Package 'OPDOE' reference manual

Title:	Optimal Design of Experiments
Description:	Several function related to Experimental Design are implemented here, see "Optimal Experimental Design with R" by Rasch D. et. al (ISBN 9781439816974).
Authors:	Petr Simecek <[email protected]>, Juergen Pilz <[email protected]>, Mingui Wang <[email protected]>, Albrecht Gebhardt <[email protected]>.
Maintainer:	Albrecht Gebhardt <[email protected]>
License:	GPL (>= 2)
Version:	1.0-10
Built:	2024-11-16 06:29:34 UTC
Source:	CRAN

Cattle data

Description

milk fat performance (in kg per lactation) of heifers of three sires from Holstein Frisian cattle to select the sire with the highest breeding value for milk fat performance.

Usage

data(cattle)data(cattle)

Format

The format is: num [1:5, 1:3] 132 128 135 121 138 173 166 172 176 169 ...

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

data(cattle)
size.seq_select.mean(data=cattle,delta=10, P=0.95)
data(cattle)
size.seq_select.mean(data=cattle,delta=10, P=0.95)

Design for Polynomial Regression

Description

Determines locations and number of replications for a polynomial regression design.

Needs specification of order of polynom, borders of intervall and total number of measurements as input.

Usage

design.regression.polynom(a, b, k, n)
design.reg.polynom(...)
design.regression.polynom(a, b, k, n)
design.reg.polynom(...)

Arguments

`a`	lower bound of interval
`b`	upper bound of interval
`k`	order of polynom
`n`	total number of planned measurements
`...`	only used for call wrapper `design.reg.polynom`

Details

Uses Legendre Polynomials to determine the support points for the design:

If $a=-1$ , $b=1$ : places $k +1$ support points in $[-1,1]$ , located at the roots of $(1-x^{2})\frac{dP_{k}(x)}{dx}$ where $P_{k}(x)$ is the Legendre polynomial of degree $k$ ).

Distributes the n measurements almost equally over the support points.

Value

Object of class design.regression

Note

design.reg.polynom is a call wrapper for backward compatibility for design.regression.polynom

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

x <- design.reg.polynom(10, 100, 3, 45)
x
x <- design.reg.polynom(10, 100, 3, 45)
x

Regression Design Object

Description

An design.regression object is created with design.regression.polynom

Arguments

A triangular.test object is a list of

`model`	character, currently only `"polynomial"` is implemented
`locations`	choosen locations
`replications`	choosen replications per location
`interval`	vector of size 2 storing the given interval

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Stored Hadmard matrices

Description

Some stored Hadmard matrices, used in hadamard.matrix

Details

Stored matrices from http://www2.research.att.com/~njas/hadamard/ filling the gaps up to 256 in hadamard.matrix, 260 is the next gap.

male / female heights data

Description

Body heights of male and female students collected in a classroom experiment.

Usage

data(heights)data(heights)

Format

A data frame with 7 observations on the following 2 variables.

female: a numeric vector
male: a numeric vector

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt, Minghui Wang

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

data(heights)
attach(heights)
tt <- triangular.test.norm(x=female[1:3],
   y=male[1:3], mu1=170,mu2=176,mu0=164,
   alpha=0.05, beta=0.2,sigma=7)
# Test is yet unfinished, add the remaining values:
tt <- update(tt,x=female[4:7], y=male[4:7])
# Test is finished now
data(heights)
attach(heights)
tt <- triangular.test.norm(x=female[1:3],
   y=male[1:3], mu1=170,mu2=176,mu0=164,
   alpha=0.05, beta=0.2,sigma=7)
# Test is yet unfinished, add the remaining values:
tt <- update(tt,x=female[4:7], y=male[4:7])
# Test is finished now

Hemp data

Description

age and height of hemp plants.

Usage

data(hemp)data(hemp)

Format

A data frame with 14 observations on the following 2 variables.

x: a numeric vector
y: a numeric vector

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

(still) undocumented functions

Description

Undocumented / internal functions

Details

Some of these functions are not intended to be called by the user, others still lack their own documentation page. In the mean time see the referenced book.

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Prints a regression design object

Description

Print method for a design.regression object.

Usage

## S3 method for class 'design.regression'
print(x, epl = 6, ...)
## S3 method for class 'design.regression'
print(x, epl = 6, ...)

Arguments

`x`	`design.regression` object
`epl`	integer, entries per line
`...`	additional print arguments

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Print method for Triangular Test Objects

Description

Prints a triangular.test object.

Usage

## S3 method for class 'triangular.test'
print(x, ...)
## S3 method for class 'triangular.test'
print(x, ...)

Arguments

`x`	`triangular.test` object
`...`	additional paramters for `print`

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Three-way analysis of variance – mixed classification $(A\times B)\succ C$ model III and VII

Description

Returns the optimal number of levels for factor A (and B).

Usage

size_a.three_way_mixed_cxbina.model_3_c(alpha, beta, delta, b, c, n, cases)
size_a.three_way_mixed_cxbina.model_7_c(alpha, beta, delta, b, c, n, cases)
size_ab.three_way_mixed_cxbina.model_7_c(alpha, beta, delta, c, n, cases)
size_a.three_way_mixed_cxbina.model_3_c(alpha, beta, delta, b, c, n, cases)
size_a.three_way_mixed_cxbina.model_7_c(alpha, beta, delta, b, c, n, cases)
size_ab.three_way_mixed_cxbina.model_7_c(alpha, beta, delta, c, n, cases)

Arguments

`alpha`	Risk of 1st kind
`beta`	Risk of 2nd kind
`delta`	The minimum difference to be detected
`b`	Number of levels of fixed factor B
`c`	Number of levels of fixed factor C
`n`	Number of replications
`cases`	Specifies whether the `"maximin"` or `"maximin"` sizes are to be determined

Details

see chapter 3 in the referenced book

Value

Integer(s) giving the size(s).

Note

Better use size.anova which allows a cleaner notation.

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt, Minghui Wang

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

size_a.three_way_mixed_cxbina.model_3_c(0.05, 0.1, 0.5, 5, 4, 1, "maximin")
size_a.three_way_mixed_cxbina.model_3_c(0.05, 0.1, 0.5, 5, 4, 1, "minimin")
size_a.three_way_mixed_cxbina.model_7_c(0.05, 0.1, 0.5, 5, 4, 1, "maximin")
size_a.three_way_mixed_cxbina.model_7_c(0.05, 0.1, 0.5, 5, 4, 1, "minimin")
size_ab.three_way_mixed_cxbina.model_7_c(0.05,0.1,0.50, 5,2,  "maximin")
size_ab.three_way_mixed_cxbina.model_7_c(0.05,0.1,0.50, 5,2,  "minimin")
size_a.three_way_mixed_cxbina.model_3_c(0.05, 0.1, 0.5, 5, 4, 1, "maximin")
size_a.three_way_mixed_cxbina.model_3_c(0.05, 0.1, 0.5, 5, 4, 1, "minimin")
size_a.three_way_mixed_cxbina.model_7_c(0.05, 0.1, 0.5, 5, 4, 1, "maximin")
size_a.three_way_mixed_cxbina.model_7_c(0.05, 0.1, 0.5, 5, 4, 1, "minimin")
size_ab.three_way_mixed_cxbina.model_7_c(0.05,0.1,0.50, 5,2,  "maximin")
size_ab.three_way_mixed_cxbina.model_7_c(0.05,0.1,0.50, 5,2,  "minimin")

Three-way analysis of variance – nested and mixed classification $A\succ B \succ C$ and $(A\times B)\succ C$ model III, IV and VII

Description

Returns the optimal number of levels for factor B.

Usage

size_b.three_way_mixed_ab_in_c.model_3_a(alpha, beta, delta, a, c, n, cases)
size_b.three_way_mixed_ab_in_c.model_3_a(alpha, beta, delta, a, c, n, cases)

Arguments

`alpha`	Risk of 1st kind
`beta`	Risk of 2nd kind
`delta`	The minimum difference to be detected
`a`	Number of levels of fixed factor A
`c`	Number of levels of fixed factor C
`n`	Number of replications
`cases`	Specifies whether the `"maximin"` or `"maximin"` sizes are to be determined

Details

see chapter 3 in the referenced book

Value

Integer giving the size.

Note

Better use size.anova which allows a cleaner notation.

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt, Minghui Wang

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

size_b.three_way_mixed_ab_in_c.model_3_a(0.05, 0.1, 0.5, 6, 5, 1, "maximin")
size_b.three_way_mixed_ab_in_c.model_3_a(0.05, 0.1, 0.5, 6, 5, 1, "minimin")
size_b.three_way_mixed_cxbina.model_4_a(0.05, 0.1, 0.5, 6, 4, 1, "maximin")
size_b.three_way_mixed_cxbina.model_4_a(0.05, 0.1, 0.5, 6, 4, 1, "minimin")
size_b.three_way_mixed_cxbina.model_4_c(0.05, 0.1, 0.5, 6, 4, 1, "maximin")
size_b.three_way_mixed_cxbina.model_4_c(0.05, 0.1, 0.5, 6, 4, 1, "minimin")
size_b.three_way_mixed_cxbina.model_4_axc(0.05, 0.1, 0.5, 6, 4, 1, "maximin")
size_b.three_way_mixed_cxbina.model_4_axc(0.05, 0.1, 0.5, 6, 4, 1, "minimin")
size_b.three_way_nested.model_6_a(0.05, 0.1, 0.5, 6, 4, 2, "maximin")
size_b.three_way_nested.model_6_a(0.05, 0.1, 0.5, 6, 4, 2, "minimin")
size_b.three_way_mixed_ab_in_c.model_3_a(0.05, 0.1, 0.5, 6, 5, 1, "maximin")
size_b.three_way_mixed_ab_in_c.model_3_a(0.05, 0.1, 0.5, 6, 5, 1, "minimin")
size_b.three_way_mixed_cxbina.model_4_a(0.05, 0.1, 0.5, 6, 4, 1, "maximin")
size_b.three_way_mixed_cxbina.model_4_a(0.05, 0.1, 0.5, 6, 4, 1, "minimin")
size_b.three_way_mixed_cxbina.model_4_c(0.05, 0.1, 0.5, 6, 4, 1, "maximin")
size_b.three_way_mixed_cxbina.model_4_c(0.05, 0.1, 0.5, 6, 4, 1, "minimin")
size_b.three_way_mixed_cxbina.model_4_axc(0.05, 0.1, 0.5, 6, 4, 1, "maximin")
size_b.three_way_mixed_cxbina.model_4_axc(0.05, 0.1, 0.5, 6, 4, 1, "minimin")
size_b.three_way_nested.model_6_a(0.05, 0.1, 0.5, 6, 4, 2, "maximin")
size_b.three_way_nested.model_6_a(0.05, 0.1, 0.5, 6, 4, 2, "minimin")

Design for Two-Way ANOVA

Description

Returns the optimal number of obervations per level of factor B.

Usage

size_b.two_way_cross.mixed_model_a_fixed_a(alpha, beta, delta, a, n, cases)
size_b.two_way_nested.b_random_a_fixed_a(alpha, beta, delta, a, cases)
size_b.two_way_cross.mixed_model_a_fixed_a(alpha, beta, delta, a, n, cases)
size_b.two_way_nested.b_random_a_fixed_a(alpha, beta, delta, a, cases)

Arguments

`alpha`	Risk of 1st kind
`beta`	Risk of 2nd kind
`delta`	The minimum difference to be detected
`a`	Number of levels of fixed factor A
`n`	Number of replications
`cases`	Specifies whether the `"maximin"` or `"maximin"` sizes are to be determined

Details

see chapter 3 in the referenced book

Value

Integer giving the size.

Note

Better use size.anova which allows a cleaner notation.

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt, Minghui Wang

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

size_b.two_way_cross.mixed_model_a_fixed_a(0.05,0.1, 1, 6, 1, "maximin")
size_b.two_way_cross.mixed_model_a_fixed_a(0.05,0.1, 1, 6, 1, "minimin")
size_b.two_way_cross.mixed_model_a_fixed_a(0.05,0.1, 1, 6, 2, "maximin")
size_b.two_way_cross.mixed_model_a_fixed_a(0.05,0.1, 1, 6, 2, "minimin")
size_b.two_way_nested.b_random_a_fixed_a(0.05, 0.1, 1, 6, "maximin")
size_b.two_way_nested.b_random_a_fixed_a(0.05, 0.1, 1, 6, "minimin")
size_b.two_way_cross.mixed_model_a_fixed_a(0.05,0.1, 1, 6, 1, "maximin")
size_b.two_way_cross.mixed_model_a_fixed_a(0.05,0.1, 1, 6, 1, "minimin")
size_b.two_way_cross.mixed_model_a_fixed_a(0.05,0.1, 1, 6, 2, "maximin")
size_b.two_way_cross.mixed_model_a_fixed_a(0.05,0.1, 1, 6, 2, "minimin")
size_b.two_way_nested.b_random_a_fixed_a(0.05, 0.1, 1, 6, "maximin")
size_b.two_way_nested.b_random_a_fixed_a(0.05, 0.1, 1, 6, "minimin")

Three-way analysis of variance – cross classification (A in B) x C – model IV, Three-way analysis of variance – mixed classification (A in B) x C model VI

Description

Returns the optimal number of levels for factor B and C.

Usage

size_bc.three_way_cross.model_4_a_case1(alpha, beta, delta, a, n, cases)
size_bc.three_way_cross.model_4_a_case2(alpha, beta, delta, a, n, cases)
size_bc.three_way_mixed_cxbina.model_6_a_case1(alpha, beta, delta, a, n, cases)
size_bc.three_way_mixed_cxbina.model_6_a_case2(alpha, beta, delta, a, n, cases)
size_bc.three_way_cross.model_4_a_case1(alpha, beta, delta, a, n, cases)
size_bc.three_way_cross.model_4_a_case2(alpha, beta, delta, a, n, cases)
size_bc.three_way_mixed_cxbina.model_6_a_case1(alpha, beta, delta, a, n, cases)
size_bc.three_way_mixed_cxbina.model_6_a_case2(alpha, beta, delta, a, n, cases)

Arguments

`alpha`	Risk of 1st kind
`beta`	Risk of 2nd kind
`delta`	The minimum difference to be detected
`a`	Number of levels of fixed factor A
`n`	Number of replications
`cases`	Specifies whether the `"maximin"` or `"maximin"` sizes are to be determined

Details

see chapter 3 in the referenced book

Value

Integers giving the sizes.

Note

Better use size.anova which allows a cleaner notation.

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt, Minghui Wang

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

size_bc.three_way_cross.model_4_a_case1(0.05, 0.1, 0.5, 6, 2, "maximin")
size_bc.three_way_cross.model_4_a_case1(0.05, 0.1, 0.5, 6, 2, "minimin")
size_bc.three_way_cross.model_4_a_case1(0.05, 0.1, 1, 6, 2, "maximin")
size_bc.three_way_cross.model_4_a_case1(0.05, 0.1, 1, 6, 2, "minimin")
size_bc.three_way_cross.model_4_a_case2(0.05, 0.1, 0.5, 6, 2, "maximin")
size_bc.three_way_cross.model_4_a_case2(0.05, 0.1, 0.5, 6, 2, "minimin")
size_bc.three_way_cross.model_4_a_case2(0.05, 0.1, 1, 6, 2, "maximin")
size_bc.three_way_cross.model_4_a_case2(0.05, 0.1, 1, 6, 2, "minimin")
size_bc.three_way_mixed_cxbina.model_6_a_case1(0.05, 0.1, 0.5, 6, 2, "maximin")
size_bc.three_way_mixed_cxbina.model_6_a_case1(0.05, 0.1, 0.5, 6, 2, "minimin")
size_bc.three_way_mixed_cxbina.model_6_a_case2(0.05, 0.1, 0.5, 6,  2, "maximin")
size_bc.three_way_mixed_cxbina.model_6_a_case2(0.05, 0.1, 0.5, 6,  2, "minimin")

size_bc.three_way_cross.model_4_a_case1(0.05, 0.1, 0.5, 6, 2, "maximin")
size_bc.three_way_cross.model_4_a_case1(0.05, 0.1, 0.5, 6, 2, "minimin")
size_bc.three_way_cross.model_4_a_case1(0.05, 0.1, 1, 6, 2, "maximin")
size_bc.three_way_cross.model_4_a_case1(0.05, 0.1, 1, 6, 2, "minimin")
size_bc.three_way_cross.model_4_a_case2(0.05, 0.1, 0.5, 6, 2, "maximin")
size_bc.three_way_cross.model_4_a_case2(0.05, 0.1, 0.5, 6, 2, "minimin")
size_bc.three_way_cross.model_4_a_case2(0.05, 0.1, 1, 6, 2, "maximin")
size_bc.three_way_cross.model_4_a_case2(0.05, 0.1, 1, 6, 2, "minimin")
size_bc.three_way_mixed_cxbina.model_6_a_case1(0.05, 0.1, 0.5, 6, 2, "maximin")
size_bc.three_way_mixed_cxbina.model_6_a_case1(0.05, 0.1, 0.5, 6, 2, "minimin")
size_bc.three_way_mixed_cxbina.model_6_a_case2(0.05, 0.1, 0.5, 6,  2, "maximin")
size_bc.three_way_mixed_cxbina.model_6_a_case2(0.05, 0.1, 0.5, 6,  2, "minimin")

Three-way analysis of variance – several cross-, nested and mixed classifications.

Description

Returns the optimal number of levels for .

Usage

size_c.three_way_cross.model_3_a          (alpha, beta, delta, a, b, n, cases)
size_c.three_way_cross.model_3_axb        (alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_ab_in_c.model_5_a  (alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_ab_in_c.model_5_axb(alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_ab_in_c.model_5_b  (alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_ab_in_c.model_6_b  (alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_cxbina.model_5_a   (alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_cxbina.model_5_b   (alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_cxbina.model_7_b   (alpha, beta, delta, a, b, n, cases)
size_c.three_way_nested.model_5_a         (alpha, beta, delta, a, b, n, cases)
size_c.three_way_nested.model_5_b         (alpha, beta, delta, a, b, n, cases)
size_c.three_way_nested.model_7_b         (alpha, beta, delta, a, b, n, cases)
size_c.three_way_cross.model_3_a          (alpha, beta, delta, a, b, n, cases)
size_c.three_way_cross.model_3_axb        (alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_ab_in_c.model_5_a  (alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_ab_in_c.model_5_axb(alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_ab_in_c.model_5_b  (alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_ab_in_c.model_6_b  (alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_cxbina.model_5_a   (alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_cxbina.model_5_b   (alpha, beta, delta, a, b, n, cases)
size_c.three_way_mixed_cxbina.model_7_b   (alpha, beta, delta, a, b, n, cases)
size_c.three_way_nested.model_5_a         (alpha, beta, delta, a, b, n, cases)
size_c.three_way_nested.model_5_b         (alpha, beta, delta, a, b, n, cases)
size_c.three_way_nested.model_7_b         (alpha, beta, delta, a, b, n, cases)

Arguments

`alpha`	Risk of 1st kind
`beta`	Risk of 2nd kind
`delta`	The minimum difference to be detected
`a`	Number of levels of fixed factor A
`b`	Number of levels of fixed factor B
`n`	Number of replications
`cases`	Specifies whether the `"maximin"` or `"maximin"` sizes are to be determined

Details

see chapter 3 in the referenced book

Value

integer, desired size of factor C

Note

Better use size.anova which allows a cleaner notation.

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt, Minghui Wang

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

size_c.three_way_cross.model_3_a(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_cross.model_3_a(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_cross.model_3_axb(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_cross.model_3_axb(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_mixed_ab_in_c.model_5_a(0.05, 0.1, 0.5, 6, 5, 1, "maximin")
size_c.three_way_mixed_ab_in_c.model_5_a(0.05, 0.1, 0.5, 6, 5, 1, "minimin")

size_c.three_way_mixed_ab_in_c.model_5_axb(0.05, 0.1, 0.5, 6, 5, 1, "maximin")
size_c.three_way_mixed_ab_in_c.model_5_axb(0.05, 0.1, 0.5, 6, 5, 1, "minimin")

size_c.three_way_mixed_ab_in_c.model_5_b(0.05, 0.1, 0.5, 6, 5, 1, "maximin")
size_c.three_way_mixed_ab_in_c.model_5_b(0.05, 0.1, 0.5, 6, 5, 1, "minimin")

size_c.three_way_mixed_ab_in_c.model_6_b(0.05, 0.1, 0.5, 6, 5, 1, "maximin")
size_c.three_way_mixed_ab_in_c.model_6_b(0.05, 0.1, 0.5, 6, 5, 1, "minimin")

size_c.three_way_mixed_cxbina.model_5_a(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_mixed_cxbina.model_5_a(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_mixed_cxbina.model_5_b(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_mixed_cxbina.model_5_b(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_mixed_cxbina.model_7_b(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_mixed_cxbina.model_7_b(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_nested.model_5_a(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_nested.model_5_a(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_nested.model_5_b(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_nested.model_5_b(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_nested.model_7_b(0.05, 0.1, 0.5, 6, 4, 1, "maximin")
size_c.three_way_nested.model_7_b(0.05, 0.1, 0.5, 6, 4, 1, "minimin")

size_c.three_way_cross.model_3_a(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_cross.model_3_a(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_cross.model_3_axb(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_cross.model_3_axb(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_mixed_ab_in_c.model_5_a(0.05, 0.1, 0.5, 6, 5, 1, "maximin")
size_c.three_way_mixed_ab_in_c.model_5_a(0.05, 0.1, 0.5, 6, 5, 1, "minimin")

size_c.three_way_mixed_ab_in_c.model_5_axb(0.05, 0.1, 0.5, 6, 5, 1, "maximin")
size_c.three_way_mixed_ab_in_c.model_5_axb(0.05, 0.1, 0.5, 6, 5, 1, "minimin")

size_c.three_way_mixed_ab_in_c.model_5_b(0.05, 0.1, 0.5, 6, 5, 1, "maximin")
size_c.three_way_mixed_ab_in_c.model_5_b(0.05, 0.1, 0.5, 6, 5, 1, "minimin")

size_c.three_way_mixed_ab_in_c.model_6_b(0.05, 0.1, 0.5, 6, 5, 1, "maximin")
size_c.three_way_mixed_ab_in_c.model_6_b(0.05, 0.1, 0.5, 6, 5, 1, "minimin")

size_c.three_way_mixed_cxbina.model_5_a(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_mixed_cxbina.model_5_a(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_mixed_cxbina.model_5_b(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_mixed_cxbina.model_5_b(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_mixed_cxbina.model_7_b(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_mixed_cxbina.model_7_b(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_nested.model_5_a(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_nested.model_5_a(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_nested.model_5_b(0.05, 0.1, 0.5, 6, 5, 2, "maximin")
size_c.three_way_nested.model_5_b(0.05, 0.1, 0.5, 6, 5, 2, "minimin")

size_c.three_way_nested.model_7_b(0.05, 0.1, 0.5, 6, 4, 1, "maximin")
size_c.three_way_nested.model_7_b(0.05, 0.1, 0.5, 6, 4, 1, "minimin")

Design for One-Way ANOVA

Description

Returns the optimal number of obervations per level of factor A.

Usage

size_n.one_way.model_1(alpha, beta, delta, a, cases)
size_n.one_way.model_1(alpha, beta, delta, a, cases)

Arguments

`alpha`	Risk of 1st kind
`beta`	Risk of 2nd kind
`delta`	The minimum difference to be detected
`a`	Number of levels of fixed factor A
`cases`	Specifies whether the `"maximin"` or `"maximin"` sizes are to be determined

Details

see chapter 3 in the referenced book

Value

Integer giving the size.

Note

Better use size.anova which allows a cleaner notation.

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt, Minghui Wang

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

size_n.one_way.model_1(0.05,0.1, 2, 4, "maximin")
size_n.one_way.model_1(0.05,0.1, 2, 4, "minimin")
size_n.one_way.model_1(0.05,0.1, 2, 4, "maximin")
size_n.one_way.model_1(0.05,0.1, 2, 4, "minimin")

Design for Three-Way ANOVA

Description

Returns the optimal number of obervations per level of each factor.

Usage

size_n.three_way_cross.model_1_a          (alpha, beta, delta, a, b, c, cases)
size_n.three_way_cross.model_1_axb        (alpha, beta, delta, a, b, c, cases)
size_n.three_way_cross.model_1_axbxc      (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_ab_in_c.model_1_a  (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_ab_in_c.model_1_b  (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_ab_in_c.model_1_c  (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_ab_in_c.model_3_c  (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_ab_in_c.model_4_c  (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_1_a   (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_1_axc (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_1_b   (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_1_bxc (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_1_c   (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_3_b   (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_3_bxc (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_1_a         (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_1_b         (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_1_c         (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_3_b         (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_3_c         (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_4_a         (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_8_c         (alpha, beta, delta, a, b, c, cases)
size_n.three_way_cross.model_1_a          (alpha, beta, delta, a, b, c, cases)
size_n.three_way_cross.model_1_axb        (alpha, beta, delta, a, b, c, cases)
size_n.three_way_cross.model_1_axbxc      (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_ab_in_c.model_1_a  (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_ab_in_c.model_1_b  (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_ab_in_c.model_1_c  (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_ab_in_c.model_3_c  (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_ab_in_c.model_4_c  (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_1_a   (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_1_axc (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_1_b   (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_1_bxc (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_1_c   (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_3_b   (alpha, beta, delta, a, b, c, cases)
size_n.three_way_mixed_cxbina.model_3_bxc (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_1_a         (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_1_b         (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_1_c         (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_3_b         (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_3_c         (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_4_a         (alpha, beta, delta, a, b, c, cases)
size_n.three_way_nested.model_8_c         (alpha, beta, delta, a, b, c, cases)

Arguments

`alpha`	Risk of 1st kind
`beta`	Risk of 2nd kind
`delta`	The minimum difference to be detected
`a`	Number of levels of fixed factor A
`b`	Number of levels of fixed factor B
`c`	Number of levels of fixed factor C
`cases`	Specifies whether the `"maximin"` or `"maximin"` sizes are to be determined

Details

see chapter 3 in the referenced book

Value

Integer giving the size.

Note

Better use size.anova which allows a cleaner notation.

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt, Minghui Wang

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

size_n.three_way_cross.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_cross.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_cross.model_1_axb(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_cross.model_1_axb(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_cross.model_1_axbxc(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_cross.model_1_axbxc(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_ab_in_c.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_ab_in_c.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_ab_in_c.model_1_axb(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_ab_in_c.model_1_axb(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_ab_in_c.model_1_b(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_ab_in_c.model_1_b(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_ab_in_c.model_1_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_ab_in_c.model_1_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_ab_in_c.model_3_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_ab_in_c.model_3_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_ab_in_c.model_4_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_ab_in_c.model_4_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_1_axc(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_1_axc(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_1_b(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_1_b(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_1_bxc(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_1_bxc(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_1_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_1_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_3_b(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_3_b(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_3_bxc (0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_3_bxc (0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_nested.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_nested.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_nested.model_1_b(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_nested.model_1_b(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_nested.model_1_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_nested.model_1_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_nested.model_3_b(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_nested.model_3_b(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_nested.model_3_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_nested.model_3_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_nested.model_4_c(0.05, 0.1, 0.5, 6, NA, 4, "maximin")
size_n.three_way_nested.model_4_c(0.05, 0.1, 0.5, 6, NA, 4, "minimin")
size_n.three_way_nested.model_8_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_nested.model_8_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")

size_n.three_way_cross.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_cross.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_cross.model_1_axb(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_cross.model_1_axb(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_cross.model_1_axbxc(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_cross.model_1_axbxc(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_ab_in_c.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_ab_in_c.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_ab_in_c.model_1_axb(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_ab_in_c.model_1_axb(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_ab_in_c.model_1_b(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_ab_in_c.model_1_b(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_ab_in_c.model_1_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_ab_in_c.model_1_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_ab_in_c.model_3_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_ab_in_c.model_3_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_ab_in_c.model_4_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_ab_in_c.model_4_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_1_axc(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_1_axc(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_1_b(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_1_b(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_1_bxc(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_1_bxc(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_1_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_1_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_3_b(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_3_b(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_mixed_cxbina.model_3_bxc (0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_mixed_cxbina.model_3_bxc (0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_nested.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_nested.model_1_a(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_nested.model_1_b(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_nested.model_1_b(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_nested.model_1_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_nested.model_1_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_nested.model_3_b(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_nested.model_3_b(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_nested.model_3_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_nested.model_3_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")
size_n.three_way_nested.model_4_c(0.05, 0.1, 0.5, 6, NA, 4, "maximin")
size_n.three_way_nested.model_4_c(0.05, 0.1, 0.5, 6, NA, 4, "minimin")
size_n.three_way_nested.model_8_c(0.05, 0.1, 0.5, 6, 5, 4, "maximin")
size_n.three_way_nested.model_8_c(0.05, 0.1, 0.5, 6, 5, 4, "minimin")

Design for Two-Way ANOVA

Description

Returns the optimal number of obervations per level of factor A.

Usage

size_n.two_way_cross.model_1_a(alpha, beta, delta, a, b, cases)
size_n.two_way_cross.model_1_axb(alpha, beta, delta, a, b, cases)
size_n.two_way_nested.model_1_test_factor_a(alpha, beta, delta, a, b, cases)
size_n.two_way_nested.model_1_test_factor_b(alpha, beta, delta, a, b, cases)
size_n.two_way_nested.a_random_b_fixed_b(alpha, beta, delta, a, b, cases)
size_n.two_way_cross.model_1_a(alpha, beta, delta, a, b, cases)
size_n.two_way_cross.model_1_axb(alpha, beta, delta, a, b, cases)
size_n.two_way_nested.model_1_test_factor_a(alpha, beta, delta, a, b, cases)
size_n.two_way_nested.model_1_test_factor_b(alpha, beta, delta, a, b, cases)
size_n.two_way_nested.a_random_b_fixed_b(alpha, beta, delta, a, b, cases)

Arguments

`alpha`	Risk of 1st kind
`beta`	Risk of 2nd kind
`delta`	The minimum difference to be detected
`a`	Number of levels of fixed factor A
`b`	Number of levels of fixed factor B
`cases`	Specifies whether the `"maximin"` or `"maximin"` sizes are to be determined

Details

see chapter 3 in the referenced book

Value

Integer giving the size.

Note

Better use size.anova which allows a cleaner notation.

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt, Minghui Wang

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

size_n.two_way_cross.model_1_a(0.05,0.1, 1, 6, 4, "maximin")
size_n.two_way_cross.model_1_a(0.05,0.1, 1, 6, 4, "minimin")
size_n.two_way_cross.model_1_axb(0.05,0.1, 1, 6, 4, "maximin")
size_n.two_way_cross.model_1_axb(0.05,0.1, 1, 6, 4, "minimin")
size_n.two_way_nested.model_1_test_factor_a(0.05, 0.1, 1, 6, 4, "maximin")
size_n.two_way_nested.model_1_test_factor_a(0.05, 0.1, 1, 6, 4, "minimin")
size_n.two_way_nested.a_random_b_fixed_b(0.05, 0.1, 1, 2, 10, "maximin")
size_n.two_way_nested.a_random_b_fixed_b(0.05, 0.1, 1, 2, 10, "minimin")
size_n.two_way_nested.a_random_b_fixed_b(0.05, 0.1, 1, 3, 10, "maximin")
size_n.two_way_nested.a_random_b_fixed_b(0.05, 0.1, 1, 3, 10, "minimin")
size_n.two_way_nested.a_random_b_fixed_b(0.05, 0.1, 1, 10, 10, "maximin")
size_n.two_way_nested.a_random_b_fixed_b(0.05, 0.1, 1, 10, 10, "minimin")
size_n.two_way_cross.model_1_a(0.05,0.1, 1, 6, 4, "maximin")
size_n.two_way_cross.model_1_a(0.05,0.1, 1, 6, 4, "minimin")
size_n.two_way_cross.model_1_axb(0.05,0.1, 1, 6, 4, "maximin")
size_n.two_way_cross.model_1_axb(0.05,0.1, 1, 6, 4, "minimin")
size_n.two_way_nested.model_1_test_factor_a(0.05, 0.1, 1, 6, 4, "maximin")
size_n.two_way_nested.model_1_test_factor_a(0.05, 0.1, 1, 6, 4, "minimin")
size_n.two_way_nested.a_random_b_fixed_b(0.05, 0.1, 1, 2, 10, "maximin")
size_n.two_way_nested.a_random_b_fixed_b(0.05, 0.1, 1, 2, 10, "minimin")
size_n.two_way_nested.a_random_b_fixed_b(0.05, 0.1, 1, 3, 10, "maximin")
size_n.two_way_nested.a_random_b_fixed_b(0.05, 0.1, 1, 3, 10, "minimin")
size_n.two_way_nested.a_random_b_fixed_b(0.05, 0.1, 1, 10, 10, "maximin")
size_n.two_way_nested.a_random_b_fixed_b(0.05, 0.1, 1, 10, 10, "minimin")

Design of Experiments for ANOVA

Description

This function provides access to several functions returning the optimal number of levels and / or observations in different types of One-Way, Two-Way and Three-Way ANOVA.

Usage

size.anova(model, hypothesis = "", assumption = "",
    a = NULL, b = NULL, c = NULL, n = NULL, alpha, beta, delta, cases)
size.anova(model, hypothesis = "", assumption = "",
    a = NULL, b = NULL, c = NULL, n = NULL, alpha, beta, delta, cases)

Arguments

`model`	A character string describing the model, allowed characters are `(>x)` and the letters `abcABC`, capital letters stand for random factors, lower case letters for fixed factors, `x` means cross classification, `>` nested classification, brackets `()` are used to specify mixed model, the term in brackets has to come first. Spaces are allowed. Examples: One-Way fixed: `a`, Two-Way: `axB`, `a>b`, Three-Way: `axbxc`, `axBxC`, `a>b>c`, `(axb)>C`, ...
`hypothesis`	Character string describiung Null hypothesis, can be omitted in most cases if it is clear that a test for no effects of factor A is performed, `"a"`. Other possibilities: `"axb"`, `"a>b"`, `"c"` and some more.
`assumption`	Character string. A few functions need an assumption on sigma, like `"sigma_AB=0,b=c"`, see the referenced book until this page is updated.
`a`	Number of levels of fixed factor A
`b`	Number of levels of fixed factor B
`c`	Number of levels of fixed factor C
`n`	Number of Observations
`alpha`	Risk of 1st kind
`beta`	Risk of 2nd kind
`delta`	The minimum difference to be detected
`cases`	Specifies whether the `"maximin"` or `"maximin"` sizes are to be determined.

Details

see chapter 3 in the referenced book

Value

named integer giving the desired size(s)

Note

Depending on the selected model and hypothesis omit one or two of the sizes a, b, c, n. The function then tries to get its optimal value.

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt, Minghui Wang

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

size.anova(model="a",a=4,
      alpha=0.05,beta=0.1, delta=2, case="maximin")
size.anova(model="a",a=4,
      alpha=0.05,beta=0.1, delta=2, case="minimin")

size.anova(model="axb", hypothesis="a", a=6, b=4, 
           alpha=0.05,beta=0.1, delta=1, cases="maximin")
size.anova(model="axb", hypothesis="a", a=6, b=4, 
           alpha=0.05,beta=0.1, delta=1, cases="maximin")

size.anova(model="axb", hypothesis="axb", a=6, b=4, 
           alpha=0.05,beta=0.1, delta=1, cases="minimin")
size.anova(model="axb", hypothesis="axb", a=6, b=4, 
           alpha=0.05,beta=0.1, delta=1, cases="minimin")

size.anova(model="axBxC",hypothesis="a",
           assumption="sigma_AC=0,b=c",a=6,n=2,
           alpha=0.05, beta=0.1, delta=0.5, cases="maximin")
size.anova(model="axBxC",hypothesis="a",
           assumption="sigma_AC=0,b=c",a=6,n=2,
           alpha=0.05, beta=0.1, delta=0.5, cases="minimin")

size.anova(model="a>B>c", hypothesis="c",a=6, b=2, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="maximin")
size.anova(model="a>B>c", hypothesis="c",a=6, b=20, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="maximin")

size.anova(model="a>B>c", hypothesis="c",a=6, b=NA, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="maximin")

size.anova(model="(axb)>c", hypothesis="a",a=6, b=5, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="maximin")
size.anova(model="(axb)>c", hypothesis="a",a=6, b=5, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="minimin")

size.anova(model="(axb)>c", hypothesis="a",a=6, b=5, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="maximin")
size.anova(model="(axb)>c", hypothesis="a",a=6, b=5, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="minimin")
size.anova(model="a",a=4,
      alpha=0.05,beta=0.1, delta=2, case="maximin")
size.anova(model="a",a=4,
      alpha=0.05,beta=0.1, delta=2, case="minimin")

size.anova(model="axb", hypothesis="a", a=6, b=4, 
           alpha=0.05,beta=0.1, delta=1, cases="maximin")
size.anova(model="axb", hypothesis="a", a=6, b=4, 
           alpha=0.05,beta=0.1, delta=1, cases="maximin")

size.anova(model="axb", hypothesis="axb", a=6, b=4, 
           alpha=0.05,beta=0.1, delta=1, cases="minimin")
size.anova(model="axb", hypothesis="axb", a=6, b=4, 
           alpha=0.05,beta=0.1, delta=1, cases="minimin")

size.anova(model="axBxC",hypothesis="a",
           assumption="sigma_AC=0,b=c",a=6,n=2,
           alpha=0.05, beta=0.1, delta=0.5, cases="maximin")
size.anova(model="axBxC",hypothesis="a",
           assumption="sigma_AC=0,b=c",a=6,n=2,
           alpha=0.05, beta=0.1, delta=0.5, cases="minimin")

size.anova(model="a>B>c", hypothesis="c",a=6, b=2, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="maximin")
size.anova(model="a>B>c", hypothesis="c",a=6, b=20, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="maximin")

size.anova(model="a>B>c", hypothesis="c",a=6, b=NA, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="maximin")

size.anova(model="(axb)>c", hypothesis="a",a=6, b=5, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="maximin")
size.anova(model="(axb)>c", hypothesis="a",a=6, b=5, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="minimin")

size.anova(model="(axb)>c", hypothesis="a",a=6, b=5, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="maximin")
size.anova(model="(axb)>c", hypothesis="a",a=6, b=5, c=4, 
           alpha=0.05, beta=0.1, delta=0.5, case="minimin")

Triangular Test Object

Description

An triangular.test object is created with triangular.test.norm or triangular.test.prop

Arguments

A triangular.test object is a list of

`x`	data for group 1
`y`	data for group 2
`n`	size of group 1
`m`	size of group 2
`alpha`	risk of 1st kind
`beta`	risk of 2nd kind
`dist`	character, either `"normal"` or `"bernoulli"`, describing the type of triangiular test
`sample`	character, `"one"` or `"two"`
`kind`	character, `"one-sided"` or `"two-sided"`
`p0`	parameter describing the Null hypothesis, see `triangular.test.prop`
`p1`	...
`p2`	...
`mu0`	parameter describing the Null hypothesis, see `triangular.test.norm`
`mu1`	...
`mu2`	...
`result`	character, outcome of the test, `"H0"` or `"H1"`
`step`	total number of steps

and some more components for internal use.

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Triangular Test for Normal Data

Description

Performs a sequential test, compares means of two normally distributed groups.

Usage

triangular.test.norm(x, y = NULL, mu0 = NULL, mu1, mu2 = NULL,
                     delta = NULL, sigma = NULL, sigma2 = NULL,
                     alpha = 0.05, beta = 0.1, plot = TRUE)
triangular.test.norm(x, y = NULL, mu0 = NULL, mu1, mu2 = NULL,
                     delta = NULL, sigma = NULL, sigma2 = NULL,
                     alpha = 0.05, beta = 0.1, plot = TRUE)

Arguments

`x`	initial data for group `x`, at least 1 entry.
`y`	initial data for group `y`, at least 1 entry for a two sample test, otherwise omitted.
`mu0`	specifies Null and alternative hypothesis, see Details below.
`mu1`	specifies Null and alternative hypothesis, see Details below.
`mu2`	specifies Null and alternative hypothesis, see Details below.
`delta`	The minimum difference to be detected, alternative way to specify `mu2=m1+delta`, see above, use either this or `mu2`.
`sigma`	prior sigma.
`sigma2`	prior sigma for group 2 if different than for grouop 1.
`alpha`	Risk of 1st kind
`beta`	Risk of 2nd kind
`plot`	logical, indicates whether a initial plot should be generated.

Details

One-sample:

This function performs a one- or two-sided sequential Test for $\mu=\code{mu1}$ versus

$\mu>\code{mu2}$ , if mu2 > mu1 (one-sided)

$\mu<\code{mu2}$ , if mu2 < mu1 (one-sided)

$\mu<\code{mu0}$ or $\mu>\code{mu2}$ , if mu2 > mu1 and mu0 < mu1 (two-sided, possibly unsymmetric)

Two-sample:

This function performs a one- or two-sided sequential Test for equal means $\mu_1=\code{mu1}$ $\mu_2=\code{mu1}$ in both groups versus

$\mu_2>\code{mu2}$ , if mu2 > mu1 (one-sided)

$\mu_2<\code{mu2}$ , if mu2 < mu1 (one-sided)

$\mu_2<\code{mu0}$ or $\mu_2>\code{mu2}$ , if mu2 > mu1 and mu0 < mu1 (two-sided, possibly unsymmetric)

Value

An object of class triangular.test, to be used for later update steps.

Note

A two-sided test may be specified by supplying both mu1 and mu2, even unsymmetric if needed.

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

data(heights)
attach(heights)
# a symmetric two sided alternative:
tt <- triangular.test.norm(x=female[1:3],
   y=male[1:3], mu1=170,mu2=176,mu0=164,
   alpha=0.05, beta=0.2,sigma=7)
# Test is yet unfinished, add the remaining values step by step:
tt <- update(tt,x=female[4])
tt <- update(tt,y=male[4])
tt <- update(tt,x=female[5])
tt <- update(tt,y=male[5])
tt <- update(tt,x=female[6])
tt <- update(tt,y=male[6])
tt <- update(tt,x=female[7])
tt <- update(tt,y=male[7])
# Test is finished now
# an unsymmetric two sided alternative:
tt2 <- triangular.test.norm(x=female[1:3],
   y=male[1:3], mu1=170,mu2=180,mu0=162,
   alpha=0.05, beta=0.2,sigma=7)
tt2 <- update(tt2,x=female[4])
data(heights)
attach(heights)
# a symmetric two sided alternative:
tt <- triangular.test.norm(x=female[1:3],
   y=male[1:3], mu1=170,mu2=176,mu0=164,
   alpha=0.05, beta=0.2,sigma=7)
# Test is yet unfinished, add the remaining values step by step:
tt <- update(tt,x=female[4])
tt <- update(tt,y=male[4])
tt <- update(tt,x=female[5])
tt <- update(tt,y=male[5])
tt <- update(tt,x=female[6])
tt <- update(tt,y=male[6])
tt <- update(tt,x=female[7])
tt <- update(tt,y=male[7])
# Test is finished now
# an unsymmetric two sided alternative:
tt2 <- triangular.test.norm(x=female[1:3],
   y=male[1:3], mu1=170,mu2=180,mu0=162,
   alpha=0.05, beta=0.2,sigma=7)
tt2 <- update(tt2,x=female[4])

Triangular Test for Bernoulli Data

Description

Performs a sequential test, compares probabilities in two groups.

Usage

triangular.test.prop(x, y = NULL, p0 = NULL, p1 = NULL, p2 = NULL, alpha
= 0.05, beta = 0.1, delta = NULL, plot = TRUE)
triangular.test.prop(x, y = NULL, p0 = NULL, p1 = NULL, p2 = NULL, alpha
= 0.05, beta = 0.1, delta = NULL, plot = TRUE)

Arguments

`x`	initial data for group `x`, at least 1 entry, values restricted to 0 and 1.
`y`	initial data for group `y`, at least 1 entry for a two sample test, otherwise omitted, values restricted to 0 and 1.
`p0`	specifies Null and alternative hypothesis, see Details below.
`p1`	specifies Null and alternative hypothesis, see Details below.
`p2`	specifies Null and alternative hypothesis, see Details below.
`alpha`	Risk of 1st kind
`beta`	Risk of 2nd kind
`plot`	logical, indicates whether a initial plot should be generated.
`delta`	The minimum difference to be detected, alternative way to specify `p2=p1+delta`, see above, use either this or `p2`.

Details

One-sample:

This function performs a one- or two-sided sequential Test for $p=\code{p1}$ versus

$p>\code{p2}$ , if p2 > p1 (one-sided)

$p<\code{p2}$ , if p2 < p1 (one-sided)

$p<\code{p0}$ or $p>\code{p2}$ , if p2 > p1 and p0 < p1 (two-sided, possibly unsymmetric)

Two-sample:

This function performs a one- or two-sided sequential Test for equal proportions $p_1=\code{p1}$ $p_2=\code{p1}$ versus

$p_2>\code{p2}$ , if p2 > p1 (one-sided)

$p_2<\code{p2}$ , if p2 < p1 (one-sided)

$p_2<\code{p0}$ or $p_2>\code{p2}$ , if p2 > p1 and p0 < p1 (two-sided, possibly unsymmetric)

Value

An object of class triangular.test, to be used for later update steps.

Note

A two-sided test may be specified by supplying both p1 and p2, even unsymmetric if needed.

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Examples

data(heights)
attach(heights)
male180 <- as.integer(male>180) 
female164 <- as.integer(female>164)
sum(male180)/length(male180) 
tt <- triangular.test.prop(x=female164[1:3],
   y=male180[1:3], p1=0.4,p2=0.8,p0=0.1,
   alpha=0.05, beta=0.2)
tt <- update(tt,x=female164[4])
tt <- update(tt,y=male180[4])
tt <- update(tt,x=female164[5])
sum(female164)/length(female164)
data(heights)
attach(heights)
male180 <- as.integer(male>180) 
female164 <- as.integer(female>164)
sum(male180)/length(male180) 
tt <- triangular.test.prop(x=female164[1:3],
   y=male180[1:3], p1=0.4,p2=0.8,p0=0.1,
   alpha=0.05, beta=0.2)
tt <- update(tt,x=female164[4])
tt <- update(tt,y=male180[4])
tt <- update(tt,x=female164[5])
sum(female164)/length(female164)

Print method for Triangular Test Objects

Description

Updates a triangular.test object and executes one or more steps in the sequence of tests.

Usage

## S3 method for class 'triangular.test'
update(object, x=NULL, y=NULL, initial=FALSE,
plot="last", recursive=FALSE, ...)
## S3 method for class 'triangular.test'
update(object, x=NULL, y=NULL, initial=FALSE,
plot="last", recursive=FALSE, ...)

Arguments

`object`	`triangular.test` object
`x`	data for group 1
`y`	data for group 2
`initial`	logical, used internally for creating a `triangular.test` object
`plot`	character, `"all"`: plot all intermediate steps, `"last"`: plot only the last state
`recursive`	logical, used internally to decide wether a plot should be generated (will be omitted if recursively called)
`...`	additional parameters for `update`

Author(s)

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt

References

Dieter Rasch, Juergen Pilz, L.R. Verdooren, Albrecht Gebhardt: Optimal Experimental Design with R, Chapman and Hall/CRC, 2011

Package 'OPDOE'

Help Index

Cattle data

Description

Usage

Format

Author(s)

References

Examples

Design for Polynomial Regression

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

Examples

Regression Design Object

Description

Arguments

Author(s)

References

See Also

Stored Hadmard matrices

Description

Details

male / female heights data

Description

Usage

Format

Author(s)

References

Examples

Hemp data

Description

Usage

Format

References

(still) undocumented functions

Description

Details

References

Prints a regression design object

Description

Usage

Arguments

Author(s)

References

See Also

Print method for Triangular Test Objects

Description

Usage

Arguments

Author(s)

References

See Also

Three-way analysis of variance – mixed classification (A×B)≻C(A\times B)\succ C(A×B)≻C model III and VII

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Examples

Three-way analysis of variance – nested and mixed classification A≻B≻CA\succ B \succ CA≻B≻C and (A×B)≻C(A\times B)\succ C(A×B)≻C model III, IV and VII

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Examples

Three-way analysis of variance – mixed classification $(A\times B)\succ C$ model III and VII

Three-way analysis of variance – nested and mixed classification $A\succ B \succ C$ and $(A\times B)\succ C$ model III, IV and VII