Size.2levFr {BDEsize}

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.

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.

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.

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

# 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)