| RandomizedBlocksExperimentSimulations {reproducer} | R Documentation |
title RandomizedBlocksExperimentSimulations description This function performs multiple simulations of 4 group balanced randomised Block experiments with two control groups and two treatment groups where one control group and one treatment group are assigned to block 1 and the other control group and treatment group are assigned to block 2. The simulations are based on one of four distributions and a specific group size. The function identifies the average value of the non-parametric effect sizes P-hat, Cliff' d and their variances and whether ot not the statistics were significant at the 0.05 level. We also present the values of the t-test as a comparison.
Description
title RandomizedBlocksExperimentSimulations description This function performs multiple simulations of 4 group balanced randomised Block experiments with two control groups and two treatment groups where one control group and one treatment group are assigned to block 1 and the other control group and treatment group are assigned to block 2. The simulations are based on one of four distributions and a specific group size. The function identifies the average value of the non-parametric effect sizes P-hat, Cliff' d and their variances and whether ot not the statistics were significant at the 0.05 level. We also present the values of the t-test as a comparison.
Usage
RandomizedBlocksExperimentSimulations(
mean,
sd,
diff,
N,
reps,
type = "n",
alpha = 0.05,
Blockmean = 0,
BlockStdAdj = 0,
StdAdj = 0,
seed = 123,
returnData = FALSE,
AlwaysTwoSidedTests = FALSE
)
Arguments
mean |
The default mean for all 4 groups. The default for the two treatment groups can be altered using the parameter diff and the block mean for block 2 can be altered using the parameter Blockmean. |
sd |
The default spread for all 4 groups. It must be a real value greater than 0. If can be altered for treatment groups using the parameter StdAdj and for Block 2 groups using BlockStdAdj |
diff |
The is is added to the parameter mean, to define the mean of the other treatment group. It can be a real value ad can take the value zero. |
N |
this is the number of observations in each group. It must be an integer greater than 3. |
reps |
this identifies the number of times the simulation is replicated. |
type |
this specifies the underlying distribution used to generate the data. it takes the values 'n' for a normal distribution, 'l' for lognormal distribution,'g' for a gamma distribution, 'lap' for a Laplace distribution. |
alpha |
is the Type 1 error level used for constructing confidence intervals and statistical tests (default 0.05) |
Blockmean |
is the effect of having two different blocks |
BlockStdAdj |
is the variance associated with the Block mean. If Blockvar is zero it means we are treat the block effect as a fixed effect. If BlockStdAdj>0, we treat the block effect as a random effect. |
StdAdj |
The value used to introduce heterogeneity into the treatment groups variance if required. |
seed |
this specifies the seed value for the simulations and allows the experiment to be repeated. |
returnData |
if TRUE the function returns the generated data otherwise it returns summary statistics. |
AlwaysTwoSidedTests |
A boolean variable. If TRUE the simulations always used two-sided tests otherwise the simulations use one-sided tests. return depending on the parameter returnData it returns the generated nonparametric and parametric values and their statistical significance (1 for significant, 0 for not significant) or the summary statistics (averages of effect sizes and their variances and the proportion significant effect sizes) |
Author(s)
Barbara Kitchenham and Lech Madeyski
Examples
as.data.frame(
RandomizedBlocksExperimentSimulations(
mean = 0, sd = 1, diff = 0.5, N = 10, reps = 50, type = "n",
alpha = 0.05, Blockmean = 0.5, BlockStdAdj = 0, StdAdj = 0, seed = 123,
AlwaysTwoSidedTests = FALSE))
# phat varphat sigphat emp.phat.var d vard sigd emp.d.var
#1 0.64415 0.008271389 0.45 0.005888917 0.2883 0.0340919 0.41 0.02355567
# StdES ES Var emp.StdESvar MedDiff tpower
#1 0.5413961 0.5264245 0.9904726 0.08811262 0.5538213 0.46
#as.data.frame(
# RandomizedBlocksExperimentSimulations(
# mean = 0, sd = 1, diff = 0.5, N = 10, reps = 500, type = "n",
# alpha = 0.05, Blockmean = 0.5, BlockStdAdj = 0, StdAdj = 0, seed = 123,
# AlwaysTwoSidedTests = FALSE))
# phat varphat sigphat emp.phat.var d vard sigd emp.d.var
# 1 0.63967 0.008322856 0.436 0.007728698 0.27934 0.03430328 0.416 0.03091479
# StdES ES Var emp.StdESvar MedDiff
# 1 0.5130732 0.5029075 1.001602 0.1116687 0.5110203
# tpower
# 1 0.45
#as.data.frame(
# RandomizedBlocksExperimentSimulations(
# mean = 0, sd = 1, diff = 0.5, N = 10, reps = 500, type = "n",
# alpha = 0.05, Blockmean = 0.5, BlockStdAdj = 0, StdAdj = 0, seed = 123,
# AlwaysTwoSidedTests = TRUE))
# phat varphat sigphat emp.phat.var d vard sigd
# 1 0.63967 0.008322856 0.326 0.007728698 0.27934 0.03430328 0.282
# emp.d.var StdES ES Var
# 1 0.03091479 0.5130732 0.5029075 1.001602
# emp.StdESvar MedDiff tpower
# 1 0.1116687 0.5110203 0.334
#RandomizedBlocksExperimentSimulations(
# mean = 0, sd = 1, diff = 0.5, N = 10, reps = 10, type = "n", alpha = 0.05,
#Blockmean = 0.5, BlockStdAdj = 0, StdAdj = 0, seed = 123, returnData = TRUE)
# A tibble: 10 x 6
# Cliffd PHat StdES CliffdSig PHatSig ESSig
# <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
# 1 0.58 0.79 1.06 1 1 1
# 2 0.21 0.605 0.383 0 0 0
# 3 0.37 0.685 0.761 1 1 1
# 4 0.44 0.72 0.821 1 1 1
# 5 0.13 0.565 0.240 0 0 0
# 6 0.16 0.58 0.222 0 0 0
# 7 0.38 0.69 0.580 1 1 1
# 8 0.48 0.74 0.882 1 1 1
# 9 0.11 0.555 0.181 0 0 0
# 10 -0.03 0.485 0.124 0 0 0