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