reproducer (version 0.4.2)

NP4GroupMetaAnalysisSimulation: NP4GroupMetaAnalysisSimulation

Description

This function simulates data from a family of experiments, where the number of experiments in a family is defined by ther parameter Exp. It simulates data from one of four distributions and uses the data to construct four of groups of equal size (GroupSize). Two groups are assigned as control groups and their distribution is based on the parameter mean and the parameter spread, however, the mean and spread for the control group in Block 2 can be adjusted using the parameters BlockEffect and BlockStdAdj respectively. The other two groups are treatment groups and their distribution is based on the mean+diff and the spread parameter, but the distributions can be adjusted using the StdAdj, BlockEffect and BlockStdAdj parameters. The data from each experiment is analysed separately to estimate the non-parametric statistics P-hat, Cliff's d and Kendall's tau and their variances. The statistics are then meta-analysed using the method specified by the MAMethod parameter. We output the average non-parametric effect statistics across the Exp experimet as if from a single large experiment and also the results of meta-analysising each non-parametric effect size. We use the standard parametric effect sizes and their meta-analysis as baselines. All tests of significance are done at the 0.05 level.

Usage

NP4GroupMetaAnalysisSimulation(
  mean,
  sd,
  diff,
  GroupSize,
  Exp = 5,
  type = "n",
  alpha = 0.05,
  seed = 123,
  StdAdj = 0,
  BlockEffect = 0,
  BlockStdAdj = 0,
  StdExp = 0,
  MAMethod,
  returnES = FALSE
)

Value

If returnES is true, the function returns the summary meta-analysis summary statistics otherwise the function returns the effect sizes for each experiment

Arguments

mean

The default value used for the group means in the simulated data. It can be any real number including zero.

sd

The default value used for the spread of the control group and the spread of the treatment group in the simulated data. The value must be a real value greater than 0.

diff

mean+diff is the value used for the mean of the treatment group. It can be zero.

GroupSize

is the size of each of the 4 groups comprising one experiment. GroupSize should be an integer of 4 or more

Exp

is the number of experiments being simulated. Exp should be an integer of 2 or more. It defaults to 5.

type

specifies the distribution being simulated. The permitted values are "n" for the normal distribution, "l" for the lognormal distribution, "g" for the gamma distribution and "lap" for the Laplace dsitribution. The parameter defaults to "n".

alpha

The Type 1 value used in all significance tests. It defaults to 0.05.

seed

specifies the seed to be used to initiate the simulation, so the simulation is repeatable. It defaults to 123.

StdAdj

The value used to introduce heterogeneity into the treatment groups variance if required.

BlockEffect

is the effect of having two different blocks

BlockStdAdj

is the variance associated with the Block. If BlockStdAdj 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 and increase the variance of Block 2 data.

StdExp

The value used to introduce heterogeneity into experiments in a family required.

MAMethod

defines the method used for meta-analysis

returnES

default to FALSE

Author

Barbara Kitchenham and Lech Madeyski

Examples

NP4GroupMetaAnalysisSimulation(mean=0,sd=1,diff=0.5,GroupSize=10,Exp=5,type="n",alpha=0.05,
seed=123,StdAdj=0,BlockEffect=0.5,BlockStdAdj=0,StdExp=0,MAMethod="PM")
# A tibble: 1 x 30
#  NumExp GroupSize AveKtau AveKtauctvar tauSigCVt AveCliffd AveCliffdvar AveCliffdsig Avephat
# Avephatvar Avephatsig
#                                                
#  
# 1      5        10   0.182      0.00188 TRUE          0.346      0.00673 TRUE           0.673
# 0.00163 TRUE
# … with 19 more variables: MAMean , MAvar , MASig , QE , QEp ,
# HetSig , P.mean ,
NP4GroupMetaAnalysisSimulation(mean=0,sd=1,diff=0.724,GroupSize=10,Exp=5,type="l",alpha=0.05,
seed=123,StdAdj=0,BlockEffect=0.5,BlockStdAdj=0,StdExp=0,MAMethod="PM")
# A tibble: 1 x 30
#  NumExp GroupSize AveKtau AveKtauctvar tauSigCVt AveCliffd AveCliffdvar AveCliffdsig Avephat
# Avephatvar Avephatsig
#                                                
#   
# 1      5        10   0.244      0.00167 TRUE          0.464      0.00593 TRUE           0.732
# 0.00144 TRUE
# … with 19 more variables: MAMean , MAvar , MASig , QE , QEp ,
# HetSig , P.mean ,
NP4GroupMetaAnalysisSimulation(mean=0,sd=1,diff=0.5,GroupSize=10,Exp=5,type="n",alpha=0.05,
seed=123,StdAdj=0,BlockEffect=0.5,BlockStdAdj=0,StdExp=0,MAMethod="PM",returnES=TRUE)
# A tibble: 5 x 16
#  MeanExp VarExp StdESExp    df  tval   tpval    tciL  tciU Cliffd Cliffdvar  PHat PHatvar
# PHatdf     g gvar.approx
#                              
#         
#1   0.940  0.783    1.06   31.3 3.36  0.00206  0.370  1.51   0.58     0.0243 0.29  0.00587
# 30.2 1.04       0.112
#2   0.372  0.943    0.383  35.0 1.21  0.234   -0.251  0.996  0.21     0.0380 0.105 0.00927
# 31.3 0.375      0.0977
#3   0.598  0.619    0.761  28.6 2.40  0.0229   0.0892 1.11   0.37     0.0336 0.185 0.00813
# 30.8 0.740      0.104
#4   0.873  1.13     0.821  28.1 2.60  0.0148   0.184  1.56   0.440    0.0333 0.220 0.00813
# 23.8 0.799      0.106
#5   0.243  1.03     0.240  31.5 0.758 0.454   -0.410  0.896  0.13     0.0390 0.065 0.00946
# 32.8 0.234      0.0961
# … with 1 more variable: Cohendvar