BDEsize (version 1.6)

Size.Block: 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.

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.

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.

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

# NOT RUN {
# 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
# }