BDEsize (version 1.6)

Size.2levFr: Sample Size Calculator for Two-level Fractional Factorial Design

Description

This function computes sample size for two-level fractional factorial design to detect a certain standardized effect size with power at the significance level. The model for fractional factorial design contains only main effects in resolution III and IV.

Usage

Size.2levFr(nfactor, nfraction, interaction = FALSE, delta_type = 1, 
    delta = c(1, 0, 1), alpha = 0.05, beta = 0.2, maxsize = 1000)

Arguments

nfactor

the number of factor.

nfraction

the number of fraction. For example, when a model is \(2^(k-p)\), k is the number of factor and p is the number of fraction. It is called a \(1/2^p\) fraction of the \(2^k\) design.

interaction

specifies whether two-way interaction effects are included in a model with the main effects. When interaction = TRUE, two-way interaction effects are include in a model.

delta_type

specifies the type of standardized effect size: 1 for standard deviation type and 2 for range type.

delta

vector of effect sizes: delta[1] for main effects, delta[2] for two-way interaction effects, and delta[3] for standard deviation of noise. When interaction=FALSE, delta[2] is 0.

alpha

Type I error.

beta

Type II error.

maxsize

tolerance for sample size.

Value

model

a character vector expressing a model. The main effects are expressed by the upper-case letters of the Roman alphabet, and two-way interaction effects are denoted by * operator for pairs of the main effects.

n

optimal sample size.

Delta

a vector of minimal detectable standardized effect sizes.

Details

This function computes sample size in two-level fractional factorial design to detect a certain standardized effect size delta with power 1-beta at the significance level alpha.

References

R. V. Lenth (2006-9). Java Applets for Power and Sample Size[Computer software]. Retrieved March 27, 2018 from https://homepage.divms.uiowa.edu/~rlenth/Power/.

Y. B. Lim (1998). Study on the Size of Minimal Standardized Detectable Difference in Balanced Design of Experiments. Journal of the Korean society for Quality Management, 26(4), 239--249.

M. A. Kastenbaum, D. G. Hoel and K. O. Bowman (1970) Sample size requirements : one-way analysis of variance, Biometrika, 57(2), 421--430.

D. C. Montgomery (2013) Design and analysis of experiments. John Wiley & Sons.

See Also

Size.Full, Size.Split, Size.Block.

Examples

# NOT RUN {
# only main effects
model1 <- Size.2levFr(nfactor=3, nfraction=1, interaction=FALSE,
    delta_type=1, delta=c(1, 0, 1), alpha=0.05, beta=0.2)
model1$model
model1$n
model1$Delta

# including two-way interaction effects
model2 <- Size.2levFr(nfactor=5, nfraction=1, interaction=TRUE,
    delta_type=1, delta=c(1, 1, 1), alpha=0.05, beta=0.2)
# }