Package 'sse' reference manual

Title:	Sample Size Estimation
Description:	Provides functions to evaluate user-defined power functions for a parameter range, and draws a sensitivity plot. It also provides a resampling procedure for semi-parametric sample size estimation and methods for adding information to a Sweave report.
Authors:	Thomas Fabbro [aut, cre]
Maintainer:	Thomas Fabbro <[email protected]>
License:	GPL-3
Version:	0.7-15
Built:	2024-10-25 04:32:09 UTC
Source:	https://github.com/thofab/sse

Extracting an actual n, theta, and xi

Description

Extracting the actual n, theta, or xi from an object of class powPar. This functions are needed within the 'power-function' for extracting always the actual element during evaluation.

Usage

n(x)
theta(x)
xi(x)
n(x)
theta(x)
xi(x)

Arguments

`x`	An object of class powPar.

Details

During the evaluation process with powCalc every combination of n, theta, and xi is evaluated. The described functions extract the actual n, theta, or xi during the evaluation process. The evaluation process with powCalc changes the actual element to ensure that all combinations are evaluated.

When a objcect of class powPar is created, the first element of n, theta, or xi is also set to be the actual element. This allows to use this method also outside the evaluation with powCalc for testing the 'power function'.

Value

An integer value for n. A numeric value for theta and xi.

Note

Do not use the method pp inside the power-function e.g. like pp(x, "n"), because this would extract the whole vector of n and not just the actual element.

Examples

## defining the range of n and theta to be evaluated
psi <- powPar(n = seq(from = 20, to = 60, by = 2),
              theta = seq(from = 0.5, to = 1.5, by = 0.1),
              muA = 0,
              muB = 1)

## extracting all elements of psi individually, starting with the first
n(psi)
theta(psi)
xi(psi)

## extracting all elements, not just the actual:
pp(psi, name = "n")
pp(psi, name = "theta")
pp(psi, name = "xi")

## an example of usage
powFun <- function(psi){
  power.t.test(n = n(psi),
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## testing the power-function
powFun(psi)

## defining the range of n and theta to be evaluated
psi <- powPar(n = seq(from = 20, to = 60, by = 2),
              theta = seq(from = 0.5, to = 1.5, by = 0.1),
              muA = 0,
              muB = 1)

## extracting all elements of psi individually, starting with the first
n(psi)
theta(psi)
xi(psi)

## extracting all elements, not just the actual:
pp(psi, name = "n")
pp(psi, name = "theta")
pp(psi, name = "xi")

## an example of usage
powFun <- function(psi){
  power.t.test(n = n(psi),
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## testing the power-function
powFun(psi)

Extracting from an object of class powPar

Description

All information needed for the 'power-function' should be provided by an object of class powPar. To extract this information the function pp should be used.

Usage

pp(x, name)pp(x, name)

Arguments

`x`	An object of class powPar.
`name`	A character indicating the name of the object to be extracted.

Value

Everything that can be stored within a list is possible.

Note

The name pp is an abbreviation for power parameter.

Examples

psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.5),
              n = seq(from = 10, to = 30, by = 10),
              muA = 0,
              muB = 1)
              

pp(psi, name = "muA")

## an example of usage
powFun <- function(psi){
  power.t.test(n = n(psi),
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## testing the power-function
powFun(psi)
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.5),
              n = seq(from = 10, to = 30, by = 10),
              muA = 0,
              muB = 1)
              

pp(psi, name = "muA")

## an example of usage
powFun <- function(psi){
  power.t.test(n = n(psi),
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## testing the power-function
powFun(psi)

Inspection Plot

Description

Creating a plot that allows to inspect the sample size calculation.

Usage

inspect(object)inspect(object)

Arguments

object

An object of class power.

Details

The plot shows for every evaluated theta the sample size and the power on a transformed scale. The method used for sample size estimation 'step' or 'lm' is indicated. If the method 'lm' is used a red regression line is shown for the range that was used for estimation.

Value

A plot is generated but nothing is returned.

Examples

## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2),
              muA = 0,
              muB = 1)

## defining a power-function               
powFun <- function(psi){
  power.t.test(n = n(psi)/2,
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun)

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc, theta = 1, power = 0.9)

## drawing an inspection plot
inspect(pow)
## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2),
              muA = 0,
              muB = 1)

## defining a power-function               
powFun <- function(psi){
  power.t.test(n = n(psi)/2,
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun)

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc, theta = 1, power = 0.9)

## drawing an inspection plot
inspect(pow)

Power Plot

Description

A sensitivity plot (called power plot) for the sample size calculation. Using a contour for a given power, it shows how sample size changes if theta is varied.

Usage

plot(x, y, ...)plot(x, y, ...)

Arguments

x

The object of class power used for plotting

y

Not used

...

additional arguments implemented:

at = c(0.9, 0.8, 0.85, 0.95) a numeric vector giving breakpoints along the power range. Contours (if any) will be drawn at these values. The contour line of the example will be emphasised. If example = FALSE the first number indicates, which contour should be emphasized.
smooth = FALSE logical that indicates if the contours should be smoothed. If TRUE a span of 0.75 will be used by default. Alternatively the argument smooth can also take a numeric value that will be used for smoothing.See the documentation of the function loess for details.
example = TRUE a logical indicating if an example should be drawn or not. An example is an arrow that points from the particular theta on the x-axis to the contour line and to the sample size on the y-axis.
reflines = TRUE a logical indicating if reference lines should be drawn or not. Reference lines are drawn at every n and theta that was used for evaluating the power function. If reference lines are drawn the background will be grey.

Details

Generates a contour plot with theta on the x-axis and n on the y-axis and the contours for the estimated power (indicated with the argument at).

Value

A plot is generated but nothing is returned.

Examples

## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2),
              muA = 0,
              muB = 1)

## defining a power-function     
powFun <- function(psi){
  power.t.test(n = n(psi)/2,
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun)

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc, theta = 1, power = 0.9)

## drawing the power plot with 3 contour lines
plot(pow,
     xlab = "Standard Deviation",
     ylab = "Total Sample Size",
     at = c(0.85, 0.9, 0.95))

## without example the contour line at the first element of at is bold
plot(pow, example = FALSE)
## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2),
              muA = 0,
              muB = 1)

## defining a power-function     
powFun <- function(psi){
  power.t.test(n = n(psi)/2,
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun)

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc, theta = 1, power = 0.9)

## drawing the power plot with 3 contour lines
plot(pow,
     xlab = "Standard Deviation",
     ylab = "Total Sample Size",
     at = c(0.85, 0.9, 0.95))

## without example the contour line at the first element of at is bold
plot(pow, example = FALSE)

Power calculation

Description

The user-defined 'power-function' provided as statistic will be evaluated for the whole range of n, theta, and xi as specified in the powPar-object.

Usage

powCalc(object, statistic, n.iter = NA, cluster = FALSE)powCalc(object, statistic, n.iter = NA, cluster = FALSE)

Arguments

`object`	An object of class `powPar`.
`statistic`	A function that takes an object of class `powPar` as argument. Ideally this is also the only argument. The function should return a vector of numeric values or a vector of logicals, depending on the `type`. See Details.
`n.iter`	A number specifying how often the power-function is evaluated.
`cluster`	Still experimental! This argument can be logical, indicating if the library parallel should be used or not, or numeric. In the latter case the number is passed as integer to the function makeCluster from library parallel. The default is FALSE.
`...`	Not used so far.

Details

If the statistic does not return the power (a numeric value between 0 and 1) but returns a logical (TRUE or FALSE) the argument n.iter is expected. The statitic will then be evaluated n.iter-times and the proportion of successes will be interpreted as the power.

Value

An object of class powCalc.

Examples

## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2),
              muA = 0,
              muB = 1)

## defining a power-function     
powFun <- function(psi){
  power.t.test(n = n(psi)/2,
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun)
## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2),
              muA = 0,
              muB = 1)

## defining a power-function     
powFun <- function(psi){
  power.t.test(n = n(psi)/2,
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun)

Defining the example to be used and the method to be used for sample size estimation.

Description

A function for constructing an object of class power used for drawing an example in a sensitivity plot and for estimating the sample size.

Usage

powEx(x, theta, xi = NA, endpoint = NA, power = 0.9, drop = 0,
             method = c("default", "lm", "step"), lm.range = NA,
             forceDivisor = FALSE)powEx(x, theta, xi = NA, endpoint = NA, power = 0.9, drop = 0,
             method = c("default", "lm", "step"), lm.range = NA,
             forceDivisor = FALSE)

Arguments

`x`	An object of class powCalc.
`theta`	a numeric value indicating for which `theta` to draw the example in the sensitivity plot and where to evaluate sample size. It makes only sense to use a `theta` in the range evaluated.
`xi`	a numeric value, as `theta` but for `xi`
`endpoint`	Object of class `character`, indidating for which endpoint sample size should be evaluated
`power`	Object of class `numeric`, indicating for what power samle size should be evaluated
`method`	Defining the method how the sample size for the is calculated. `method = "default"` uses `"lm"` if resampling was used to calculate the powCalc object, otherwise `"step"` is used.
`lm.range`	The range of evaluations that are used for estimating the sample size if the `method = "lm"` or evaluates to `"lm"`. For the default `lm.range` = 0.2 this means from 80 to 120 % of the power in the example, e.g. for the power of 0.9 this is a range from 0.72 to 1.08. Note that the range is cut at 0 and 1.
`drop`	Object of class `numeric` (range: 0 to 1), indicating how many drop outs are expected. This information is used to calculate the number of subject that should be recruited (addressed e.g. by the function `tex` using type `nRec`).
`forceDivisor`	If `TRUE` the biggest common divisor of all evaluated sample sizes is used as divisor and the estimated sample size is increased to be divisible by this divisor. If an integer is provided it is used as divisor.

Details

For method equal to "lm" a linear model is fit as lm(sample.size ~ transformed(power)) with all data where theta, and xi are equal to the theta and xi of the example and within the power-range as defined by the argument lm.range. This model is then used for predicting the sample size. Always inspect the result using inspect!

The method "step" returns the last element in the sequence of sample sizes - power pairs, sorted with decreasing power, where the power is above the power defined for the example.

Value

An object of class power.

Note

In older verstions of the package: The function merge was used together with an object of class powEx to form an object of class power.

Examples

## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2),
              muA = 0,
              muB = 1)

## defining a power-function     
powFun <- function(psi){
  power.t.test(n = n(psi)/2,
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun)

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc, theta = 1, power = 0.9)

## drawing the power plot with 3 contour lines
plot(pow,
     xlab = "Standard Deviation",
     ylab = "Total Sample Size",
     at = c(0.85, 0.9, 0.95))

## changing the estimation method
pow2 <- powEx(calc, theta = 1, power = 0.9, method = "lm")

## drawing an inspection plot
inspect(pow2)
## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2),
              muA = 0,
              muB = 1)

## defining a power-function     
powFun <- function(psi){
  power.t.test(n = n(psi)/2,
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun)

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc, theta = 1, power = 0.9)

## drawing the power plot with 3 contour lines
plot(pow,
     xlab = "Standard Deviation",
     ylab = "Total Sample Size",
     at = c(0.85, 0.9, 0.95))

## changing the estimation method
pow2 <- powEx(calc, theta = 1, power = 0.9, method = "lm")

## drawing an inspection plot
inspect(pow2)

Constructing an object of class 'powPar'.

Description

A function for constructing an object of class powPar. Such an object is used for evaluating the user defined 'power function' for a parameter range. All information that is needed for calculating the power (e.g. a pilot data set) should be provided by making use of the ... argument.

Usage

powPar(n, theta = NA, xi = NA, ...)powPar(n, theta = NA, xi = NA, ...)

Arguments

`n`	A numeric vector, indicating for which sample sizes to evaluate the power function.
`theta`	A numeric vector that will be used for evaluating the power function. The method `theta` can be used within the power function to extract the elements of this vector one by one.
`xi`	A numeric vector that will be used for evaluating the power function. Since for every element of`xi` an individuall sensitivity plot has to be constructed, the length of the `xi` vector is usually short.
`...`	This arguemt is used to provide additional parameters needed by the power function for calculating the power. This parameters can be extracted using the function `pp`.

Details

An object of class powPar is used to evaluate the 'power function' for a range of n and theta and optionally for several xi values.

The user can write a 'power function' and extract the individual elements using the functions n, theta, xi and pp.

It is a good practice to include everything that is needed for the calculation, also data sets etc.

To extract the vector of theta, instead of individual values, you can use the method pp with the name theta.

For historical reasons: If the argument theta = NA the argument theta.name (a character) has to be used, to indicate the name of a numeric vector that was passed to the argument (...). The same is true for the argument xi.

Value

An object of the class powPar

Examples

## defining the range of n and theta to be evaluated
psi <- powPar(n = seq(from = 20, to = 60, by = 2),
              theta = seq(from = 0.5, to = 1.5, by = 0.05)
              )

## defining a power-function  
powFun <- function(psi){
  return(power.t.test(n = n(psi)/2, delta = theta(psi), sig.level = 0.05)$power)
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, statistic = powFun)

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc, theta = 1)

## drawing the power plot
plot(pow,
     xlab = "Difference",
     ylab = "Total Sample Size")
## defining the range of n and theta to be evaluated
psi <- powPar(n = seq(from = 20, to = 60, by = 2),
              theta = seq(from = 0.5, to = 1.5, by = 0.05)
              )

## defining a power-function  
powFun <- function(psi){
  return(power.t.test(n = n(psi)/2, delta = theta(psi), sig.level = 0.05)$power)
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, statistic = powFun)

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc, theta = 1)

## drawing the power plot
plot(pow,
     xlab = "Difference",
     ylab = "Total Sample Size")

Refining the estimation

Description

Increasing the number of iterations for estimating the sample size for the 'theta' and 'xi' as specified for the example.

Usage

refine(object, factor = 10)refine(object, factor = 10)

Arguments

`object`	An object of class power.
`factor`	An integer larger than one that is multiplied with the available number of iterations to from the target number of iterations.

Value

An object of class power.

Note

This function is only useful if the object of class power was generated using a resamling approach.

Examples

 ## takes quite some time
## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2))

## defining a power-function               
powFun <- function(psi){
  x <- rnorm(n(psi)/2)
  y <- rnorm(n(psi)/2) + theta(psi)
  return(wilcox.test(x = x, y = y)$p.value < 0.05)
}


## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun, n.iter = 10)

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc, theta = 1, power = 0.9)

## another 900 (= 1000 - 100) iterations
refine(pow)

## takes quite some time
## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2))

## defining a power-function               
powFun <- function(psi){
  x <- rnorm(n(psi)/2)
  y <- rnorm(n(psi)/2) + theta(psi)
  return(wilcox.test(x = x, y = y)$p.value < 0.05)
}


## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun, n.iter = 10)

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc, theta = 1, power = 0.9)

## another 900 (= 1000 - 100) iterations
refine(pow)

Preparing text for using with LaTeX

Description

Methods for function tex

Usage

tex(x, type, ...)tex(x, type, ...)

Arguments

x

The object of class power used for extraction

type

Currently available:

"drop", indicating the drop-out rate used for calculation.
"nRec", sample size that was increased to take into account the drop-out rate.
"nEval", sample size needed for evaluation without taking into account the drop-out rate.
"n.iter", nuber of iterations used for calculation.
"power", 'power' used for calculation.
"sampling", a description of the sampling process.
"theta", 'theta' used for calculation.

...

Not used so far

Value

A character string.

Methods

This methods prepare strings that can directly be used for including information from objects of power into Sweave reports.

Examples

## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2),
              muA = 0,
              muB = 1)

## defining a power-function     
powFun <- function(psi){
  power.t.test(n = n(psi)/2,
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun)

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc, theta = 1, power = 0.9)

## drawing the power plot with 3 contour lines
plot(pow,
     xlab = "Standard Deviation",
     ylab = "Total Sample Size",
     at = c(0.85, 0.9, 0.95))

## 
tex(pow, type = "sampling")
## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2),
              muA = 0,
              muB = 1)

## defining a power-function     
powFun <- function(psi){
  power.t.test(n = n(psi)/2,
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun)

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc, theta = 1, power = 0.9)

## drawing the power plot with 3 contour lines
plot(pow,
     xlab = "Standard Deviation",
     ylab = "Total Sample Size",
     at = c(0.85, 0.9, 0.95))

## 
tex(pow, type = "sampling")

Updating a powCalc or a power object.

Description

A function for updating an existing object of class powCalc or power.

Usage

update(object, ...)update(object, ...)

Arguments

object

An object of class powCalc or power.

...

The following elements (slots) of the object can be updated:

n.iter: A number indicating the number of iterations used to dertermine the power if the calcualation is based on resampling. The existing iterations will be kept. n.iter indicates the number of iterations after evaluation, therefore n.iter has to be equal or larger than the existing number of iterations.
n: A vector with numbers for evaluating the power. New elements will be evaluated and existing elements reused. If some elements of the original are not part of n they will be ommitted.
theta: see n for details.
xi: see n for details.
statistic: A function of an object of class psi. If a new statistic is provided all elements will be evaluated again.

Value

An object of class powCalc.

Note

Be careful if you use this function to update objects of class power.

Examples

## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2),
              muA = 0,
              muB = 1)

## defining a power-function     
powFun <- function(psi){
  power.t.test(n = n(psi)/2,
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun)

## updating by using additional elements for "n"
calc2 <- update(calc, n = seq(from = 20, to = 90, by = 2))

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc2, theta = 1, power = 0.9)

## drawing the power plot with 3 contour lines
plot(pow,
     xlab = "Standard Deviation",
     ylab = "Total Sample Size",
     at = c(0.85, 0.9, 0.95))
## defining the range of n and theta to be evaluated
psi <- powPar(theta = seq(from = 0.5, to = 1.5, by = 0.1),
              n = seq(from = 20, to = 60, by = 2),
              muA = 0,
              muB = 1)

## defining a power-function     
powFun <- function(psi){
  power.t.test(n = n(psi)/2,
               delta = pp(psi, "muA") - pp(psi, "muB"),
               sd = theta(psi)
               )$power
}

## evaluating the power-function for all combinations of n and theta
calc <- powCalc(psi, powFun)

## updating by using additional elements for "n"
calc2 <- update(calc, n = seq(from = 20, to = 90, by = 2))

## adding example at theta of 1 and power of 0.9
pow <- powEx(calc2, theta = 1, power = 0.9)

## drawing the power plot with 3 contour lines
plot(pow,
     xlab = "Standard Deviation",
     ylab = "Total Sample Size",
     at = c(0.85, 0.9, 0.95))

Package 'sse'

Help Index

Extracting an actual n, theta, and xi

Description

Usage

Arguments

Details

Value

Note

See Also

Examples

Extracting from an object of class powPar

Description

Usage

Arguments

Value

Note

See Also

Examples

Inspection Plot

Description

Usage

Arguments

Details

Value

Examples

Power Plot

Description

Usage

Arguments

Details

Value

See Also

Examples

Power calculation

Description

Usage

Arguments

Details

Value

Examples

Defining the example to be used and the method to be used for sample size estimation.

Description

Usage

Arguments

Details

Value

Note

Examples

Constructing an object of class 'powPar'.

Description

Usage

Arguments

Details

Value

Examples

Refining the estimation

Description

Usage

Arguments

Value

Note

Examples

Preparing text for using with LaTeX

Description

Usage

Arguments

Value

Methods

Examples

Updating a powCalc or a power object.

Description

Usage

Arguments

Value

Note

See Also

Examples