RandomizedBlocksAnalysis function

RandomizedBlocksAnalysis

The function performs a heteroscedastic test of a two treatment by J blocks randomized blocks effect size. The data are assumed to be stored in $x$ in list mode. All groups are assumed to be independent. Missing values are not permitted.

RandomizedBlocksAnalysis(
  x,
  con = c(-0.5, 0.5, -0.5, 0.5),
  alpha = 0.05,
  alternative = "two.sided"
)

Arguments

• x: the structure holding the data. In list format, for a 2 treatment by J block randomized blocks experiments, there are 2J list elements each one specifying the outcome for a specific block and a specific treatment.
• con: is a 2J list containing the contrast coefficients that are used to calculate the mean effect size.
• alpha: is the Type 1 error level used for the test of significance (default 0.05)
• alternative: The type of statistical test. Valid values are one of c('two.sided', 'greater', 'less')

Returns

The t-test and its associated metrics (i.e., critical value standard error and degrees of freedom) and the estimate of the contrast with its upper and lower confidence interval bounds and p-value.

Examples

set.seed(123)
x <- list()
x[[1]] <- rnorm(10, 0, 1)
x[[2]] <- rnorm(10, 0.8, 1)
x[[3]] <- rnorm(10, 0.5, 1)
x[[4]] <- rnorm(10, 1.3, 1)
vec <- c(-1, 1, -1, 1) / 2
RandomizedBlocksAnalysis(x, con = vec, alpha = 0.05)
# $n
# [1] 10 10 10 10
# $test
#      test     crit        se       df
# [1,] 4.432644 2.038622 0.2798104 31.33793
# $psihat
#      psihat  ci.lower ci.upper      p.value
# [1,] 1.2403 0.6698721 1.810728 0.0001062952
# $sig
# [1] TRUE
RandomizedBlocksAnalysis(x,con=vec,alpha=0.05,alternative='greater')
# n
# [1] 10 10 10 10
# $test
#          test     crit        se       df
# [1,] 4.432644 1.694956 0.2798104 31.33793
# $psihat
# psihat  ci.lower ci.upper      p.value
#[1,] 1.2403 0.7660336      Inf 5.314762e-05
# $sig
# [1] TRUE
RandomizedBlocksAnalysis(x,con=-vec,alpha=0.05,alternative='greater')
#$n
#[1] 10 10 10 10
#$test
#          test     crit        se       df
#[1,] -4.432644 1.694956 0.2798104 31.33793
#$psihat
#      psihat  ci.lower ci.upper   p.value
#[1,] -1.2403 -1.714566      Inf 0.9999469
#$sig
#[1] FALSE
x[[5]]=rnorm(10,-0.2,1)
x[[6]]=rnorm(10,0.6,1)
vec=c(1,-1,1,-1,1,-1)/3
RandomizedBlocksAnalysis(x,con=vec,alpha=0.05,alternative='less')
#$n
#[1] 10 10 10 10 10 10
#$test
#          test     crit       se       df
#[1,] -4.946987  1.677021 0.236575 48.29776
#$psihat
#        psihat ci.lower   ci.upper     p.value
#[1,] -1.170334     -Inf -0.7735925 4.76961e-06
#$sig
#[1] TRUE

Author(s)

Barbara Kitchenham and Lech Madeyski