Power calculation for multiple alternative (at least one) primary continuous endpoints assuming known covariance matrix

Description

Calculates power and sample size for the case of comparing two groups on the means of K continuous endpoints and concluding that the trial is a 'success' if the null hypothesis is rejected for at least one of the K endpoints. All mean differences must be specified as positive; the scale for some outcomes may need to be reversed to meet this condition. All tests are assumed to be upper-tailed, one-sided tests. Can solve for power, n1, n.ratio or alpha.

To use a Bonferroni correction for multiple comparisons, specify alpha as the desired familywise error rate (FWER) divided by K. For example, for one-sided FWER of 0.025 and K = 2 endpoints, specify alpha as 0.0125.

Either sd and rho or Sigma must be specified.

A known covariance matrix is assumed, which can result in a slight overestimate of power and underestimate of required sample size.

Usage

altprimary(
  K,
  n1 = NULL,
  n.ratio = 1,
  delta = NULL,
  Sigma,
  sd,
  rho,
  alpha = 0.025,
  power = NULL,
  v = FALSE
)

Arguments

Details

Sozu T, Sugimoto T, Hamasaki T, Evans SR (2015) Sample Size Determination in Clinical Trials with Multiple Endpoints. Springer International Publishing, Switzerland.

Value

A list of the arguments (including the computed one).

Examples

altprimary(K = 2, n1 = 100, delta = c(0.4, 0.5), sd = c(1, 1), rho = 0.3,
alpha = 0.025 / 2, power = NULL)

Sigma <- matrix(c(1, 0.3, 0.3, 0.3, 1, 0.3, 0.3, 0.3, 1), nrow = 3, ncol = 3)
altprimary(K = 3, n1 = 100, delta = c(0.2, 0.2, 0.4), Sigma = Sigma,
   alpha = 0.025 / 3, power = NULL)

Power calculation for balanced one-way ANOVA omnibus F test

Description

This function performs power and sample size calculations for the overall (omnibus) F test in a balanced (equal-sized groups) one-way analysis of variance (ANOVA). Can be used to solve for power, n (sample size per group), or alpha. For an unbalanced one-way ANOVA F test (that is, unequal group sample sizes), use 'anova1way.F.unbal'. For contrast tests in a one-way ANOVA, see 'anova1way.c.bal' and 'anova1way.c.unbal'.

Usage

anova1way.F.bal(
  n = NULL,
  mvec = NULL,
  sd = 1,
  Rsq = 0,
  ncov = 0,
  alpha = 0.05,
  power = NULL,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

anova1way.F.bal(n = 20, mvec = c(5, 10, 12), sd = 10)
anova1way.F.bal(n = NULL, mvec = c(-0.25, 0.25), sd = 1, Rsq = 0.5^2, ncov = 1, power = 0.8)

Power calculation for unbalanced one-way analysis of variance omnibus F test

Description

Performs power calculation for an unbalanced (unequal group sizes) one-way ANOVA omnibus F test, which tests for any differences among group means. This function solves for power given other parameters. For balanced data (equal-sized groups), anova1way.F.bal can be used and solves for more parameters.

Usage

anova1way.F.unbal(
  nvec = NULL,
  mvec = NULL,
  sd = NULL,
  Rsq = 0,
  ncov = 0,
  alpha = 0.05,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed power).

Examples

anova1way.F.unbal(nvec = c(10, 20, 30), mvec = c(5, 10, 12), sd = 10)

Power calculation for one-way balanced analysis of variance contrast test

Description

Performs sample size and power calculations for a test of a contrast in a one-way ANOVA with balanced data (that is, equal sized groups). Can be used to solve for power, n (sample size per group), or alpha. For unbalanced data, see anova1way.c.unbal.

Usage

anova1way.c.bal(
  n = NULL,
  mvec = NULL,
  cvec = NULL,
  sd = 1,
  Rsq = 0,
  ncov = 0,
  alpha = 0.05,
  power = NULL,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

anova1way.c.bal(n = 20, mvec = c(5, 10, 12), cvec = c(1, -1, 0), sd = 10, alpha = 0.025)
anova1way.c.bal(n = 20, mvec = c(5, 10, 12), cvec = c(1, 0, -1), sd = 10, alpha = 0.025)

Power calculation for one-way unbalanced analysis of variance contrast test

Description

Calculates power for a test of a contrast in a one-way ANOVA with unbalanced data (that is, unequal sized groups). This function only solves for power. For a one-way balanced ANOVA, (equal group sizes), anova1way.c.bal can also be used, and will solve for quantities other than power.

Usage

anova1way.c.unbal(
  nvec = NULL,
  mvec = NULL,
  cvec = NULL,
  sd = NULL,
  Rsq = 0,
  ncov = 0,
  alpha = 0.05,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed power).

Examples

anova1way.c.unbal(nvec = c(20, 20, 20), mvec = c(5, 10, 12), cvec = c(1, -1, 0),
sd = 10, alpha = 0.025)
anova1way.c.unbal(nvec = c(20, 20, 20), mvec = c(5, 10, 12), cvec = c(1, 0, -1),
sd = 10, alpha = 0.025)

Power calculation for two-way balanced analysis of variance F tests

Description

Performs sample size and power calculations for F tests in a two-way ANOVA with balanced data (that is, equal cell sizes). For a given matrix of cell means, computes power or required cell size for each factor and for their interaction, if an interaction is present. For unbalanced data (unequal cell sizes), see anova2way.F.unbal.

Usage

anova2way.F.bal(
  n = NULL,
  mmatrix = NULL,
  sd = 1,
  Rsq = 0,
  ncov = 0,
  alpha = 0.05,
  power = NULL,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

mmatrix <- matrix(c(9.3, 8.9, 8.5, 8.7, 8.3, 7.9), nrow = 2, byrow = TRUE)
anova2way.F.bal(n = 30, mmatrix = mmatrix, sd = 2, alpha = 0.05)
mmatrix <- matrix(c(9.3, 8.9, 8.5, 8.7, 8.3, 7.3), nrow = 2, byrow = TRUE)
anova2way.F.bal(n = 30, mmatrix = mmatrix, sd = 2, alpha = 0.05)
mmatrix <- matrix(c(9.3, 8.9, 8.5, 8.7, 8.3, 7.9), nrow = 2, byrow = TRUE)
anova2way.F.bal(n = 30, mmatrix = mmatrix, sd = 2, Rsq = 0.4, ncov = 1, alpha = 0.05)

Power calculation for two-way unbalanced analysis of variance F tests

Description

Performs sample size and power calculations for F tests in a two-way ANOVA with unbalanced data (that is, unequal sized cells). For given matrix of cell means and matrix of cell sample sizes, computes power for each factor and for their interaction, if an interaction is present. This function does not solve for cell sizes. For balanced data (equal cell sizes), see anova2way.F.unbal, which can solve for cell size.

Usage

anova2way.F.unbal(
  nmatrix = NULL,
  mmatrix = NULL,
  sd = NULL,
  Rsq = 0,
  ncov = 0,
  alpha = 0.05,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed power).

Examples

nmatrix <- matrix(c(30, 30, 30, 30, 30, 30), nrow = 2, byrow = TRUE)
mmatrix <- matrix(c(9.3, 8.9, 8.5, 8.7, 8.3, 7.9), nrow = 2, byrow = TRUE)
anova2way.F.unbal(nmatrix = nmatrix, mmatrix = mmatrix, sd = 2, alpha = 0.05)
nmatrix <- matrix(c(30, 30, 30, 30, 30, 30), nrow = 2, byrow = TRUE)
mmatrix <- matrix(c(9.3, 8.9, 8.5, 8.7, 8.3, 7.3), nrow = 2, byrow = TRUE)
anova2way.F.unbal(nmatrix = nmatrix, mmatrix = mmatrix, sd = 2, alpha = 0.05)
nmatrix <- matrix(c(30, 30, 30, 30, 30, 30), nrow = 2, byrow = TRUE)
mmatrix <- matrix(c(9.3, 8.9, 8.5, 8.7, 8.3, 7.9), nrow = 2, byrow = TRUE)
anova2way.F.unbal(nmatrix = nmatrix, mmatrix = mmatrix, sd = 2, Rsq = 0.4^2,
ncov = 1, alpha = 0.05)

Power calculation for two-way balanced analysis of variance contrast test

Description

Performs sample size and power calculations for a test of a contrast between levels of a factor in a two-way ANOVA with balanced data (that is, equal sized cells). Can be used to solve for power, n (sample size per cell), or alpha. For unbalanced data, see anova2way.c.unbal. For a test of a contrast among cell means, see anova2way.se.bal.

Usage

anova2way.c.bal(
  n = NULL,
  mmatrix = NULL,
  cvec = NULL,
  factor = c("a", "b"),
  sd = 1,
  Rsq = 0,
  ncov = 0,
  alpha = 0.05,
  power = NULL,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

mmatrix <- matrix(c(9.3, 8.9, 8.5, 8.7, 8.3, 7.3), nrow = 2, byrow = TRUE)
anova2way.c.bal(n = 30, mmatrix = mmatrix, cvec = c(1, 0, -1), factor = "b",
sd = 2, alpha = 0.05)

Power calculation for two-way unbalanced analysis of variance contrast test

Description

Calculates power for a test of a contrast between levels of a factor in a two-way ANOVA with unbalanced data (that is, unequal cell sizes). This function only solves for power. For a two-way balanced ANOVA, (equal cell sizes), anova2way.c.bal can also be used, and will solve for quantities other than power. For a test of a contrast among cell means, see anova2way.se.unbal.

Usage

anova2way.c.unbal(
  nmatrix = nmatrix,
  mmatrix = NULL,
  cvec = NULL,
  factor = c("a", "b"),
  sd = NULL,
  Rsq = 0,
  ncov = 0,
  alpha = 0.05,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

nmatrix <- matrix(c(30, 30, 30, 30, 30, 30), nrow = 2, byrow = TRUE)
mmatrix <- matrix(c(9.3, 8.9, 8.5, 8.7, 8.3, 7.3), nrow = 2, byrow = TRUE)
anova2way.c.unbal(nmatrix = nmatrix, mmatrix = mmatrix, cvec = c(1, 0, -1),
factor = "b", sd = 2, alpha = 0.05)

Power calculation for test of simple effect for two-way balanced analysis of variance

Description

Conducts power and sample size calculations for a test of a simple effect in a two-way balanced (equal cell sizes) ANOVA. A "simple effect" is a contrast among the cell means. For a test of a contrast in an unbalanced (unequal cell sizes) two-way ANOVA, see anova2way.se.unbal. For a test of contrast among factor levels, see anova2way.c.bal.

Usage

anova2way.se.bal(
  n = NULL,
  mmatrix = NULL,
  cmatrix = NULL,
  sd = 1,
  Rsq = 0,
  ncov = 0,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

mmatrix <- matrix(c(9.3, 8.9, 8.5, 8.7, 8.3, 7.3), nrow = 2, byrow = TRUE)
cmatrix <- matrix(c(-1, 0, 0, 1, 0, 0), nrow = 2, byrow = TRUE)
anova2way.se.bal(n = 30, mmatrix = mmatrix, cmatrix = cmatrix, sd = 2, alpha = 0.025, sides = 1)

Power calculation for test of simple effect for two-way unbalanced analysis of variance

Description

Conducts power calculations for a test of a simple effect in a two-way unbalanced (unequal cell sizes) ANOVA. A "simple effect" is a contrast among the cell means. This function does not solve for sample size. For a test of a contrast in a balanced (equal cell sizes) two-way ANOVA, anova2way.se.bal can also be used and can solve for sample size. For a test of contrast among factor levels, see anova2way.c.unbal.

Usage

anova2way.se.unbal(
  nmatrix = NULL,
  mmatrix = NULL,
  cmatrix = NULL,
  sd = 1,
  Rsq = 0,
  ncov = 0,
  alpha = 0.05,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed power).

Examples

nmatrix <- matrix(c(30, 30, 30, 30, 30, 30), nrow = 2, byrow = TRUE)
mmatrix <- matrix(c(9.3, 8.9, 8.5, 8.7, 8.3, 7.3), nrow = 2, byrow = TRUE)
cmatrix <- matrix(c(-1, 0, 0, 1, 0, 0), nrow = 2, byrow = TRUE)
anova2way.se.unbal(nmatrix = nmatrix, mmatrix = mmatrix, cmatrix = cmatrix,
sd = 2, alpha = 0.025, sides = 1)

Internal-use function for quality checking sets of parameters

Description

Internal-use function for quality checking sets of parameters

Usage

check.many(paramlist = NULL, type = c("oneof"))

Arguments

Value

If the check passes, returns nothing. If the check does not pass, throw an error.

Examples

N <- 10
power <- NULL
check.many(list(N, power), "oneof")

Internal-use function for quality checking individual parameters

Description

Internal-use function for quality checking individual parameters

Usage

check.param(
  param = NULL,
  type = c("req", "num", "unit", "uniti", "unitii", "pos", "int", "bool", "vals", "min",
    "mini", "vec", "mat", "sum1", "sum0"),
  valslist = NULL,
  min = NULL
)

Arguments

Value

If the check passes, returns nothing. If the check does not pass, throw an error.

Examples

power <- 0.8
check.param(power, "unit")

Power calculation for chi-square goodness-of-fit test

Description

Performs sample size and power calculations for chi-square goodness-of-fit test, which is used to test whether a sample of data arises from a population with a specific discrete distribution. This function can solve for power, total sample size or alpha.

Usage

chisq.gof(
  p0vec = NULL,
  p1vec = NULL,
  N = NULL,
  alpha = 0.05,
  power = NULL,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

chisq.gof(p0vec = c(0.5, 0.3, 0.2), p1vec = c(0.7, 0.15, 0.15), N = 50)

Power calculation for chi-square test of independence

Description

Performs power and sample size calculations for a chi-square test of independence. The user inputs a matrix of cell probabilities for a two-way table. The function computes the power (or required total sample size) for a test of no association between the two factors.

Usage

chisq.indep(pmatrix = NULL, N = NULL, alpha = 0.05, power = NULL, v = FALSE)

Arguments

Value

A list of the arguments (including the computed one).

Examples

chisq.indep(pmatrix = matrix(c(0.050, 0.350, 0.100, 0.075, 0.250, 0.175),
nrow = 2, byrow = TRUE), N = 230)
chisq.indep(pmatrix = matrix(c(0.3, 0.2, 0.4, 0.1), nrow = 2, byrow = TRUE), N = 200)

Power calculation for precision analysis (confidence interval) for one mean

Description

Calculates the "power" of a confidence interval for one mean, that is, the probability of achieving a 100(1 - alpha) percent confidence interval with halfwidth not greater than a specified value. Can solve for power, N or alpha.

Usage

ci.mean(
  N = NULL,
  halfwidth = NULL,
  sd = 1,
  alpha = 0.05,
  power = NULL,
  cond = FALSE,
  v = FALSE
)

Arguments

Details

The unconditional probability is the probability of obtaining the desired precision (i.e., that the observed halfwidth does not exceed the desired halfwidth) regardless of whether or not the confidence interval includes the true parameter value. The conditional probability is the probability of both obtaining the desired precision and having the interval include the true parameter value.

Value

A list of the arguments (including the computed one).

Examples

ci.mean(N = NULL, halfwidth = 0.25, power = 0.8)
ci.mean(N = 62, halfwidth = 0.25, power = NULL)
ci.mean(N = 73, halfwidth = 0.25, cond = TRUE)

Power calculation for precision analysis (confidence interval) for a difference between two means

Description

Calculates the "power" of a confidence interval for a difference between two means, that is, the probability of achieving a 100(1 - alpha) percent confidence interval with halfwidth not greater than a specified value. This function can solve for power, n1, n.ratio or alpha.

Usage

ci.meandiff(
  n1 = NULL,
  n.ratio = 1,
  halfwidth = NULL,
  sd = 1,
  alpha = 0.05,
  power = NULL,
  cond = FALSE,
  v = FALSE
)

Arguments

Details

The unconditional probability is the probability of obtaining the desired precision (i.e., that the observed halfwidth does not exceed the desired halfwidth) regardless of whether or not the confidence interval includes the true parameter value. The conditional probability is the probability of both obtaining the desired precision and having the interval include the true parameter value.

Value

A list of the arguments (including the computed one).

Examples

ci.meandiff(n1 = NULL, halfwidth = 0.25, power = 0.8)
ci.meandiff(n1 = 134, halfwidth = 0.25, cond = TRUE)

Power calculations for multiple co-primary continuous endpoints assuming unknown covariance matrix

Description

Computes power for test involving multiple co-primary continuous endpoints, assuming that the covariance matrix (variances and covariances between endpoints) is unknown and therefore t-based test statistics will be used. Studies with co-primary endpoints use “all-or-none” testing procedures and only declare the trial to be a “success” if all endpoints are affirmed. All true mean differences must be positive (the scale for some outcomes may need to be reversed to meet this condition) and upper-tailed one-sided tests are assumed. For known covariance matrix, see coprimary.z.

Either sd and rho or Sigma must be specified.

Usage

coprimary.t(
  K,
  n1 = NULL,
  n.ratio = 1,
  delta = NULL,
  Sigma,
  sd,
  rho,
  alpha = 0.025,
  power = NULL,
  M = 10000,
  v = FALSE
)

Arguments

Details

See Crespi et al. (2025) for more details. This function is based on the power.unknown.var function from the mpe R package and material from Sozu T, Sugimoto T, Hamasaki T, Evans SR. (2015) Sample Size Determination in Clinical Trials with Multiple Endpoints. Springer International Publishing, Switzerland.

This function can be computationally intensive and slow when solving for sample size. Smaller M can descrease computation time. The function coprimary.z provides a close approximation and is much faster.

Value

A list of the arguments (including the computed one).

Examples

# M is set to 10 in these examples to reduce runtime;
# please increase M or do not specify M (defaults to M = 10000) for optimal results
coprimary.t(K = 2, n1 = 100, delta = c(0.4, 0.5), sd = c(1, 1), rho = 0.3, alpha = 0.025,
power = NULL, M = 10)

Sigma <- matrix(c(1, 0.3, 0.3, 0.3, 1, 0.3, 0.3, 0.3, 1), nrow = 3, ncol = 3)
coprimary.t(K = 3, n1 = 200, delta = c(0.2, 0.3, 0.4), Sigma = Sigma, alpha = 0.025,
power = NULL, M = 10)

Power calculations for multiple co-primary continuous endpoints assuming known covariance matrix

Description

Computes power for test involving multiple co-primary continuous endpoints, assuming that the covariance matrix (variances and covariances between endpoints) is known and therefore z-based test statistics will be used. Studies with co-primary endpoints use “all-or-none” testing procedures and only declare the trial to be a “success” if all endpoints are affirmed. All true mean differences must be positive (the scale for some outcomes may need to be reversed to meet this condition) and upper-tailed one-sided tests are assumed. For the more realistic case that the covariance matrix is not known, see coprimary.t.

Either sd and rho or Sigma must be specified.

Usage

coprimary.z(
  K,
  n1 = NULL,
  n.ratio = 1,
  delta = NULL,
  Sigma,
  sd,
  rho,
  alpha = 0.025,
  power = NULL,
  v = FALSE
)

Arguments

Details

See Crespi et al. (2025) for more details. This function is based on the power.known.var function from the mpe R package and material from Sozu T, Sugimoto T, Hamasaki T, Evans SR. (2015) Sample Size Determination in Clinical Trials with Multiple Endpoints. Springer International Publishing, Switzerland.

Value

A list of the arguments (including the computed one).

Examples

coprimary.z(K = 2, n1 = 100, delta = c(0.4, 0.5), sd = c(1, 1), rho = 0.3,
alpha = 0.025, power = NULL)

Sigma <- matrix(c(1, 0.3, 0.3, 0.3, 1, 0.3, 0.3, 0.3, 1), nrow = 3, ncol = 3)
coprimary.z(K = 3, n1 = NULL, delta = c(0.2, 0.3, 0.4), Sigma = Sigma, alpha = 0.025, power = 0.8)

Power calculation for test of one correlation coefficient

Description

Calculates power and sample size for a test that the correlation coefficient in a single population is equal to (or less than or greater than) a specified value. Can solve for power, N or alpha.

Usage

corr.1samp(
  N = NULL,
  rho0 = 0,
  rhoA = NULL,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

corr.1samp(N = 100, rhoA = 0.2, sides = 1)
corr.1samp(N = 100, rho0 = 0.2, rhoA = 0.4, sides = 1)

Power calculation for comparing two correlation coefficients

Description

Calculates power and sample size for a test that the correlation coefficients in two groups/populations are equal. Can solve for power, n1, n.ratio or alpha.

Usage

corr.2samp(
  n1 = NULL,
  n.ratio = 1,
  rho1 = NULL,
  rho2 = NULL,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

corr.2samp(n1 = 300, rho1 = 0.3, rho2 = 0.1, sides = 1)

Power for test of treatment effect in longitudinal cluster randomized trial with baseline measurement

Description

This function computes power and sample size for a cluster randomized trial in which a continuous outcome variable is measured during both baseline and follow-up periods among the cluster members, and it is planned that the outcome data will be analyzed using a linear mixed model in which the dependent variable vector includes both baseline and follow up measurements and there is a random intercept for cluster. This function can solve for power, J1, J.ratio, m or delta.

Usage

crt.long.cont(
  m = NULL,
  J1 = NULL,
  J.ratio = 1,
  delta = NULL,
  sd = 1,
  icc = 0,
  cac = 0,
  sac = 0,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Details

The intraclass correlation coefficient (icc) is the correlation between two observations from different subjects in the same cluster and same time period. Denote the correlation between observations from two different subjects in the same cluster but different time periods as iccb. The cluster autocorrelation (cac) is iccb/icc and is interpreted as the proportion of the cluster-level variance that is time-invariant. Denote the correlation between two observations from the same subject in different time periods as rhoa. The subject autocorrelation (sac) is (rhoa - icc)/(iccb - icc) and is interpreted as the proportion of the subject-level variance that is time-invariant. The sac is only relevant for design in which the same subjects are measured at both baseline and follow up. If different subjects are measured during different time periods, sac should be set to zero.

Value

A list of the arguments (including the computed one).

Examples

crt.long.cont(m = 30, J1 = 8, delta = 0.3, icc = 0.05, cac = 0.4, sac = 0.5)

Correlation between a cluster mean at baseline and follow up

Description

For a cluster randomized trial with a continuous outcome, this function calculates the correlation between a cluster's mean at baseline and at follow up based on various inputs. For cross-sectional sampling of subjects, that is, different subjects are measured at baseline and follow up, specify sac = 0.

Usage

crt.means.r(m, icc, cac, sac)

Arguments

Value

The computed correlation.

Examples

crt.means.r(m = 30, icc = 0.05, cac = 0.4, sac = 0.5)

Power calculation for cluster randomized trial with binary outcome

Description

This function performs power and sample size calculations for a two-arm cluster randomized trial with a binary outcome. It assumes the outcome analysis will be conducted using a mixed effect logistic regression model that has a random intercept for cluster. Equal allocation of clusters to arms is assumed. Can solve for power, J, m or alpha.

Usage

crt.parallel.bin(
  m = NULL,
  m.sd = 0,
  J = NULL,
  pc = NULL,
  pt = NULL,
  sigma.u = NULL,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Details

For help selecting a reasonable value for sigma.u, consider using the crt.varexplore function.

Value

A list of the arguments (including the computed one).

Examples

crt.parallel.bin(m = 60, J = NULL, pc = 0.25, pt = 0.15, sigma.u = 0.3, power = 0.8)
crt.parallel.bin(m = 60, m.sd = 1, J = NULL, pc = 0.25, pt = 0.15, sigma.u = 0.3, power = 0.8)

Power for cluster randomized trial with continuous outcome

Description

This function performs power and sample size calculations for a two-arm cluster randomized trial with a continuous, normal outcome. Can solve for power, J1, J.ratio, m or alpha.

Usage

crt.parallel.cont(
  m = NULL,
  m.sd = 0,
  J1 = NULL,
  J.ratio = 1,
  delta = NULL,
  sd = 1,
  icc1 = 0,
  icc2 = 0,
  ncov = 0,
  RsqB = 0,
  RsqW = 0,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

crt.parallel.cont(m = 30, J1 = 8, delta = 0.4, icc1 = 0.05, icc2 = 0.05)
crt.parallel.cont(m = NULL, J1 = 6, delta = 0.5, icc1 = 0.05, icc2 = 0.05, power = 0.8)
crt.parallel.cont(m = 25, m.sd = 15, J1 = NULL, delta = 0.3, icc1 = 0.05,
icc2 = 0.05, power = 0.8)
crt.parallel.cont(m = 20, J1 = 15, delta = 0.3, icc1 = 0.05, icc2 = 0.05,
RsqB = 0.1, ncov = 1, sides = 1)

Power for detecting treatment effect heterogeneity in a cluster randomized trial with a continuous outcome

Description

This function performs power and sample size calculations for detecting a treatment-by-covariate interaction effect in a two-arm cluster randomized trial with a continuous outcome when the data will be analyzed using a linear mixed effects model (random intercept for cluster and fixed effect for the treatment-by-covariate interaction). Can solve for power, beta, J1, J.ratio or m.

Usage

crt.parallel.hte(
  m = NULL,
  J1 = NULL,
  J.ratio = 1,
  beta = NULL,
  sd.x = NULL,
  sd.yx = NULL,
  icc.x = 0,
  icc.yx = 0,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Details

This function is based on Yang et al (2020). If the covariate is a cluster-level covariate, then icc.x should be set to 1 (the covariate does not vary within cluster).

Yang S, Li F, Starks MA, Hernandez AF, Mentz RJ, Choudhury KR (2020) Sample size requirements for detecting treatment effect heterogeneity in cluster randomized trials. Statistics in Medicine 39:4218-4237.

Value

A list of the arguments (including the computed one).

Examples

crt.parallel.hte(beta = 1, m = 27, J1 = 20, sd.x = 12.7, sd.yx = 71, icc.x = 0.08, icc.yx = 0.04)

Variance exploration for cluster randomized trials with binary outcomes

Description

This function can be used to help select a plausible value for the variance/SD of the random intercept for cluster in a cluster randomized trial with a binary outcome. Based on user-supplied values of the outcome proportions in the two arms, the function outputs, for a range of possible values of the SD of the random intercept, the intervals within which we expect about 95% of the cluster-level proportions to lie in each arm.

Usage

crt.varexplore(pc, pt, print = TRUE)

Arguments

Details

The use of this function is illustrated in Crespi CM (2025) Power and Sample Size in R.

Value

A list of the arguments and a dataframe of outputs.

Examples

crt.varexplore(pc = 0.25, pt = 0.15)
output <- crt.varexplore(pc = 0.25, pt = 0.15, print = FALSE)
output$pc

Power for test of treatment effect in 2x2 crossover cluster randomized trial

Description

Power and sample size calculation for a 2x2 crossover cluster randomized trial. Can solve for power, number of clusters per arm (assumes equal number of cluster per arm), m, delta or alpha.

Usage

crt.xo.cont(
  m = NULL,
  J.arm = NULL,
  delta = NULL,
  sd = 1,
  icc = 0,
  icca = 0,
  iccb = NULL,
  cac = NULL,
  sac = 0,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

crt.xo.cont(m = 30, J.arm = 4, delta = 0.3, icc = 0.05, cac = 0.8, sac = 0.4)
crt.xo.cont(m = 30, J.arm = 4, delta = 0.3, icc = 0.05, icca = 0.42, iccb = 0.04)
crt.xo.cont(m = 30, J.arm = 4, delta = 0.3, icc = 0.05, cac = 0.5)

Cohen f effect size calculation for one- or two- way analysis of variance

Description

Calculates teh Cohen f effect size for a one- or two-way ANOVA. Takes as input the cell or group means for a one- or two-way ANOVA and the common standard deviation and outputs the f effect size, as defined by Cohen (1988). Note that this effect size calculation is only valid when cell/group sizes are equal.

Usage

es.anova.f(means = NULL, sd = NULL, v = TRUE)

Arguments

Details

Cohen J (1988) Statistical Power Analysis for the Behavioral Sciences, 2nd edition. Lawrence Erlbaum Associates, Hillsdale, New Jersey

Value

Various calculated f effect sizes.

Examples

es.anova.f(means = c(5, 10, 12), sd = 10)
mmatrix <- matrix(c(9.3, 8.9, 8.5, 8.7, 8.3, 7.9), nrow = 2, byrow = TRUE)
es.anova.f(means = mmatrix, sd = 2)

Cohen d effect size calculation for one or two means

Description

This function takes as inputs a difference between two means and a standard deviation and outputs the d effect size as defined by Cohen (1988), also called the standardized mean difference.

Usage

es.d(delta = NULL, sd = 1)

Arguments

Details

Cohen J (1988) Statistical Power Analysis for the Behavioral Sciences, 2nd edition. Lawrence Erlbaum Associates, Hillsdale, New Jersey

Value

A list of the arguments and the d effect size.

Examples

es.d(delta = 6.5 - 5.7, sd = 0.4)

Cohen f-squared effect size for overall F test in multiple linear regression

Description

Computes the f-squared (f^2) effect size for an overall F test in a multiple linear regression model based on the model R^2 (Rsq). Based on Cohen (1988).

Usage

es.fsq.overall(Rsq = 0.02)

Arguments

Details

Cohen J (1988) Statistical Power Analysis for the Behavioral Sciences, 2nd edition. Lawrence Erlbaum Associates, Hillsdale, New Jersey

Value

A list of the arguments and the f^2 effect size.

Examples

es.fsq.overall(Rsq = 0.02)

Cohen f-squared effect size for partial F test in multiple linear regression

Description

Computes the f-squared (f^2) effect size for a partial F test in a multiple linear regression model using either model R^2 (Rsq) values or a partial correlation. Based on Cohen (1988). (EDIT THIS)

Usage

es.fsq.partial(Rsq.red = NULL, Rsq.full = NULL, Rsq.diff = NULL, pc = NULL)

Arguments

Details

Cohen J (1988) Statistical Power Analysis for the Behavioral Sciences, 2nd edition. Lawrence Erlbaum Associates, Hillsdale, New Jersey

Value

A list of the arguments and the f^2 effect size.

Examples

es.fsq.partial(pc = 0.2)
es.fsq.partial(Rsq.red = 0.25, Rsq.full = 0.35)
es.fsq.partial(Rsq.red = 0.25, Rsq.diff = 0.1)
es.fsq.partial(Rsq.full = 0.35, Rsq.diff = 0.1)

Cohen h effect size calculation for two proportions

Description

Takes as input the outcome proportions in two groups and returns the h effect size as defined by Cohen (1988).

Usage

es.h(p1 = NULL, p2 = NULL)

Arguments

Details

Cohen J (1988) Statistical Power Analysis for the Behavioral Sciences, 2nd edition. Lawrence Erlbaum Associates, Hillsdale, New Jersey

Value

A list of the arguments and the h effect size.

Examples

es.h(p1 = 0.8, p2 = 0.6)

Cohen q effect size calculation for two correlation coefficients

Description

Calculates the q effect size for comparing two correlation coefficients. Based on Cohen (1988).

Usage

es.q(rho1 = NULL, rho2 = NULL)

Arguments

Details

Cohen J (1988) Statistical Power Analysis for the Behavioral Sciences, 2nd edition. Lawrence Erlbaum Associates, Hillsdale, New Jersey

Value

A list of the arguments and the q effect size.

Examples

es.q(rho1 = 0.3, rho2 = 0.1)

Cohen w effect size calculation for chi-square tests

Description

Calculates the w effect size for chi-square tests. For chi-square goodness of fit tests, specify p0vec and p1vec. For chi-square tests of independence, provide a matrix of cell probabilities. Based on Cohen (1988).

Usage

es.w(p0vec = NULL, p1vec = NULL, pmatrix = NULL)

Arguments

Details

Cohen J (1988) Statistical Power Analysis for the Behavioral Sciences, 2nd edition. Lawrence Erlbaum Associates, Hillsdale, New Jersey

Value

A list of the arguments and the w effect size.

Examples

es.w(p0vec = c(0.5, 0.3, 0.2), p1vec = c(0.7, 0.2, 0.1))
es.w(pmatrix = matrix(c(0.050, 0.350, 0.100, 0.075, 0.250, 0.175), nrow = 2, byrow = TRUE))

Power for individual randomized group treatment trial with binary outcome

Description

Computes power and sample size for an individually randomized group treatment trial with a binary outcome, in which after individual randomization, individuals in the intervention/treatment arm are clustered. Can solve for power, J, m, n, or alpha.

Usage

irgtt.bin(
  m = NULL,
  J = NULL,
  n = NULL,
  p1 = NULL,
  p2 = NULL,
  icc = 0,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

irgtt.bin(m = 20, J = 5, n = 100, p1 = 0.8, p2 = 0.6, icc = 0.04, sides = 2)
irgtt.bin(m = 20, J = 6, n = 120, p1 = 0.8, p2 = 0.6, icc = 0.04, sides = 2)

Power for individually randomized group treatment trial with continuous outcome

Description

Computes power and sample size for an individually randomized group treatment trial with a continuous outcome, in which after individual randomization, individuals in the intervention/treatment arm are clustered. Can solve for power, J, m, n, delta or alpha.

Usage

irgtt.cont(
  m = NULL,
  J = NULL,
  n = NULL,
  delta = NULL,
  sd = 1,
  icc = 0,
  Theta = 1,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Details

Power is solved for using noncentral t or F distribution; other quantities (for example, sample sizes) are solved for using normal approximation.

Value

A list of the arguments (including the computed one).

Examples

irgtt.cont(m = 10, J = 12, n = 120, delta = 0.4, icc = 0.05, Theta = 1, power = NULL)
irgtt.cont(m = 10, J = 12, n = NULL, delta = 0.4, icc = 0.05, Theta = 1, power = 0.8)

Power for detecting treatment effect heterogeneity in an individually randomized trial with a continuous outcome

Description

This function performs power and sample size calculations for detecting a treatment-by-covariate interaction effect in a two-arm randomized trial with a continuous outcome. Can solve for power, beta, n1 or n.ratio.

Usage

irt.hte(
  n1 = NULL,
  n.ratio = 1,
  beta = NULL,
  sd.x = NULL,
  sd.yx = NULL,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Details

Shieh G (2009) Detecting interaction effects in moderated multiple regression with continuous variables: power and sample size considerations. Organizational Research Methods 12(3):510-528.

Yang S, Li F, Starks MA, Hernandez AF, Mentz RJ, Choudhury KR (2020) Sample size requirements for detecting treatment effect heterogeneity in cluster randomized trials. Statistics in Medicine 39:4218-4237.

Value

A list of the arguments (including the computed one).

Examples

irt.hte(n1 = 540, n.ratio = 1, beta = 1, sd.x = 12.7, sd.yx = 71)

Internal-use function for displaying matrices in function outputs

Description

Internal-use function for displaying matrices in function outputs

Usage

matrix.format(matrix = NULL, nspaces = 18)

Arguments

Value

The matrix printed as a string with rows separated by newline.

Examples

matrix <- matrix(c(1, 2, 3, 4), nrow = 2)
matrix.format(matrix = matrix)

Power calculation for a multiple linear regression overall F test

Description

Conducts power and sample size calculations for an overall (or omnibus) F test in a multiple linear regression model. This is a test that all coefficients other than the intercept are equal to zero. Can solve for power, N or alpha.

Usage

mlrF.overall(
  N = NULL,
  p = NULL,
  Rsq = NULL,
  fsq = NULL,
  alpha = 0.05,
  power = NULL,
  random = FALSE,
  v = FALSE
)

Arguments

Details

Either Rsq OR fsq must be specified. These are related as fsq = Rsq/(1-Rsq). Rsq is the proportion of the total variation in Y that is explained by linear relationship with the predictors. Specifying random = TRUE yields a calculation in which Y and the predictors are assumed to have a multivariate normal distribution; see Crespi (2025).

Value

A list of the arguments (including the computed one).

Examples

mlrF.overall(N = 400, p = 2, Rsq = 0.02)
mlrF.overall(N = 400, p = 2, fsq = 0.02 / (1 - 0.02))
mlrF.overall(N = 109, p = 1, Rsq = 0.3^2)
mlrF.overall(N = 50, p = 1, Rsq = 0.2)
mlrF.overall(N = 50, p = 3, Rsq = 0.2)
mlrF.overall(N = 50, p = 5, Rsq = 0.2)
mlrF.overall(N = 400, p = 2, Rsq = 0.02, random = TRUE)

Power calculation for a multiple linear regression partial F test

Description

Conducts power and sample size calculations for a partial F test in a multiple linear regression model. This is a test that one or more coefficients are equal to zero after controlling for a set of control predictors. Can solve for power, N or alpha.

Usage

mlrF.partial(
  N = NULL,
  p = NULL,
  q = NULL,
  pc = NULL,
  Rsq.red = NULL,
  Rsq.full = NULL,
  alpha = 0.05,
  power = NULL,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

mlrF.partial(N = 80, p = 3, q = 2, Rsq.red = 0.25, Rsq.full = 0.35)
mlrF.partial(N = 150, p = 4, q = 1, pc = 0.2)

Variance exploration for a multisite trial with a binary outcome

Description

This function can be used to help select a plausible value for the variance/SD of the random intercept for site in a multisite trial with a binary outcome. Based on user-supplied values of the outcome proportions in the two conditions, this function outputs, for a range of possible values of the SD, the intervals within which we expect about 95% of the site-specific odds ratios to lie.

Usage

ms.varexplore(pc, pt, print = TRUE)

Arguments

Details

In a multisite trial design, participants are randomized to conditions within site. The use of this function is illustrated in Crespi CM (2025) Power and Sample Size in R.

Value

A list containing the calculated OR and a dataframe of outputs.

Examples

ms.varexplore(pc = 0.1, pt = 0.2)
output <- ms.varexplore(pc = 0.1, pt = 0.2, print = FALSE)
output$OR

Power for a multisite trial with a binary outcome

Description

Performs power and sample size calculations for a multisite trial with a binary outcome. Can solve for power, J, m or alpha.

Usage

multisite.bin(
  m = NULL,
  alloc.ratio = 1,
  J = NULL,
  pc = NULL,
  pt = NULL,
  sigma.u = NULL,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Details

In a multisite trial design, participants are randomized to conditions within site. Consider using ms.varexplore to select plausible values for sigma.u.

Value

A list of the arguments (including the computed one).

Examples

multisite.bin(m = 30, J = 25, pc = 0.1, pt = 0.2, sigma.u = 0.4, power = NULL)
multisite.bin(m = 30, J = NULL, pc = 0.1, pt = 0.2, sigma.u = 0.4, power = 0.9)

Power for test of average treatment effect in a multisite trial

Description

Performs power and sample size calculations for a multisite trial with a continuous (normal) outcome variable. Can solve for power, J, m or alpha.

Usage

multisite.cont(
  m = NULL,
  m.sd = 0,
  alloc.ratio = 1,
  J = NULL,
  delta = NULL,
  sd = 1,
  icc0 = NULL,
  icc1 = NULL,
  Rsq = 0,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Details

In a multisite trial design, participants are randomized to conditions within site.

Value

A list of the arguments (including the computed one).

Examples

multisite.cont(m = 20, J = 10, delta = 3, sd = sqrt(40), icc0 = 0.1, icc1 = 0)
multisite.cont(m = 20, J = 10, delta = 3, sd = sqrt(48), icc0 = 0.095, icc1 = 0.048)
multisite.cont(m = 20, alloc.ratio = 1.5, J = 10, delta = 0.43, icc0 = 0.095, icc1 = 0.048)
multisite.cont(m = 10, J = NULL, delta = 0.5, sd = 1, icc0 = 0, icc1 = 0.05, power = 0.8)
multisite.cont(m = 20, m.sd = 5, J = 10, delta = 3, sd = sqrt(48), icc0 = 0.095, icc1 = 0.048)
multisite.cont(m = 20, J = 10, delta = 3, sd = sqrt(48), icc0 = 0.095,
icc1 = 0.048, Rsq = 0.5^2)

Power for test of heterogeneity of treatment effect in a multisite trial

Description

Calculates power for a test of heterogeneity of the treatment effect in a multisite trial with a continuous outcome variable. In particular, let sigma.u1^2 be the variance of the site-level treatment effects. The test of heterogeneity tests the null hypothesis that sigma.u1^2 = 0 versus the alternative that sigma.u1^2 > 0. Can solve for power, J, or m.

Usage

multisite.hte(
  m = NULL,
  alloc.ratio = 1,
  J = NULL,
  VR = NULL,
  alpha = 0.05,
  power = NULL,
  v = FALSE
)

Arguments

Details

See Crespi CM (2025) for details.

Value

A list of the arguments (including the computed power).

Examples

multisite.hte(m = 10, J = 30, VR = 8 / 36)

Power calculation for one-sample proportion test

Description

Performs power and sample size calculations for a one-sample test of a proportion. Calculations use the large-sample normal approximation to the binomial. Can solve for power, N or alpha.

Usage

prop.1samp(
  N = NULL,
  p0 = NULL,
  pA = NULL,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

prop.1samp(N = NULL, p0 = 0.2, pA = 0.3, power = 0.8, sides = 1)
prop.1samp(N = NULL, p0 = 0.4, pA = 0.5, power = 0.8, sides = 1)

Power calculation for two-sample proportion test

Description

Performs power and sample size calculations for two-sample tests of proportions using normal approximation to the binomial. Can solve for power, n1, n.ratio or alpha.

Usage

prop.2samp(
  n1 = NULL,
  n.ratio = 1,
  p1 = NULL,
  p2 = NULL,
  margin = 0,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Details

For a noninferiority or superiority by a margin test, a one-sided test should be used. See Crespi (2025) for more guidance. For an equivalence test for two proportions, see the prop.test.equiv.

Value

A list of the arguments (including the computed one).

Examples

prop.2samp(n1 = NULL, p1 = 0.6, p2 = 0.8, alpha = 0.025, power = 0.9, sides = 1)
prop.2samp(n1 = NULL, p1 = 0.25, p2 = 0.25, margin = 0.1, alpha = 0.025, power = 0.8, sides = 1)

Power calculation for McNemar test of two correlated proportions

Description

Performs power and sample size calculation for McNemar test of two correlated proportions using normal approximation. Can solve for power, N or alpha.

Usage

prop.paired(
  N = NULL,
  p1 = NULL,
  p2 = NULL,
  phi = NULL,
  paid = NULL,
  dpr = NULL,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Details

Either p1, p2 and phi, OR paid and dpr must be specified.

Value

A list of the arguments (including the computed one).

Examples

prop.paired(N = NULL, p1 = 0.8, p2 = 0.9, phi = 0, power = 0.9, sides = 2)
prop.paired(N = NULL, paid = 0.08, dpr = 0.18 / 0.08, power = 0.9, sides = 2)

Power calculation for test of equivalence of two proportions

Description

Performs power and sample size calculations for a test of equivalence for two proportions. Can solve for power, n1, n.ratio or alpha.

Usage

prop.test.equiv(
  n1 = NULL,
  n.ratio = 1,
  p1 = NULL,
  p2 = NULL,
  margin = NULL,
  alpha = 0.05,
  power = NULL,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

prop.test.equiv(n1 = NULL, p1 = 0.5, p2 = 0.5, margin = 0.1, alpha = 0.05, power = 0.8)

Power calculations for ordinal categorical variable under proportional odds assumption

Description

Performs power and sample size calculation for a comparison of two groups on an ordinal categorical response variable. Assumes that response probabilities follow the proportional odds assumption. Can solve for power, n1, n.ratio and alpha.

Usage

propodds(pC, OR, n1, n.ratio = 1, alpha = 0.05, power = NULL, v = FALSE)

Arguments

Details

Whitehead J. (1993) Sample size calculations for ordered categorical data. Statistics in Medicine, 12(24):2257–2271

Value

A list of the arguments (including the computed one).

Examples

library(Hmisc)
pC <- c(0.2, 0.5, 0.2, 0.1)
propodds(pC = pC, OR = 2.5, n1 = 65, n.ratio = 1, alpha = 0.05)

Power calculation for rank-sum test

Description

This function performs power and sample size calculations for the Wilcoxon-Mann-Whitney rank-sum test, also called the Mann-Whitney U test, which is the nonparametric analog of the two independent sample t test. Calculations are based on the approximation given by Noether (1987) Sample size determination for some common nonparametric tests. JASA 82(398):645-647.

Usage

ranksum(
  n1 = NULL,
  n.ratio = 1,
  p = NULL,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Details

Due to symmetry, the power for p is equal to the power for 1 - p. Therefore, when solving for p, two values, p and 1 - p, are returned.

Value

A list of the arguments (including the computed one).

Examples

ranksum(n1 = 10, n.ratio = 1, p = 0.8, alpha = 0.05, power = NULL, sides = 2)

Relative efficiency of a cluster randomized or multisite trial with binary outcome with varying cluster sizes

Description

For a binary outcome, computes the relative efficiency (ratio of the variances) of a cluster randomized or multisite trial with varying cluster (site) sizes to that of a trial with constant cluster sizes, assuming equal total number of subjects. This approximation may not be valid for all combinations of parameters, for example when m.sd is large.

Usage

re.clustsize.bin(m, m.sd, pc, pt, sigma.u)

Arguments

Details

Candel MJJM and van Breukelen GJP (2010) Sample size adjustments for varying cluster sizes in cluster randomized trials with binary outcomes analyzed with second-order PQL mixed logistic regression. Statistics in Medicine 29(14):1488-1501.

Value

The computed RE.

Examples

re.clustsize.bin(m = 60, m.sd = 45, pc = 0.25, pt = 0.15, sigma.u = 0.3)

Relative efficiency of a cluster randomized or multisite trial with continuous outcome with varying cluster sizes

Description

For a continuous outcome, computes the relative efficiency (ratio of the variances) of a cluster randomized or multisite trial with varying cluster (site) sizes to that of a trial with constant cluster sizes, assuming equal total number of subjects. This approximation may not be valid for all combinations of parameters, for example when m.sd is large.

Usage

re.clustsize.cont(m, m.sd, icc)

Arguments

Value

The computed RE.

Examples

re.clustsize.cont(m = 25, m.sd = 15, icc = 0.05)

Power calculation for relative risk

Description

Performs power and sample size calculations for a test of relative risk, p2/p1. Can solve for power, N1, n.ratio or alpha.

Usage

relrisk(
  n1 = NULL,
  n.ratio = 1,
  p1 = NULL,
  p2 = NULL,
  RR0 = 1,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

relrisk(n1 = NULL, n.ratio = 1/6, p1 = 0.1, p2 = 0.1 * 2, power = 0.8)

Internal-use wrapper for catching errors induced by stats::uniroot

Description

Internal-use wrapper for catching errors induced by stats::uniroot

Usage

safe.uniroot(f = NULL, interval = NULL)

Arguments

Value

If no error occurs, returns the solved root. If an error occurs, output a custom message.

Examples

f <- function(x) x - 3
safe.uniroot(f, c(-10, 10))$root

Power calculation for signed-rank test

Description

The signed-rank test is a nonparametric alternative to a one-sample or paired t test. This function performs power and sample size calculations for the signed-rank test using Noether's approximation; see Noether (1987) Sample size determination for some common nonparametric tests. JASA 82(398):645-647.

Usage

signedrank(
  N = NULL,
  ps = NULL,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Details

Due to symmetry, the power for p is equal to the power for 1 - p. Therefore, when solving for p, two values, p and 1 - p, are returned.

Value

A list of the arguments (including the computed one).

Examples

signedrank(N = 20, ps = 0.87, power = NULL, sides = 2)

Power calculation for sign test

Description

The sign test is a nonparametric one-sample test of location, specifically, a test of whether the median equals (or is less than or greater than) zero. Its typical use is in place of a one-sample or paired t test when the normality assumption is violated. This function performs power and sample size calculations for a sign test using the normal approximation to the binomial distribution, based on Noether (1987) Sample size determination for some common nonparametric tests. JASA 82(398):645-647.

Power calculation for an exact sign test using the exact binomial test can be performed using the power_binom_test function from the MESS package; see Crespi CM (2025) Power and Sample Size in R. Routledge, New York, NY.

Usage

signtest(N = NULL, p = NULL, alpha = 0.05, power = NULL, sides = 2, v = FALSE)

Arguments

Details

When solving for p, two values, p and 1 - p, are returned. For a two-sided test, due to symmetry, the power for p is equal to the power for 1 - p. For a one-sided upper-tailed test (rejecting null hypothesis when median > 0), select the higher value. For a one-sided lower-tailed test (rejecting null hypothesis when median < 0), select the lower value.

Value

A list of the arguments (including the computed one).

Examples

signtest(N = 40, p = 0.7, power = NULL, alpha = 0.05, sides = 1)

Power calculation for a simple linear regression

Description

Performs sample size and power calculations for a simple linear regression. Can solve for power, N or alpha. Required inputs include the values of the slope regression coefficient under the null hypothesis and the alternative, the variance of the covariate X, and the SD of the error. Power calculations for a simple linear regression can also be conducted using the mlrF.overall function, which requires fewer inputs.

Usage

slr(
  N = NULL,
  beta10 = 0,
  beta1A = NULL,
  var.x = NULL,
  sigma.e = NULL,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

# Yi = beta0 + beta1 * Xi + ei, i = 1,...,N
slr(N = 100, beta10 = 1, beta1A = 1.5, var.x = 25, sigma.e = 10, sides = 1)

Power calculation for one-sample t test

Description

This function computes power and sample size for a one-sample t test. Can solve for power, N, delta, sd or alpha.

Usage

ttest.1samp(
  N = NULL,
  delta = NULL,
  sd = 1,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

ttest.1samp(N = 36, delta = 4.9 - 5.7, sd = 2, sides = 1)
ttest.1samp(N = 36, delta = 6.3 - 5.7, sd = 2, sides = 1)
ttest.1samp(N = 36, delta = 4.9 - 5.7, sd = 2, sides = 2)
ttest.1samp(delta = 0.6, sd = 1, power = 0.8, sides = 1)

Power calculation for two-sample t test

Description

This function computes power and sample size for a two-sample t test. Unequal sample sizes and/or unequal variances in the two groups are allowed. Can solve for power, n1, n.ratio, sd1, sd.ratio, delta or alpha.

Usage

ttest.2samp(
  n1 = NULL,
  n.ratio = 1,
  delta = NULL,
  sd1 = 1,
  sd.ratio = 1,
  df.method = c("welch", "classical"),
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Details

For a noninferiority or superiority by a margin test, the margin should be subtracted as part of the specification of delta and a one-sided test should be used. See Crespi (2025) for specific guidance. For an equivalence test for two means, see the sampleN.TOST function from the PowerTOST package.

Value

A list of the arguments (including the computed one).

Examples

ttest.2samp(n1 = 50, delta = 2, sd1 = 5, sides = 1)
ttest.2samp(n1 = NULL, n.ratio = 2, delta = 0.5, sd1 = 1, power = 0.8, sides = 2)
ttest.2samp(n1 = 49, n.ratio = 2, delta = 0.5, sd1 = 1, power = NULL, sides = 2)
ttest.2samp(n1 = 25, n.ratio = 3, delta = 3, sd1 = 4, sd.ratio = 1.5, alpha = 0.025, sides = 1)
ttest.2samp(n1 = NULL, delta = 0.5, sd1 = 1, power = 0.8, sides = 2)

Power calculation for paired t test

Description

Performs power and sample size calculations for a paired t test. Can solve for power, N, delta or alpha.

Usage

ttest.paired(
  N = NULL,
  delta = NULL,
  sd1 = 1,
  sd2 = NULL,
  rho = NULL,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

ttest.paired(N = NULL, delta = 4, sd1 = 10, sd2 = 10, rho = 0.4, power = 0.8, sides = 2)

Power calculation for one-sample z test

Description

This function performs power and sample size calculations for a one-sample z test which is analogous to a one-sample t test with the variance assumed to be known. This function is provided largely for pedagogical purposes; in general, for real studies, the one-sample t test procedure should be used.

Usage

ztest.1samp(
  N = NULL,
  delta = NULL,
  sd = 1,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

ztest.1samp(N = NULL, delta = 6.5 - 5.7, sd = 2, power = 0.8, sides = 2)
ztest.1samp(N = 40, delta = NULL, sd = 1, power = 0.9, sides = 2)
ztest.1samp(N = NULL, delta = 0.6, sd = 1, power = 0.8, sides = 1)

Power calculation for two-sample z test

Description

This function performs power and sample size calculations for a two-sample z test. which is analogous to a two-sample t test but with the variances assumed to be known. The function allows for unequal sample sizes and/or variances in the two groups. This function is provided largely for pedagogical purposes; in general, for real studies, the two-sample t test procedure should be used.

Usage

ztest.2samp(
  n1 = NULL,
  n.ratio = 1,
  delta = NULL,
  sd1 = 1,
  sd.ratio = 1,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Details

For a noninferiority or superiority by a margin test, the margin should be subtracted as part of the specification of delta and a one-sided test should be used. See Crespi (2025) for specific guidance.

Value

A list of the arguments (including the computed one).

Examples

ztest.2samp(n1 = NULL, n.ratio = 1, delta = 0.5, sd1 = 1, power = 0.8, sides = 2)

Power calculation for paired z test

Description

This function performs power and sample size calculations for a paired z test which is analogous to a paired t test with variance assumed to be known. This function is provided largely for pedagogical purposes; in general, for real studies, the paired t test procedure should be used.

Usage

ztest.paired(
  N = NULL,
  delta = NULL,
  sd1 = 1,
  sd2 = NULL,
  rho = NULL,
  alpha = 0.05,
  power = NULL,
  sides = 2,
  v = FALSE
)

Arguments

Value

A list of the arguments (including the computed one).

Examples

ztest.paired(N = NULL, delta = 4, sd1 = 10, sd2 = 10, rho = 0.4, power = 0.8, sides = 2)