Size.Split {BDEsize} | R Documentation |
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 |
delta_type |
specifies the type of standardized effect size: 1 for standard deviation type and 2 for range type. |
delta |
vector of effect sizes: |
alpha |
Type I error. |
beta |
Type II error. |
maxsize |
tolerance for sample size. |
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.
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. |
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
# 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