FSM (version 1.0.0)

perm_test: 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.

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

# NOT RUN {
# 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
# }