tau_min {RCT}

tau_min() computes the minimum detectable difference between control group and each treatment

Description

tau_min() computes the minimum detectable difference between control group and each treatment

Usage

tau_min(
  outcome_var,
  N,
  power = 0.8,
  significance = 0.05,
  share_control,
  n_groups = 2
)

Arguments

outcome_var

the variable for which you wish to test the impact of treatment

N

number of observations in the RCT, usually nrow(data)

power

The level of power of the test (1 - Pr(Reject H_0 | H_0 True) ). Default is 0.8

significance

The level of significance of the test Pr(Reject H_0 | H_0 False). Default is 0.05

share_control

The share of observations in N assigned to control. This argument allows for sequences (i.e. seq(0,1,0.1))

n_groups

Number of groups (control + # treatment groups)

Details

This function calculates the minimum difference that could show significant E[Y(1)-Y(0)] = tau, between any two given groups (e.g. control vs each treatment), given the population size (N), the outcome variable, power and significance

Value

A tibble with the share_control and N observations in control group (N_control), the share and N of each treatment c(share_ti, N_ti), total share of treatment rows and N treated (share_treat, N_treat), N, the minimum detectable difference between control and all treatments together (tau_min_global), the minimum detectable difference between control and each treatment (tau_min_each_treat)

Examples

data <- data.frame(y_1 = rbinom(n = 100, size = 1, prob = 0.3), 
                  y_2 = rnorm(n = 100, mean = 8, sd = 2))
tau_min(data$y_1, N = nrow(data), share_control = seq(0,1,0.1), n_groups = 3)