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 2^(k-p), k is the number of factor and p is the number of fraction. It is called a 1/2^p fraction of the 2^k design. `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` for standard deviation of noise. 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 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.

`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)
```

[Package BDEsize version 1.6 Index]