Sunday, March 01, 2020

How Not to Be Wrong: The Power of Mathematical Thinking

How Not To Be Wrong is part an exploration of the joys of math, and part a manual on how to avoid getting duped (or duping oneself) with math. There is also a bit of namedropping of famous mathematicians for good measure. Politicians are great at coming up with good sounding, but meaningless numbers. Wisconsin may have claimed that its 5000 net new jobs accounted for 50% of all new jobs for a year. That could be technically correct. However, since some states lost jobs, a state with 12000 net new jobs would claim to account for 120% of net new jobs, showing the craziness of the data. Science is also rife with "statistically significant random results" from insufficiently large or small studies. There is also a "survivors bias", with many failed studies not being published. If 20 people study something, one is likely to randomly discover a significant result. If that person is the only one to publish, we don't realize the significant result was just random. The "5%" p-value acceptance threshold is just an arbitrary value. However, it does result in a serious amount of 'p-hacking' There are a lot more studies that just meet the threshold than would be suspected by a normal distribution. Similarly, people tend to favor numbers ending in 7 as "random numbers". Thus, an excessive preponderance of vote counts ending in 7, may indicate a rigged election.

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