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 `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` for main effects, `delta` for two-way interaction effects, and `delta` and `delta` for standard deviation of whole-plot noise and subplot noise, respectively. When `interaction=FALSE`, `delta` is 0. `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} = μ + τ_i + β_j + γ_k + (βτ)_{ik} + θ_{ijk} + δ_l + λ_m + (δλ)_{im} + (βδ)_{jl} + (βλ)_{jm} + (γδ)_{kl} + (δλ)_{lm} + ε_{ijklm}

where τ_i is the replicate effect, β_j, γ_k is the whole-plot main effects, θ_{ijk} is the whole-plot error, δ_l, λ_m is the subplot main effects, and ε_{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.

`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
```

[Package BDEsize version 1.6 Index]