✎ Statistics [The Physics Travel Guide]

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====== Statistics ======

<tabbox Why is it interesting?> 
For many extremely illuminating visualizations, see http://students.brown.edu/seeing-theory/

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* **Probability** is starting with an animal, and figuring out what footprints it will make
  * **Statistics** is seeing a footprint, and guessing the animal.

Probability is straightforward: you have the bear. Measure the foot size, the leg length, and you can deduce the footprints. "Oh, Mr. Bubbles weighs 400lbs and has 3-foot legs, and will make tracks like this." More academically: "We have a fair coin. After 10 flips, here are the possible outcomes."

Statistics is harder. We measure the footprints and have to guess what animal it could be. A bear? A human? If we get 6 heads and 4 tails, what're the chances of a fair coin?#

<cite>[[https://betterexplained.com/articles/a-brief-introduction-to-probability-statistics/|A Brief Introduction to Probability & Statistics]] by Kalid Azad</cite>

</blockquote>

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** Important related concepts:**

* [[advanced_tools:bayesian_statistics|Bayesian Statistics]]

<note tip>
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
</note>
  
<tabbox Student>

**Recommended Reading:**

* [[https://betterexplained.com/articles/a-brief-introduction-to-probability-statistics/|A Brief Introduction to Probability & Statistics]] by Kalid Azad
  * [[https://psyarxiv.com/85ywt|Introduction to the concept of likelihood and its applications]] by Alexander Etz
  * [[https://amva4newphysics.wordpress.com/2017/10/21/what-is-statistical-significance/|What is Statistical Significance?]] by Tommaso Dorigo
  * http://www.science20.com/tommaso_dorigo/decision_trees_explained_to_kids-224948
  * [[https://brownmath.com/swt/|Stats without Tears]] by Stan Brown (free online textbook)
  * Statistics: (for Bayesian) Statistical Rethinking - A Bayesian Course with Examples in R and Stan - by McElreath 
  * [[https://arxiv.org/pdf/1310.1284.pdf|DISCOVERING THE SIGNIFICANCE OF 5σ]] Louis Lyons
 
<tabbox Researcher>

* Data Analysis in High Energy Physics: A Practical Guide to Statistical Methods  by Olaf Behnke et. al.

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