How to calculate power with welch t-test formula
This is based on a two-tailed T-test when the two groups have different mean and variance. power_cal_welch_t_test <- function (mean_control,mean_treatment, sample_size_control,sample_size_treatment, sd_control, sd_treatment) { m2 <- mean_treatment m1 <- mean_control n1 <- sample_size_control n2 <- sample_size_treatment s1 <- sd_control s2 <- sd_treatment true_mean <- m2-m1 se_pool <- sqrt(sd1*sd1/n1+sd2*sd2/n2) ## Below is the welch t-test degree of freedom degree_of_up <- (sd1*sd1/n1 + sd2*sd2/n2)^2 degree_of_buttom <- (sd1*sd1)^2/(n1*n1*(n1-1)) + (sd2*sd2)^2/(n2*n2*(n2-1)) degree_of <- degree_of_up/degree_of_buttom ## End of calculating degree of freedom t_critical <- abs(qt(0.025,df=degree_of)) margin_error <- t_critical*se_pool t_left <- (-true_mean+margin_error)/se_pool t_right <- (-true_mean-margin_error)/se_pool power_val <- 1 - pt(t_left, degree_of) + pt(t_right, deg