BDEsize (version 1.6)

Size.Split: Sample Size Calculator for Split-Plot Design

Description

This function computes sample size for split-plot design to detect a certain standardized effect size with power at the significance level.

Usage

Size.Split(whole.factor.lev, split.factor.lev, interaction = FALSE, 
    delta_type = 1, delta = c(1, 0, 1, 1), alpha = 0.05, beta = 0.2, 
    maxsize = 1000)

Arguments

whole.factor.lev

vector of the numbers of levels for each whole factor.

split.factor.lev

vector of the numbers of levels for each split factor.

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] and delta[4] for standard deviation of whole-plot noise and subplot noise, respectively. 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 whole factor effects and the split factor effects are expressed by the lower-case letters and sequential upper-case letters of the Roman alphabet, and two-way interaction effects are denoted by * operator for pairs of the those effects.

n

optimal sample size.

Delta

a vector of minimal detectable standardized effect sizes.

Details

This function computes sample size in split-plot design to detect a certain standardized effect size delta with power 1-beta at the significance level alpha. The number of whole-plot factors and split plot factors are up to 2 in the current package version. The linear model for the split-plot design is $$y_{ijklm} = \mu + \tau_i + \beta_j + \gamma_k + (\beta\tau)_{ik} + \theta_{ijk} + \delta_l + \lambda_m + (\delta\lambda)_{im} + (\beta\delta)_{jl} + (\beta\lambda)_{jm} + (\gamma\delta)_{kl} + (\delta\lambda)_{lm} + \epsilon_{ijklm}$$ where \(\tau_i\) is the replicate effect, \(\beta_j, \gamma_k\) is the whole-plot main effects, \(\theta_{ijk}\) is the whole-plot error, \(\delta_l, \lambda_m\) is the subplot main effects, and \(\epsilon_{ijklm}\) is the subplot error.

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.2levFr, Size.Block.

Examples

# NOT RUN {
# only main effects
splitmodel1 <- Size.Split(whole.factor.lev=c(2, 2), split.factor.lev=c(2, 2), interaction=FALSE,
    delta_type=1, delta=c(1, 0, 1, 1), alpha=0.05, beta=0.2)
splitmodel1$model
splitmodel1$n
splitmodel1$Delta

# including two-way interaction effects
splitmodel2 <- Size.Split(whole.factor.lev=c(2, 2), split.factor.lev=c(2, 2), interaction=TRUE,
    delta_type=1, delta=c(1, 1, 1, 1), alpha=0.05, beta=0.2)
splitmodel2
# }