Size.Block {BDEsize} | R Documentation |

## The number of Blocks Calculator for Randomized Complete Block Design

### Description

This function computes the number of blocks for randomized complete block design to detect a certain standardized effect size with power at the significance level.

### Usage

```
Size.Block(factor.lev, interaction = FALSE, delta_type = 1, delta = c(1, 0, 1),
alpha = 0.05, beta = 0.2, maxsize = 1000)
```

### Arguments

`factor.lev` |
vector of the numbers of levels for each 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 the number of blocks. |

### Details

In a randomized complete block design (without replications), the optimal number of blocks need to be determined.
This function computes the number of blocks for randomized complete block 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.
The block factor is denoted by |

`n` |
optimal the number of blocks. |

`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.Split`

.

### Examples

```
# only main effects
model1 <- Size.Block(factor.lev=c(2, 2), 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.Block(factor.lev=c(2, 2), interaction=TRUE,
delta_type=1, delta=c(1, 1, 1), alpha=0.05, beta=0.2)
model2
```

*BDEsize*version 1.6 Index]