layout: true .absolute.top-0.right-1.tr.w-10[ <!-- --> ] --- name: title class: left bottom hide-count background-color: #FBFCFF; <div class="talk-meta"> <div class="talk-title"> <h1>Introduction to Data Analysis with R</h1> <p>Lecture 5: The Nature of Randomness</p> </div> <div class="talk-author"> Jannik Buhr <br/> <span>Heidelberg University, WS20/21</span> </div> <div class="talk-date">2020-11-29</div> </div> .absolute.bottom-0.right-1.mid-gray[ With Artwork by @allison_horst ] --- class: inverse center middle > To understand statistics means understanding the nature of randomness first. --- class: inverse center middle <img src="img/statistically-significant.jpg" width="50%" /> --- class: center middle <img src="slides5_files/figure-html/chess-board-1.png" width="504" /> --- class: center middle animated fadeInUp <div class="figure"> <img src="img/paste-5E31A2FF.png" alt="Artwork by @allison_horst" width="213" class=.external /> <p class="caption">Artwork by @allison_horst</p> </div> --- ## Definitions - **alternative hypothesis** ( `\(H_1\)` ) ("I am the better player.") - **null hypothesis** ( `\(H_0\)` ) ("This is just luck") ## `\(\rightarrow\)` to R! --- ## Making Decisions - How likely is certain event is under the assumption of the null hypothesis (only chance)? - Decide on some threshold `\(\alpha\)`, at which we reject the null hypothesis. - This is called the **significance threshold**. - For `\(P[X \ge x]< \alpha\)`: **statistically significant** - This probability is called the **p-value**. --- class: middle > »A p value is not a measure of how right you are, or how significant the difference is; it’s a measure of how surprised you should be if there is no actual difference between the groups, but you got data suggesting there is. A bigger difference, or one backed up by more data, suggests more surprise and a smaller p value.« > — Alex Reinhart [@reinhartStatisticsDoneWrong2015] --- class: middle [I Fooled Millions Into Thinking Chocolate Helps Weight Loss. Here's How.](https://io9.gizmodo.com/i-fooled-millions-into-thinking-chocolate-helps-weight-1707251800) by John Bohannon --- ## Example: Medical Testing - Sensitivity = Power = true positive rate = `\(1-\beta\)` - Specificity = true negative rate = `\(1-\alpha\)` Let us assume a test with a sensitivity of 90% and a specificity of 92%. -- - 1000 people - 10 positive - 9 tested true positive - 1 false negative - 79 false positives -- <img src="slides5_files/figure-html/unnamed-chunk-3-1.png" width="90%" /> Probability of being positive after positive test: `$$\frac{true~positives}{true~positives + false~positives}=10\%$$` Formally, this is described by Bayes's Formula `$$P(A|B)=\frac{P(B|A)*P(A)}{P(B)}$$`