power.1 {odr}

Budget and/or sample size, power, MDES calculation for single-level experiments detecting main effects

Description

This function can calculate required budget for desired power, power or minimum detectable effect size (MDES) under fixed budget for single-level experiments. It also can perform conventional power analyses (e.g., required sample size, power, and MDES calculation).

Usage

power.1(
  cost.model = TRUE,
  expr = NULL,
  constraint = NULL,
  sig.level = 0.05,
  two.tailed = TRUE,
  d = NULL,
  power = NULL,
  m = NULL,
  n = NULL,
  p = NULL,
  r12 = NULL,
  q = NULL,
  c1 = NULL,
  c1t = NULL,
  dlim = NULL,
  powerlim = NULL,
  nlim = NULL,
  mlim = NULL,
  rounded = TRUE
)

Arguments

cost.model

Logical; power analyses accommodating costs and budget (e.g., required budget for desired power, power/MDES under fixed budget) if TRUE, otherwise conventional power analyses (e.g., required sample size, power, or MDES calculation); default value is TRUE.

expr

Returned object from function od.1; default value is NULL; if expr is specified, parameter values of r12, c1, c1t, and p used or solved in function od.1 will be passed to the current function; only the value of p that specified or solved in function od.1 can be overwritten if constraint is specified.

constraint

Specify the constrained value of p in list format to overwrite that from expr; default value is NULL.

sig.level

Significance level or type I error rate, default value is 0.05.

two.tailed

Logical; two-tailed tests if TRUE, otherwise one-tailed tests; default value is TRUE.

d

Effect size.

power

Statistical power.

m

Total budget.

n

The total sample size.

p

The proportion of individuals to be assigned to treatment.

r12

The proportion of outcome variance explained by covariates.

q

The number of covariates.

c1

The cost of sampling one unit in control condition.

c1t

The cost of sampling one unit in treatment condition.

dlim

The range for solving the root of effect size (d) numerically, default value is c(0, 5).

powerlim

The range for solving the root of power (power) numerically, default value is c(1e-10, 1 - 1e-10).

nlim

The range for searching the root of sample size (n) numerically, default value is c(4, 10e10).

mlim

The range for searching the root of budget (m) numerically, default value is the costs sampling nlim units across treatment conditions or c(4 * ncost, 10e10 * ncost) with ncost = ((1 - p) * c1 + p * c1t).

rounded

Logical; round p that is from functions od.1 to two decimal places if TRUE, otherwise no rounding; default value is TRUE.

Value

Required budget (or required sample size), statistical power, or MDES depending on the specification of parameters. The function also returns the function name, design type, and parameters used in the calculation.

Examples

# Unconstrained optimal design
  myod1 <- od.1(r12 = 0.5, c1 = 1, c1t = 5, varlim = c(0, 0.2))
  myod1$out   # p = 0.31

# ------- Power analyses by default considering costs and budget -------
# Required budget and sample size
  mym.1 <- power.1(expr = myod1, d = 0.2, q = 1, power = 0.8)
  mym.1$out  # m = 1032 n = 461
  # mym.1$par  # parameters and their values used for the function
# Or, equivalently, specify every argument in the function
  mym.1 <- power.1(d = 0.2, power = 0.8, c1 = 1, c1t = 5,
                  r12 = 0.5, p = 0.31, q = 1)
# Required budget and sample size with constrained p
  mym.2 <- power.1(expr = myod1, d = 0.2, q = 1, power = 0.8,
               constraint = list(p = 0.5))
  mym.2$out  # m = 1183, n = 394

# Power calculation
  mypower <- power.1(expr = myod1, q = 1, d = 0.2, m = 1032)
  mypower$out  # power = 0.80
# Power calculation under constrained p (p = 0.5)
  mypower.1 <- power.1(expr = myod1, q = 1, d = 0.2, m = 1032,
               constraint = list(p = 0.5))
  mypower.1$out  # power = 0.74

# MDES calculation
  mymdes <- power.1(expr = myod1, q = 1, power = 0.80, m = 1032)
  mymdes$out  # d = 0.20


# ------- Conventional power analyses with cost.model = FALSE-------
# Required sample size n
  myn <- power.1(cost.model = FALSE, expr = myod1, d = 0.2, q = 1, power = 0.8)
  myn$out  # n = 461
  # myn$par  # parameters and their values used for the function
# Or, equivalently, specify every argument in the function
  myn <- power.1(cost.model = FALSE, d = 0.2, power = 0.8,
                  r12 = 0.5, p = 0.31, q = 1)

# Power calculation
  mypower1 <- power.1(cost.model = FALSE, expr = myod1, n = 461, d = 0.2, q = 1)
  mypower1$out  # power = 0.80

# MDES calculation
  mymdes1 <- power.1(cost.model = FALSE, expr = myod1, n = 461, power = 0.8, q = 1)
  mymdes1$out  # d = 0.20