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
```

*BDEsize*version 1.6 Index]