reproducer (version 0.5.2)

RandomizedBlocksExperimentSimulations: 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

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
#               
# 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