class: center, middle, inverse, title-slide # Point Estimates and Confidence intervals ## NEUS 643 ### Ted Laderas ### 2020-05-14 --- # Learning Objectives - **Understand** point estimates as measurements - **Understand** that Standard Deviation and confidence intervals are not the same thing - **Learn** about *confidence intervals* and how we can estimate them from observed data using *bootstrapping* - **Learn** about *sampling with replacement*. - *Utilize* bootstrap distributions to estimate confidence intervals - **Understand** that sampling is the basis for both confidence intervals and hypothesis testing --- # Cellular Imaging measurements - We tend to generate a lot of individual measurements from single cells, such as ~500 cells in an image - We can utilize this to our advantage - Larger data means we can do better statistics --- <img src="image/week6_2/01_point_estimate.JPG" width = 800> --- <img src="image/week6_2/01_point_estimate2.JPG" width = 800> --- <img src="image/week6_2/02_ci_definition.JPG" width = 800> --- <img src="image/week6_2/02_ci_definition2.JPG" width = 800> --- <img src="image/week6_2/03_ci_vs_sd.JPG" width = 800> --- <img src="image/week6_2/03_ci_vs_sd2.JPG" width = 800> --- <img src="image/week6_2/04_most_experiments.JPG" width = 800> --- <img src="image/week6_2/05_why_formulas.JPG" width = 800> --- <img src="image/week6_2/09_visualize.png" width = 800> ??? https://moderndive.com/9-hypothesis-testing.html --- <img src="image/week6_2/06_sampling_with_replacement.JPG" width = 800> --- <img src="image/week6_2/07_bootstrap1.JPG" width = 800> --- <img src="image/week6_2/08_bootstrap2.JPG" width = 800> --- <img src="image/week6_2/09_bootstrap2.JPG" width = 800> --- # Who Cares? - Data centric view of calculating CIs - Does not rely on assumptions of the data - Can be calculated for any dataset with enough measurements --- <img src="image/week6_2/10_ht.png" width=800> ??? https://moderndive.com/9-hypothesis-testing.html We'll expand this into *hypothesis testing*. We can simulated data under a null hypothesis through permutation.