diff --git a/Practical_c.Rmd b/Practical_c.Rmd index 8c3ab9d9c2e7b53da164c60ad978f512ecfba1f8..c1116eb170b1c30b1329267d1a7c12179c40a2bc 100644 --- a/Practical_c.Rmd +++ b/Practical_c.Rmd @@ -310,11 +310,11 @@ What are type I and type II risks? <details><summary>Solution</summary> <p> -- Type I risk: $\alpha = \PP(\text{reject } \H_0\ \vert\ \H_0 \text{ is true}$ +- Type I risk: $\alpha = \PP(\text{reject } \H_0\ \vert\ \H_0 \text{ is true})$ -- Type II risk: $\beta = \PP(\text{not reject } \H_0\ \vert\ \H_0 \text{ is false}$ +- Type II risk: $\beta = \PP(\text{not reject } \H_0\ \vert\ \H_0 \text{ is false})$ -- Power $= 1 - \beta = \PP(\text{reject } \H_0\ \vert\ \H_0 \text{ is false}$ +- Power $= 1 - \beta = \PP(\text{reject } \H_0\ \vert\ \H_0 \text{ is false})$ --- @@ -614,7 +614,7 @@ Imagine a procedure based on simulation to estimate the power of the previous T- <details><summary>Solution</summary> <p> -The power of a test is $1 - \beta = \PP(\text{reject } \H_0\ \vert\ \H_0 \text{ is false}$ where $\beta = \PP(\text{not reject } \H_0\ \vert\ \H_0 \text{ is false}$ is the type II risk. +The power of a test is $1 - \beta = \PP(\text{reject } \H_0\ \vert\ \H_0 \text{ is false})$ where $\beta = \PP(\text{not reject } \H_0\ \vert\ \H_0 \text{ is false})$ is the type II risk. To estimate $\beta$, we need to repeat the same experiment multiple time and estimate the corresponding probability. @@ -690,7 +690,7 @@ Decreasing $\alpha$ to reduce the type I error decreases the power of the test. **Important:** - confirm a detected effect with additional experiments/studies -- the more (independent) studies, the lower risk of incorrect conclusion +- the more (independent) studies, the lower risk of incorrect conclusions --- @@ -1749,7 +1749,7 @@ ggplot(test_result) + geom_line(aes(x=p_values, y=fdr_adj_p_values)) + </p> </details> -Eventually, we can also compare the number of significant SNPs found before and after p-value correction depending on the chosen type I risk alpha. +Eventually, we can also compare the number of significant SNPs found before and after p-value correction depending on the chosen type I risk $\alpha$. ```{r} # compute the number of significant SNPs @@ -1839,4 +1839,4 @@ Write me! --- -[The .Rmd file corresponding to this page is available here under the AGPL3 Licence](https://lbmc.gitbiopages.ens-lyon.fr/hub/formations/ens_m1_ml/Practical_b.Rmd) +[The .Rmd file corresponding to this page is available here under the AGPL3 Licence](https://lbmc.gitbiopages.ens-lyon.fr/hub/formations/ens_m1_ml/Practical_c.Rmd)