Size.Split {BDEsize} | R Documentation |

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

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)

`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. |

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.

`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. |

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`

.

# 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]