Computes the lower boundary value for the empirical CDF

Description

Computes the lower boundary value for the empirical CDF

Usage

create_lower_extension(x)

Arguments

Value

numeric

Computes the upper boundary value for the empirical CDF

Description

Computes the upper boundary value for the empirical CDF

Usage

create_upper_extension(x)

Arguments

Value

numeric

Empirical probability density function (EPDF)

Description

Empirical probability density function based on a sample of observations, as described by Chakraborti (2006).

Usage

demp(x, sample)

Arguments

Value

numeric vector of density values based on the EPDF

References

Chakraborti, S., Hong, B., & Van De Wiel, M. A. (2006). A note on sample size determination for a nonparametric test of location. Technometrics, 48(1), 88–94. https://doi.org/10.1198/004017005000000193

Examples

x <- 1:5
demp(1, x)

Computes an empirical estimate of p (P(X < X + \delta))

Description

Computes an empirical estimate of p (P(X < X + \delta))

Usage

estimate_p(sample, delta)

Arguments

Value

An empirical estimate of P(X < X + \delta)

Extends a vector by adding a lower and upper boundary.

Description

Extends a vector by adding a lower and upper boundary.

Usage

extend_sample(x)

Arguments

Value

extended and sorted numeric vector

Finds the index of the smaller neighbour of the given value in the vector x.

Description

Finds the index of the smaller neighbour of the given value in the vector x.

Usage

find_smaller_index(value, x)

Arguments

Value

integer

Calculate sample size for binomial distribution

Description

Estimation of required sample size as given by Cundill & Alexander (2015).

Usage

n_binom(
  p0,
  effect,
  size = 1,
  alpha = 0.05,
  power = 0.9,
  q = 0.5,
  link = c("logit", "identity"),
  two_sided = TRUE
)

Arguments

Value

Returns an object of class "sample_size". It contains the following components:

References

Cundill, B., & Alexander, N. D. E. (2015). Sample size calculations for skewed distributions. BMC Medical Research Methodology, 15(1), 1–9. https://doi.org/10.1186/s12874-015-0023-0

Examples

n_binom(p0 = 0.5, effect = 0.3)

Calculate sample size for gamma distribution

Description

Estimation of required sample size as given by Cundill & Alexander (2015).

Usage

n_gamma(
  mean0,
  effect,
  shape0,
  shape1 = shape0,
  alpha = 0.05,
  power = 0.9,
  q = 0.5,
  link = c("log", "identity"),
  two_sided = TRUE
)

Arguments

Value

Returns an object of class "sample_size". It contains the following components:

References

Cundill, B., & Alexander, N. D. E. (2015). Sample size calculations for skewed distributions. BMC Medical Research Methodology, 15(1), 1–9. https://doi.org/10.1186/s12874-015-0023-0

Examples

n_gamma(mean0 = 8.46, effect = 0.7, shape0 = 0.639,
           alpha = 0.05, power = 0.9)

Calculate sample size for a group comparison via generalized linear models

Description

Estimation of required sample size as given by Cundill & Alexander (2015).

Usage

n_glm(
  mean0,
  mean1,
  dispersion0,
  dispersion1,
  alpha,
  power,
  link_fun = function(mu) NULL,
  variance_fun = function(mu, dispersion) NULL,
  dmu_deta_fun = function(mu) NULL,
  q
)

Arguments

Value

Total sample size (numeric)

References

Cundill, B., & Alexander, N. D. E. (2015). Sample size calculations for skewed distributions. BMC Medical Research Methodology, 15(1), 1–9. https://doi.org/10.1186/s12874-015-0023-0

Estimate N on the basis of two pilot samples.

Description

Estimation as described by Chakraborti, Hong, & van de Wiel (2006).

Usage

n_locshift(s1, s2, delta, alpha = 0.05, power = 0.9, q = 0.5)

Arguments

Details

WARNING: Note that the estimation has high variability due to its dependence on pilot samples. The smaller the pilot sample, the more uncertain is the estimation of the required sample size. In a simulation study, we found that the method may also be inaccurate on average, depending on the investigated data.

Value

Returns an object of class "sample_size". It contains the following components:

References

Chakraborti, S., Hong, B., & van de Wiel, M. A. (2006). A note on sample size determination for a nonparametric test of location. Technometrics, 48(1), 88–94. https://doi.org/10.1198/004017005000000193

Examples

n_locshift(s1 = rexp(10), s2 = rexp(10),
           alpha = 0.05, power = 0.9, delta = 0.35)

Compute an upper bound the sample size based on two pilot samples.

Description

Based on the procedure described by Chakraborti, Hong, & van de Wiel (2006)

Usage

n_locshift_bound(
  s1,
  s2,
  delta,
  alpha = 0.05,
  power = 0.9,
  quantile = 0.9,
  n_resamples = 500,
  q = 0.5
)

Arguments

Details

WARNING: Note that the underlying estimation has high variability due to its dependence on pilot samples. The smaller the pilot sample, the more uncertain is the estimation of the required sample size. In a simulation study, we found that the underlying method may also be inaccurate on average, depending on the investigated data.

Value

Returns an object of class "sample_size". It contains the following components:

References

Chakraborti, S., Hong, B., & van de Wiel, M. A. (2006). A note on sample size determination for a nonparametric test of location. Technometrics, 48(1), 88–94. https://doi.org/10.1198/004017005000000193

Examples

## Not run: 
n_locshift_bound(s1 = rexp(10), s2 = rexp(10),
           delta = 0.35, alpha = 0.05, power = 0.9, n_resamples = 5)
## End(Not run)

Estimate N on the basis of one pilot sample.

Description

Estimate N on the basis of one pilot sample.

Usage

n_locshift_one(sample, alpha, power, delta, q)

Arguments

Value

numeric value, an estimate of the sample size required to detect a location shift of delta with a Wilcoxon Mann-Whitney test with power and alpha.

Calculate sample size for negative binomial distribution

Description

Estimation of required sample size as given by Cundill & Alexander (2015).

Usage

n_negbinom(
  mean0,
  effect,
  dispersion0,
  dispersion1 = dispersion0,
  alpha = 0.05,
  power = 0.9,
  q = 0.5,
  link = c("log", "identity"),
  two_sided = TRUE
)

Arguments

Value

Returns an object of class "sample_size". It contains the following components:

References

Cundill, B., & Alexander, N. D. E. (2015). Sample size calculations for skewed distributions. BMC Medical Research Methodology, 15(1), 1–9. https://doi.org/10.1186/s12874-015-0023-0

Examples

n_negbinom(mean0 = 71.4, effect = 0.7, dispersion0 = 0.33,
           alpha = 0.05, power = 0.9)

Noether's (1987) formula for obtaining a sample size estimation for the two-sample Wilcoxon Mann-Whitney test.

Description

Noether's (1987) formula for obtaining a sample size estimation for the two-sample Wilcoxon Mann-Whitney test.

Usage

n_noether(alpha, power, p, q = 0.5)

Arguments

Value

estimated required total sample size

Calculate sample size for poisson distribution

Description

Estimation of required sample size as given by Cundill & Alexander (2015).

Usage

n_poisson(
  mean0,
  effect,
  alpha = 0.05,
  power = 0.9,
  q = 0.5,
  link = c("log", "identity"),
  two_sided = TRUE
)

Arguments

Value

Returns an object of class "sample_size". It contains the following components:

References

Cundill, B., & Alexander, N. D. E. (2015). Sample size calculations for skewed distributions. BMC Medical Research Methodology, 15(1), 1–9. https://doi.org/10.1186/s12874-015-0023-0

Examples

n_poisson(mean0 = 5, effect = 0.3)

Empirical cumulative density function (ECDF)

Description

Empirical cumulative density function based on a sample of observations, as used by described by Chakraborti (2006).

Usage

pemp(q, sample)

Arguments

Value

Returns the probabilities that a value drawn at random from the empirical cumulative density based on sample is smaller than or equal to the elements of x.

References

Chakraborti, S., Hong, B., & Van De Wiel, M. A. (2006). A note on sample size determination for a nonparametric test of location. Technometrics, 48(1), 88–94. https://doi.org/10.1198/004017005000000193

Examples

x <- 1:5
pemp(1, x)

Empirical quantile function

Description

Empirical quantile function, i.e. inverse of the empirical cumulative density function pemp(). Based on the latter function as presented by Chakraborti (2006).

Usage

qemp(p, sample)

Arguments

Value

Returns the value for which pemp(x, sample) = p, i.e. the probability that a value drawn at random from the ECDF is smaller or equal to x is p.

References

Chakraborti, S., Hong, B., & Van De Wiel, M. A. (2006). A note on sample size determination for a nonparametric test of location. Technometrics, 48(1), 88–94. https://doi.org/10.1198/004017005000000193

Examples

x <- 1:5
qemp(0.1, x)

Draws random values from the ECDF obtained from sample

Description

Based on the empirical cumulative density function as presented by Chakraborti (2006).

Usage

remp(n, sample)

Arguments

Value

numeric vector of random values drawn from the ECDF

References

Chakraborti, S., Hong, B., & Van De Wiel, M. A. (2006). A note on sample size determination for a nonparametric test of location. Technometrics, 48(1), 88–94. https://doi.org/10.1198/004017005000000193

Examples

x <- 1:5
remp(10, x)

Compute a distribution of estimates of N based on two pilot samples.

Description

Estimation of sample sizes based on resampled pilot samples from the empirical cumulative density. Based on the work of Chakraborti, Hong, & van de Wiel (2006).

Usage

resample_n_locshift(
  s1,
  s2,
  delta,
  alpha = 0.05,
  power = 0.9,
  n_resamples = 500,
  q = 0.5
)

Arguments

Details

WARNING: Note that the estimation has high variability due to its dependence on pilot samples. The smaller the pilot sample, the more uncertain is the estimation of the required sample size. In a simulation study, we found that the method may also be inaccurate on average, depending on the investigated data.

Value

numeric vector of sample size estimates (total sample size)

References

Chakraborti, S., Hong, B., & van de Wiel, M. A. (2006). A note on sample size determination for a nonparametric test of location. Technometrics, 48(1), 88–94. https://doi.org/10.1198/004017005000000193

Compute n_resamples estimates of N

Description

Compute n_resamples estimates of N

Usage

resample_n_locshift_one(sample, alpha, power, delta, n_resamples, q)

Arguments

Value

numeric vector of sample size estimates