====== Statistics ====== For many extremely illuminating visualizations, see http://students.brown.edu/seeing-theory/ ----
* **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?# [[https://betterexplained.com/articles/a-brief-introduction-to-probability-statistics/|A Brief Introduction to Probability & Statistics]] by Kalid Azad
---- ** Important related concepts:** * [[advanced_tools:bayesian_statistics|Bayesian Statistics]] 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. **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 * Data Analysis in High Energy Physics: A Practical Guide to Statistical Methods by Olaf Behnke et. al. *[[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4877414/| Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations]] by Sander Greenland et. al. *[[https://bayes.wustl.edu/|Probability Theory as Extended Logic]] Edwin T. Jaynes - Washington University website *[[https://www.amazon.com/exec/obidos/tg/detail/-/0521592712/qid=1055853130/sr=8-1/ref=sr_8_1/103-5027289-6942223?v=glance&s=books&n=507846| Probability Theory: The Logic of Science]] by Edwin T. Jaynes --> Example1# <-- --> Example2:# <--