Version: 1.0-10
Title: Optimal Design of Experiments
Author: Petr Simecek <simecek@gmail.com>, Juergen Pilz <juergen.pilz@aau.at>, Mingui Wang <mail.mwang@gmail.com>, Albrecht Gebhardt <albrecht.gebhardt@aau.at>.
Maintainer: Albrecht Gebhardt <albrecht.gebhardt@aau.at>
Description: Several function related to Experimental Design are implemented here, see "Optimal Experimental Design with R" by Rasch D. et. al (ISBN 9781439816974).
Imports: mvtnorm, orthopolynom, nlme, crossdes, polynom
Depends: gmp
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Packaged: 2018-03-16 20:06:41 UTC; alge
NeedsCompilation: no
Repository: CRAN
Date/Publication: 2018-03-17 22:49:18 UTC

(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

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)

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)

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(...)

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

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

See Also

design.regression.polynom

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)

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

Hemp data

Description

age and height of hemp plants.

Usage

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

Prints a regression design object

Description

Print method for a design.regression object.

Usage

## 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

See Also

design.regression

Print method for Triangular Test Objects

Description

Prints a triangular.test object.

Usage

## 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

See Also

triangular.test.norm, triangular.test.prop

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)

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")

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)

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

See Also

size.anova

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")

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)

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

See Also

size.anova

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")

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)

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

See Also

size.anova

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")

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)

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

See Also

size.anova

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")

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)

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

See Also

size.anova

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")

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)

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

See Also

size.anova

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")

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)

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

See Also

size.anova

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")

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)

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

See Also

size.anova

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")

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

See Also

triangular.test.norm, triangular.test.prop

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)

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

See Also

triangular.test, triangular.test.prop, update.triangular.test

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])

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)

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

See Also

triangular.test, triangular.test.norm, update.triangular.test

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)

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, ...)

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

See Also

triangular.test.norm, triangular.test.prop

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