size.anova: Design of Experiments for ANOVA

In OPDOE: Optimal Design of Experiments

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")

Example output

Loading required package: gmp

Attaching package: 'gmp'

The following objects are masked from 'package:base':

    %*%, apply, crossprod, matrix, tcrossprod

n 
9 
n 
5 
n 
9 
n 
9 
n 
5 
n 
5 
b c 
9 9 
b c 
6 6 
  n 
262 
  n 
693 

minimum value of b*n is  524 

  n   b 
262   2 
n 
7 
n 
3 
n 
7 
n 
3 

OPDOE documentation built on May 1, 2019, 8:45 p.m.