05a-variation-and-inference.Rmd

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# Variation and inference

## What is variation and uncertainty?

Debby Swayne, famous for her work on XGobi [XXX], and GGobi [XXX], liked to say that probability was what she found hardest about learning statistics. Her example was a coin flip. She observed the result of a coin flip, and so there was nothing uncertain. It either was a head or a tail. Maybe this transition is hard for many people. Once we have observed something, it is difficult to step backwards and imagine the uncertainty -- "hindsight is 20/20". 

Debby took issue with the teaching of the probability of a head for a coin flip being $1/2$. Prior to tossing the coin, assuming that it is a fair coin, we are told that the probability, or the long term average, for observing a head is the same as for a tail, a half. Half the time, the coin will show a head and half the time it will show a tail. This thinking assumes that someone tosses the coin for their entire life and beyond. 

Not enough emphasis is given to once the event has happened, the result is known. It either occurred or didn't occur, probability 1 or 0. The former is a vague concept, but the latter is a certainty.

This has a name, *hindsight bias*, which is the inclination after an event has occurred to see it as predictable. It is also called *knew-it-all-along effect* or *creeping determinism* [(wikipedia)](https://en.wikipedia.org/wiki/Hindsight_bias). 

We often have the sample in hand, which is like seeing the result of the coin flip, without knowing what the original options were. 

More about short term coin flip sequences. 


## Ways of sampling the data 

## What is inference?

## Collecting data

## Randomization tests

Using randomization tests

## Visual inference