Size.2levFr {BDEsize} | R Documentation |

## Sample Size Calculator for Two-level Fractional Factorial Design

### Description

This function computes sample size for two-level fractional factorial design to detect a certain standardized effect size with power at the significance level. The model for fractional factorial design contains only main effects in resolution III and IV.

### Usage

```
Size.2levFr(nfactor, nfraction, interaction = FALSE, delta_type = 1,
delta = c(1, 0, 1), alpha = 0.05, beta = 0.2, maxsize = 1000)
```

### Arguments

`nfactor` |
the number of factor. |

`nfraction` |
the number of fraction. For example, when a model is |

`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 two-level fractional factorial design to detect a certain standardized effect size `delta`

with power `1-beta`

at the significance level `alpha`

.

### Value

`model` |
a character vector expressing a model. The main effects are expressed by the upper-case letters of the Roman alphabet, and two-way interaction effects are denoted by * operator for pairs of the main 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.Split`

, `Size.Block`

.

### Examples

```
# only main effects
model1 <- Size.2levFr(nfactor=3, nfraction=1, interaction=FALSE,
delta_type=1, delta=c(1, 0, 1), alpha=0.05, beta=0.2)
model1$model
model1$n
model1$Delta
# including two-way interaction effects
model2 <- Size.2levFr(nfactor=5, nfraction=1, interaction=TRUE,
delta_type=1, delta=c(1, 1, 1), alpha=0.05, beta=0.2)
```

*BDEsize*version 1.6 Index]