## Expertise and statistics

**psychology**, **statistics**, **education**, **communication**, **personal development**, **werk**

It’s been a while since I wrote anything here, so I’m going to briefly write about some things that I learned recently.

An article with the captivating title “Ability to See Expertise is a Milestone Worth Aiming For” discusses how being able to see expertise requires expertise, and therefore worth striving for if you care about knowing what you’re doing. (There’s also a tangent (or main thread?) of how you should use social networks (no, not websites) to get a better salary.) I’ve recognized this in myself and others: that you were missing or recently gained the ability to see the expertise of someone or fully appreciate a particular insight.

One such moment was reading this article, on how long it takes to become gaussian (for convoluting non-gaussian distribution, i.e. having various sets of sampling from an arbitrary non-gaussian distribution). Turns out: sometimes really long! I’ve not had much of a statistical education, but it has always had my interested ever since I discovered a quantity that had a non-gaussian distribution, which illuminated for me the fact that we assume this perhaps way too often. A quote written after my own heart:

Blindly slapping a normal distribution on things is a convenience from the time when we didn’t have fast computers, because the normal distribution has nice theoretical properties that make pen-and-paper analysis convenient.

I failed to convince people in my time working in a hospital research group of this, probably because I lacked the ability to express myself as a layman as described in the Expertise article. The Gaussian is everywhere in medicine, and the mean is usually the only thing that’s calculated and reported. I argued that we had the data to investigate this, but it fell on deaf ears, and since I was not tasked with data analysis I didn’t have the time to do it myself. What I learned now is a bit of vocabulary to express this, and also the sifnificance of mathematical moments. I’m sure someone has tried to educate me on them, but I never remembered the concept or their significance. I would use the difference between the measures of centralcy to explain myself, and now I can use the four basic moments instead, because distributions can be categorized according to these values. A table of `P(exceeding)`

for the normal distribution and the Cantelli and Chebychev estimates is a good way to illustrate the relevance for medicine: outliers may be much more normal than doctors think!

Sigma | Normal | Cantelli | Chebyshev |
---|---|---|---|

1 | 16 % | 50 % | 50% |

2 | 2.3 % | 20 % | 25% |

3 | 0.14 % | 10 % | 11.11% |

4 | 0.003 % | 6 % | 6.25% |

5 | 0.00003 % | 4 % | 4% |