perm_test {FSM}

Fisher's randomization test for sharp null hypothesis.

Description

Performs Fisher's randomization test for sharp null hypotheses of the form H_0: c_1 Y_i(1) + c_2 Y_i(2) - \tau = 0, for a vector of contrasts (c_1, c_2).

Usage

perm_test(
  Y_obs,
  alloc_obs,
  alloc,
  contrast = c(1, -1),
  tau = 0,
  method = "marginal mean",
  alternative = "not equal"
)

Arguments

Y_obs

Vector of observed outcome.

alloc_obs

Vector of observed treatment assignment.

alloc

A matrix of treatment assignments over which the randomization distribution of the test statistic is computed. Each row of alloc should correspond to an assignment vector.

contrast

A vector of the coefficients of the treatment contrast of interest. For example, for estimating the average treatment effect of treatment 1 versus treatment 2, contrast = c(1,-1).

tau

The value of the treatment contrast specified by the sharp null hypothesis.

method

The method of computing the test statistic. If method = 'marginal mean', the test statistic is c_1 \hat{Y}_i(1) + c_2 \hat{Y}_i(2), where \hat{Y}(z) is the mean of the observed outcome in the group Z = z, for z = 0,1. If method = 'marginal rank', the test statistic is c_1 \hat{Y}_i(1) + c_2 \hat{Y}_i(2), where \hat{Y}(z) is the mean of the rank of the observed outcome in the group Z = z, for z = 0,1

alternative

The type of alternative hypothesis used. For right-sided test, alternative = 'greater'. For left-sided test, alternative = 'less'. For both-sided test, alternative = 'not equal'.

Value

A list containing the following items.

test_stat_obs: The observed value of the test statistic.

test_stat_iter: A vector of values of the test statistic across repeated randomizations.

p_value: p-value of the test.

Author(s)

Ambarish Chattopadhyay, Carl N. Morris and Jose R. Zubizarreta.

References

Chattopadhyay, A., Morris, C. N., and Zubizarreta, J. R. (2020), “Randomized and Balanced Allocation of Units into Treatment Groups Using the Finite Selection Model for R".

Examples

# Consider N = 12, n1 = n2 = 6. 
# We test the sharp null of no treatment effect under CRD.
df_sample = data.frame(index = 1:12, x = c(20,30,40,40,50,60,20,30,40,40,50,60))
# True potential outcomes.
Y_1_true = 100 + (df_sample$x - mean(df_sample$x)) + rnorm(12, 0, 4)
Y_2_true = Y_1_true + 50
# Generate the realized assignment under CRD.
fc = crd(data_frame = df_sample, n_treat = 2, treat_sizes = c(6,6), control = FALSE)
Z_crd_obs = fc$Treat
# Get the observed outcomes
Y_obs = Y_1_true
Y_obs[Z_crd_obs == 2] = Y_2_true[Z_crd_obs == 2]
# Generate 1000 assignments under CRD.
Z_crd_iter = matrix(rep(0, 1000 * 12), nrow = 1000)
for(i in 1:1000)
{
fc = crd(data_frame = df_sample, n_treat = 2, treat_sizes = c(6,6), control = FALSE)
Z_crd_iter[i,] = fc$Treat
}
# Test for the sharp null H0: Y_i(1) = Y_i(0) for all i.
# Alternative: not H0 (two-sided test).
perm = perm_test(Y_obs = Y_obs, alloc_obs = Z_crd_obs, alloc = Z_crd_iter, 
contrast = c(1,-1), tau = 0, method = "marginal mean", alternative = 'not equal')
# Obtain the p-value.
perm$p_value