𝕎e want to calculate the power to detect an association a genetic marker and a quantitative phenotype. […] As a concrete example, we pre-specify the model for continuous trait \(Y\) and genotype \(X\) as \[Y = \beta X + \epsilon, ~~~~ \text{with } \epsilon \sim N(0, \sigma_\epsilon^2)\] where … Read more →

ℕotice that the estimated effect size divided by the standard error behaves like a normal(0,1) random variable when the sample size is large enough: […] \[ Z = \frac{\hat\beta}{\text{se}(\hat\beta)}\] \[Z \approx N(0,1) ~~~~~~ \text{as } n \rightarrow \infty\] Let’s simulate zscore vector … Read more →

𝕀n draft folder Gentle introduction to hypothesis testing from Kahn Academy A drug effect example of hypothesis testing and p-values from Kahn Academy Read more →

## simulate two independent, normally distributed random variables X and epsi ## set seed to make simulations reproducible set.seed(20210108) ## parameter definition nsamp = 100 beta = 2 h2 = 0.1 sig2X = h2 sig2epsi = (1 - sig2X) * beta^2 sigX = sqrt(sig2X) sigepsi = sqrt(sig2epsi) ## simulate … Read more →