Size.Block {BDEsize}

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 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[1] for main effects, delta[2] for two-way interaction effects, and delta[3] for standard deviation of noise. When interaction=FALSE, delta[2] is 0.

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 Block.

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