13 July 2016

"How Not to Be Wrong: The Power of Mathematical Thinking" by Jordan Ellenberg

It was not until I was halfway through this way thick book that I realized something important: the book's title is incredibly clever. Reading the title, I assumed that in explaining how not to be wrong that it would explain how to be correct. In reality, there is a lot of ground between not being wrong and being correct. Some interesting points:
  • All lines are curves so stop drawing straight lines all the time. Basically, anytime you are using a linear graph, with a straight line, you can be very confident that your chart is wrong.
  • Be careful with regression calculations. They are easy to do but often make up a story that is far different than reality.
  • Beware of the Gamblers fallacy. Each instance has an equal chance of occurrence regardless of how many instances there have been before.
  • Don't talk about percentages of numbers when the numbers might be negative. For example, percent of sales is a bad practice because it deludes the story: if sales are down 50%, is everything down 50% or is a single category doing so poorly it drags everything else down? Expenses, revenue and populations, however, are rarely negative (an expense that pays you?) so they are acceptably expressed in percentages.
  • Small data sets are susceptible sample volatility. Beware.
  • Inference is a tricky sport that can often lead to dangerous conclusions.
  • Things are not usually equal and the inequalities often matter a lot.
  • Lead with data, it will show who should win.
  • Instead of asking what the chances of getting into a slot are, ask what are the chances that something in the slot is wrong. The chances you got something wrong are often the scary numbers we should be concerned about.

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