1. BMS 617 Lecture 17 : Summary Marshall University Genomics Core Facility

2. A conversation Biologist: I made measurements on three control samples and three treated samples. The difference was so big, I really don’t need to run any stats Statistician: But without running any stats, you only know about your samples. You don’t know anything about the population values Biologist: I don’t understand what you mean Statistician: OK, let me explain. … Biologist: OK, but look at the data. All the treated values are way bigger than all the control values. What are the chances of that? Statistician: Exactly. Marshall University School of Medicine

3. Discussion What do you think the statistician said after “Let me explain”? What did the statistician mean by “Exactly” at the end? Marshall University School of Medicine

4. Hypothesis testing: big picture • All statistical hypothesis testing works along the following plan: • Identify the null hypothesis • Compute a test statistic • The test statistic should be a measure • related to the effect size, and • whose distribution is known (or can be approximated) under the assumption of the null hypothesis • Using the value of the test statistic, and its “null distribution”, compute the p-value • The probability of seeing this big a value assuming the null hypothesis is true Marshall University School of Medicine

5. Test statistics • The most important feature of test statistics is that they have a known (or approximately known) distribution • Not necessarily an intuitive quantity • In fact, rarely so • t-test: t ratio (ratio of differences of means to pooled standard error) • ANOVA, and model comparison: F ratio • Chi-squared test: sum of squares of differences between observed and expected values, divided by expected value • Fisher’s exact test: the whole contingency matrix! Marshall University School of Medicine