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anova.power {AMC}                                                                  R Documentation
 
                               Monte Carlo ANOVA power analysis 
                               
Description:

This function calculates the power (1-p(error type II)) of an ANOVA made by Monte Carlo methods.

Usage:

anova.power(dados,N,n,p.c=.05)

Arguments:

dados  data.frame with the data.
N      number of times the Monte Carlo test is performed.
n      number of times randomization is performed in each Monte Carlo test.
p.c    critical value of α (error type I probability).

Details:

Data input must be an object of class data.frame in which the first column must be a random factor (block), the 
second and third columns must be the two factors of interest and the fourth column must be the 
response variable.
The columns names must be "bloco","A","B" and "resp".
The factors being tested must be dummy variables in the form of 0 (presence) or 1 (absence) and the 
blocks, which is not going to be tested, must be represented by an integer, ranging from 1 untill "nb" 
(the total number of blocks).

Value:

The function returns the probability, in percentage, of detecting a treatment effect when it is assumed 
that it exists for each of the two factors and also for the interaction between then.
The factors are called "A" and "B", for the factors on the second and third columns of input data.frame, 
respectively; the interaction between these two factors is called "A.B".

Warning:

The power analysis is made upon simulated data assuming that the differences among treatments and the 
controls are not random.
Ellapsed time untill result is given may take too long depending on "N" and on "n" combined.

Note:

This analysis is not recommended to be done a posteriori.
It should be done before doing the experiment so one can choice a better number of replicates, blocks etc.

Author(s):

Original version by Marcel Vaz 
marcel.vaz@usp.br

References:

Gotelli, N. J. and Ellison, A. M. (2004) A primer of ecological statistics. Sinauer Associates.
Manly, B. F. J. (2007) Randomization, bootstrap and Monte Carlo methods in Biology. (3rd ed.)
Chapman & Hall/CRC.

See also:

data.gen to create random data conformed with the randomized block design involving two factors.
anova.MC to do a Monte Carlo test the effects of two factor from randomized block designs.
anova.graphs for nice graphics of two-factor factorial experiments.

Examples:

dados=data.gen(10,50,8,3,12,15,5)
anova.power(dados,10,99)

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