Use mdes.bird3() to calculate minimum detectable effect size, power.bird3() to calculate statistical power, and cosa.bird3() for bound constrained optimal sample size allocation (BCOSSA).
mdes.bird3(score = NULL, dists = "normal", k1 = -6, k2 = 6,
order = 1, interaction = FALSE,
treat.lower = TRUE, cutoff = 0, p = NULL,
power = .80, alpha = .05, two.tailed = TRUE, df = n3 - g3 - 1,
rho2, rho3, omega2, omega3, r21 = 0, r2t2 = 0, r2t3 = 0, g3 = 0,
rate.tp = 1, rate.cc = 0, n1, n2, n3)power.bird3(score = NULL, dists = "normal", k1 = -6, k2 = 6,
order = 1, interaction = FALSE,
treat.lower = TRUE, cutoff = 0, p = NULL,
es = .25, alpha = .05, two.tailed = TRUE, df = n3 - g3 - 1,
rho2, rho3, omega2, omega3, r21 = 0, r2t2 = 0, r2t3 = 0, g3 = 0,
rate.tp = 1, rate.cc = 0, n1, n2, n3)
cosa.bird3(score = NULL, dists = "normal", k1 = -6, k2 = 6, rhots = NULL,
order = 1, interaction = FALSE,
treat.lower = TRUE, cutoff = 0, p = NULL,
cn1 = 0, cn2 = 0, cn3 = 0, cost = NULL,
n1 = NULL, n2 = NULL, n3 = NULL,
n0 = c(10, 3, 100), p0 = .499,
constrain = "power", round = TRUE, max.power = FALSE,
local.solver = c("LBFGS", "SLSQP"),
power = .80, es = .25, alpha = .05, two.tailed = TRUE,
rho2, rho3, omega2, omega3,
g3 = 0, r21 = 0, r2t2 = 0, r2t3 = 0)
vector or list; an empirical score variable or an object with class 'score' returned from the inspect.score() function.
character; distribution of the score variable, "normal" or "uniform". By default, dists = "normal" specification implies a truncated normal distribution with k1 = -6 and k2 = 6.
left truncation point for (uncentered) empirical, truncated normal, or uniform distribution. Ignored when rhots = 0 or order = 0.
right truncation point for (uncentered) empirical, truncated normal, or uniform distribution. Ignored when rhots = 0 or order = 0.
integer >= 0; order of polynomial functional form specification for the score variable.
logical; if TRUE polynomial specification interacts with the treatment variable.
obsolote; use order = 0 to obtain results equivalent to random assignment designs.
logical; if TRUE units below the cutoff are treated.
decision threshold.
proportion of level 1 units in the treatment condition.
statistical power (1 - \(\beta\)).
effect size (Cohen's d).
probability of type I error (\(\alpha\)).
logical; TRUE for two-tailed hypothesis testing.
degrees of freedom.
proportion of variance in the outcome between level 2 units (unconditional ICC2).
proportion of variance in the outcome between level 3 units (unconditional ICC3).
ratio of the treatment effect variance between level 2 units to the variance in the outcome between level 2 units.
ratio of the treatment effect variance between level 3 units to the variance in the outcome between level 3 units.
number of covariates at level 3.
proportion of level 1 variance in the outcome explained by level 1 covariates.
proportion of treatment effect variance between level 2 units explained by level 2 covariates.
proportion of treatment effect variance between level 3 units explained by level 3 covariates.
treatment group participation rate.
control group crossover rate.
average number of level 1 units per level 2 unit.
average number of level 2 units (blocks) per level 3 unit.
number of level 3 units (blocks).
marginal costs per level 1 unit in treatment and control conditions (positional), e.g. c(10, 5).
marginal cost per level 2 unit.
marginal cost per level 3 unit.
total cost or budget. Ignored when constrain = "power" or constrain = "es".
starting value for p when rhots = 0 and p = NULL. Starting value is replaced with the average when p is constrained by bounds.
vector of starting values for n1, n2, n3 (positional). Starting values are replaced with the averages when sample sizes are constrained by bounds.
character; constrains one of the "cost", "power", or "es" at the specified value.
logical; TRUE for rounded BCOSSA solution.
logical; TRUE for maximizing the power rate instead of minimizing the variance. Applies when constrain = "cost".
subset of c("LBFGS", "SLSQP")
list of parameters used in the function.
degrees of freedom.
standardized standard error.
BCOSSA solution.
minimum detectable effect size and (1 - \(\alpha\))% confidence limits.
statistical power (1 - \(\beta\))
# NOT RUN {
score.obj <- inspect.score(rnorm(1000),
order = 1, interaction = FALSE,
cutoff = 0, k1 = -1, k2 = 1)
power.bird3(score.obj,
es = 0.25, rho2 = .20, rho3 = .10,
omega2 = .30, omega3 = .30,
g3 = 0, r2t3 = 0,
n1 = 20, n2 = 3, n3 = 20)
# minimum required number of level 1 units for each one of the level 2 block
cosa.bird3(score.obj,
es = 0.25, rho2 = .20, rho3 = .10,
omega2 = .30, omega3 = .30,
g3 = 0, r2t3 = 0,
n1 = NULL, n2 = 3, n3 = 20)
# }
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