# Study4.1.Results.txt # Analysis of small sample size data from Study 3, Poisson heterogeneity in # sample size, Gamma in effect size, F-tests, numerator df=1 > ################################################################################## > # AnalyzeStudy4.txt > ################################################################################## > # Analysis of small sample size data from Study 4, Poisson heterogeneity in > # sample size, Gamma in effect size, F-tests > > rm(list=ls()) > options(scipen=999) # To avoid scientific notation! > # read.table chokes on large data sets > # simdata = scan("Testoutput.txt") > simdata = scan("Study4.1.Data.txt") # Numerator df: .1=1df, .3=3df, .5=5df Read 4195800 items > # Calculate the number of simulations. It might not be exactly 10,000. There are > # 3 values of SD(Effect size) after selection > # 5 values of k = Number of studies > # 3 values of mean power after selection > # 9 data values per line, for a total of > # 3*5*3*9 = 405 numbers produced by each simulation. > nsim = length(simdata)/405 > cat("\nAnalyzing data from",nsim," simulations \n\n") Analyzing data from 10360 simulations > nrows = length(simdata)/9; ncols = 9 > dim(simdata) = c(ncols,nrows) # Reversed: R reads by columns, rows > simdata = t(simdata) > colnames(simdata) = c("Simulation", "SD_EffectSize", "Nstudies", "PopMeanPower", + "SampleMeanPower", "Pcurve", "Puniform", "MaxLike", "Zcurve") > head(simdata) ; tail(simdata) Simulation SD_EffectSize Nstudies PopMeanPower SampleMeanPower Pcurve Puniform MaxLike Zcurve [1,] 1 0.1 100 0.25 0.2321242 0.3050088 0.4192304 0.31347370 0.3660493 [2,] 1 0.1 100 0.50 0.4761754 0.4628101 0.5293550 0.45413800 0.5157663 [3,] 1 0.1 100 0.75 0.7537764 0.7710850 0.7815476 0.75752620 0.7630793 [4,] 1 0.1 250 0.25 0.2496946 0.2378034 0.3317095 0.05932222 0.2573114 [5,] 1 0.1 250 0.50 0.5234309 0.5941338 0.5950173 0.55869780 0.5890031 [6,] 1 0.1 250 0.75 0.7467437 0.7793569 0.7998705 0.74476660 0.7399810 Simulation SD_EffectSize Nstudies PopMeanPower SampleMeanPower Pcurve Puniform MaxLike Zcurve [466195,] 37 0.3 1000 0.25 0.2669473 0.3170015 0.9650522 0.3022109 0.2817741 [466196,] 37 0.3 1000 0.50 0.5132854 0.7840484 0.9988431 0.5065493 0.4631129 [466197,] 37 0.3 1000 0.75 0.7609082 0.9680747 0.9999869 0.7564007 0.8029723 [466198,] 37 0.3 2000 0.25 0.2563483 0.3471247 0.9561630 0.3000503 0.2237489 [466199,] 37 0.3 2000 0.50 0.4988032 0.7635491 0.9965234 0.5123016 0.4840946 [466200,] 37 0.3 2000 0.75 0.7263385 0.9562988 0.9999346 0.7191980 0.7292596 > simdata[,8][simdata[,8]>1] = NA # A few bizarre values slipped through out of 1.8 million > # Assembing data in univariate format for nice easy tables > # This way is fast. > nlines = dim(simdata)[1] # Will be bigger for full data set. > # Four copies of the IV columns > SD_EffectSize = rep(simdata[,2],each=4) > Nstudies = rep(simdata[,3],each=4) > PopMeanPower = rep(simdata[,4],each=4) > SampleMeanPower = rep(simdata[,5],each=4) > Methods = c("Pcurve","Puniform","MaxLike","Zcurve") > Method = factor(rep(1:4,times=nlines),labels=Methods) > est = as.matrix(simdata[,6:9]) # Estimates > Estimate = as.numeric(t(est)) > # cbind(SD_EffectSize, Nstudies, PopMeanPower, SampleMeanPower, Estimate)[1:8,] > Bias = Estimate - PopMeanPower > AbsError = abs(Bias) > # Call the estimate close enough if it's within 5% of the target. > CloseEnough = numeric(length(AbsError)); CloseEnough[AbsError<0.05] = 1 > > > ######################### Sample sizes ############################# > kounts = table(Method, SD_EffectSize, PopMeanPower,Nstudies) > cat("\n Sample sizes \n\n"); print(kounts) Sample sizes , , PopMeanPower = 0.25, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10360 10360 10360 Puniform 10360 10360 10360 MaxLike 10360 10360 10360 Zcurve 10360 10360 10360 > > ###################### Average Performance ###################### > estframe = aggregate(Estimate,by=list(Method, SD_EffectSize, PopMeanPower,Nstudies),FUN=mean, na.rm=T) > meanest = estframe$x; dim(meanest) = c(4,3,3,5) # Numbers of factor levels, in order > MeanEstimatedPower = kounts # To use the nice labels > for(j in 1:5) MeanEstimatedPower[,,,j] = meanest[,,,j] > cat("\n Mean Estimated Power \n\n") Mean Estimated Power > print(round(MeanEstimatedPower,3)) , , PopMeanPower = 0.25, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.221 0.252 0.292 Puniform 0.295 0.666 0.903 MaxLike 0.230 0.270 0.282 Zcurve 0.254 0.240 0.240 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.538 0.661 0.738 Puniform 0.595 0.899 0.988 MaxLike 0.500 0.505 0.508 Zcurve 0.524 0.521 0.520 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.817 0.921 0.957 Puniform 0.856 0.988 1.000 MaxLike 0.753 0.751 0.751 Zcurve 0.742 0.766 0.781 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.222 0.262 0.307 Puniform 0.294 0.684 0.933 MaxLike 0.230 0.270 0.282 Zcurve 0.243 0.230 0.231 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.543 0.670 0.750 Puniform 0.600 0.907 0.993 MaxLike 0.503 0.502 0.507 Zcurve 0.517 0.506 0.503 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.821 0.925 0.961 Puniform 0.859 0.991 1.000 MaxLike 0.752 0.750 0.751 Zcurve 0.744 0.761 0.773 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.223 0.268 0.315 Puniform 0.294 0.691 0.944 MaxLike 0.229 0.269 0.283 Zcurve 0.237 0.226 0.228 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.547 0.676 0.754 Puniform 0.602 0.911 0.995 MaxLike 0.502 0.503 0.506 Zcurve 0.511 0.499 0.493 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.823 0.926 0.962 Puniform 0.860 0.991 1.000 MaxLike 0.752 0.750 0.750 Zcurve 0.745 0.758 0.767 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.225 0.272 0.320 Puniform 0.294 0.694 0.949 MaxLike 0.230 0.269 0.283 Zcurve 0.233 0.225 0.226 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.549 0.679 0.757 Puniform 0.602 0.913 0.995 MaxLike 0.501 0.502 0.506 Zcurve 0.504 0.492 0.487 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.824 0.928 0.962 Puniform 0.861 0.992 1.000 MaxLike 0.752 0.750 0.750 Zcurve 0.746 0.755 0.760 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.228 0.275 0.324 Puniform 0.294 0.695 0.953 MaxLike 0.229 0.269 0.284 Zcurve 0.232 0.226 0.227 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.551 0.681 0.759 Puniform 0.603 0.914 0.996 MaxLike 0.501 0.502 0.506 Zcurve 0.501 0.488 0.484 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.825 0.928 0.963 Puniform 0.861 0.992 1.000 MaxLike 0.751 0.750 0.750 Zcurve 0.746 0.751 0.755 > > > ########################## Standard deviations ######################### > vframe = aggregate(Estimate,by=list( Method, SD_EffectSize,PopMeanPower,Nstudies),FUN=var, na.rm=T) > vest = vframe$x; dim(vest) = c(4,3,3,5) # Numbers of factor levels, in order > SDestimatedPower = kounts # To use the nice labels > for(j in 1:5) SDestimatedPower[,,,j] = sqrt(vest[,,,j]) > cat("\n Standard deviations of estimated power \n\n") Standard deviations of estimated power > print(round(SDestimatedPower,3)) , , PopMeanPower = 0.25, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.072 0.093 0.109 Puniform 0.089 0.168 0.120 MaxLike 0.084 0.048 0.042 Zcurve 0.069 0.062 0.059 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.077 0.087 0.086 Puniform 0.076 0.064 0.020 MaxLike 0.084 0.058 0.055 Zcurve 0.071 0.072 0.072 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.042 0.030 0.022 Puniform 0.038 0.011 0.001 MaxLike 0.062 0.047 0.046 Zcurve 0.046 0.038 0.038 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.047 0.062 0.074 Puniform 0.057 0.112 0.066 MaxLike 0.075 0.029 0.027 Zcurve 0.046 0.041 0.039 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.049 0.054 0.052 Puniform 0.048 0.040 0.008 MaxLike 0.049 0.036 0.035 Zcurve 0.048 0.048 0.046 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.027 0.018 0.013 Puniform 0.024 0.006 0.000 MaxLike 0.043 0.031 0.029 Zcurve 0.034 0.028 0.026 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.033 0.046 0.053 Puniform 0.040 0.079 0.042 MaxLike 0.072 0.021 0.020 Zcurve 0.035 0.032 0.031 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.035 0.038 0.037 Puniform 0.034 0.027 0.005 MaxLike 0.036 0.026 0.025 Zcurve 0.035 0.035 0.034 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.018 0.013 0.009 Puniform 0.017 0.004 0.000 MaxLike 0.030 0.024 0.021 Zcurve 0.026 0.022 0.021 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.024 0.033 0.039 Puniform 0.029 0.056 0.028 MaxLike 0.069 0.016 0.015 Zcurve 0.027 0.026 0.024 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.024 0.027 0.026 Puniform 0.024 0.019 0.003 MaxLike 0.025 0.019 0.019 Zcurve 0.026 0.026 0.025 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.013 0.009 0.006 Puniform 0.012 0.003 0.000 MaxLike 0.022 0.017 0.014 Zcurve 0.021 0.017 0.016 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.017 0.023 0.027 Puniform 0.020 0.041 0.019 MaxLike 0.070 0.012 0.013 Zcurve 0.022 0.022 0.020 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.017 0.019 0.018 Puniform 0.017 0.013 0.002 MaxLike 0.019 0.014 0.013 Zcurve 0.019 0.020 0.019 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.009 0.006 0.004 Puniform 0.008 0.002 0.000 MaxLike 0.015 0.013 0.010 Zcurve 0.016 0.014 0.012 > > ########################## Sample mean true power ######################### > TPframe = aggregate(SampleMeanPower,by=list(Method, SD_EffectSize, PopMeanPower,Nstudies),FUN=mean, na.rm=T) > tp = TPframe$x; dim(tp) = c(4,3,3,5) > TPOW = kounts > for(j in 1:5) TPOW[,,,j] = tp[,,,j] > cat("\n Sample mean true power \n\n") Sample mean true power > print(round(TPOW,3)) , , PopMeanPower = 0.25, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.250 0.250 0.250 Puniform 0.250 0.250 0.250 MaxLike 0.250 0.250 0.250 Zcurve 0.250 0.250 0.250 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.502 0.501 0.500 Puniform 0.502 0.501 0.500 MaxLike 0.502 0.501 0.500 Zcurve 0.502 0.501 0.500 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.752 0.750 0.750 Puniform 0.752 0.750 0.750 MaxLike 0.752 0.750 0.750 Zcurve 0.752 0.750 0.750 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.250 0.250 0.250 Puniform 0.250 0.250 0.250 MaxLike 0.250 0.250 0.250 Zcurve 0.250 0.250 0.250 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.502 0.500 0.500 Puniform 0.502 0.500 0.500 MaxLike 0.502 0.500 0.500 Zcurve 0.502 0.500 0.500 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.752 0.750 0.750 Puniform 0.752 0.750 0.750 MaxLike 0.752 0.750 0.750 Zcurve 0.752 0.750 0.750 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.250 0.250 0.250 Puniform 0.250 0.250 0.250 MaxLike 0.250 0.250 0.250 Zcurve 0.250 0.250 0.250 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.502 0.500 0.500 Puniform 0.502 0.500 0.500 MaxLike 0.502 0.500 0.500 Zcurve 0.502 0.500 0.500 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.752 0.750 0.750 Puniform 0.752 0.750 0.750 MaxLike 0.752 0.750 0.750 Zcurve 0.752 0.750 0.750 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.250 0.250 0.250 Puniform 0.250 0.250 0.250 MaxLike 0.250 0.250 0.250 Zcurve 0.250 0.250 0.250 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.502 0.500 0.500 Puniform 0.502 0.500 0.500 MaxLike 0.502 0.500 0.500 Zcurve 0.502 0.500 0.500 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.752 0.750 0.750 Puniform 0.752 0.750 0.750 MaxLike 0.752 0.750 0.750 Zcurve 0.752 0.750 0.750 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.250 0.250 0.250 Puniform 0.250 0.250 0.250 MaxLike 0.250 0.250 0.250 Zcurve 0.250 0.250 0.250 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.502 0.500 0.500 Puniform 0.502 0.500 0.500 MaxLike 0.502 0.500 0.500 Zcurve 0.502 0.500 0.500 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.752 0.750 0.750 Puniform 0.752 0.750 0.750 MaxLike 0.752 0.750 0.750 Zcurve 0.752 0.750 0.750 > > ###################### Bias ###################### > biasframe = aggregate(Bias,by=list(Method, SD_EffectSize, PopMeanPower,Nstudies),FUN=mean, na.rm=T) > meanbias = biasframe$x; dim(meanbias) = c(4,3,3,5) > MeanBias = kounts > for(j in 1:5) MeanBias[,,,j] = meanbias[,,,j] > cat("\n Mean Bias \n\n") Mean Bias > print(round(MeanBias,3)) , , PopMeanPower = 0.25, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.029 0.002 0.042 Puniform 0.045 0.416 0.653 MaxLike -0.020 0.020 0.032 Zcurve 0.004 -0.010 -0.010 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.038 0.161 0.238 Puniform 0.095 0.399 0.488 MaxLike 0.000 0.005 0.008 Zcurve 0.024 0.021 0.020 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.067 0.171 0.207 Puniform 0.106 0.238 0.250 MaxLike 0.003 0.001 0.001 Zcurve -0.008 0.016 0.031 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.028 0.012 0.057 Puniform 0.044 0.434 0.683 MaxLike -0.020 0.020 0.032 Zcurve -0.007 -0.020 -0.019 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.043 0.170 0.250 Puniform 0.100 0.407 0.493 MaxLike 0.003 0.002 0.007 Zcurve 0.017 0.006 0.003 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.071 0.175 0.211 Puniform 0.109 0.241 0.250 MaxLike 0.002 0.000 0.001 Zcurve -0.006 0.011 0.023 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.027 0.018 0.065 Puniform 0.044 0.441 0.694 MaxLike -0.021 0.019 0.033 Zcurve -0.013 -0.024 -0.022 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.047 0.176 0.254 Puniform 0.102 0.411 0.495 MaxLike 0.002 0.003 0.006 Zcurve 0.011 -0.001 -0.007 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.073 0.176 0.212 Puniform 0.110 0.241 0.250 MaxLike 0.002 0.000 0.000 Zcurve -0.005 0.008 0.017 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.025 0.022 0.070 Puniform 0.044 0.444 0.699 MaxLike -0.020 0.019 0.033 Zcurve -0.017 -0.025 -0.024 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.049 0.179 0.257 Puniform 0.102 0.413 0.495 MaxLike 0.001 0.002 0.006 Zcurve 0.004 -0.008 -0.013 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.074 0.178 0.212 Puniform 0.111 0.242 0.250 MaxLike 0.002 0.000 0.000 Zcurve -0.004 0.005 0.010 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.022 0.025 0.074 Puniform 0.044 0.445 0.703 MaxLike -0.021 0.019 0.034 Zcurve -0.018 -0.024 -0.023 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.051 0.181 0.259 Puniform 0.103 0.414 0.496 MaxLike 0.001 0.002 0.006 Zcurve 0.001 -0.012 -0.016 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.075 0.178 0.213 Puniform 0.111 0.242 0.250 MaxLike 0.001 0.000 0.000 Zcurve -0.004 0.001 0.005 > > ########################## Z-tests for bias ######################### > # Calculate Z > ZforBias = kounts > for(j in 1:5) ZforBias[,,,j] = + sqrt(kounts[1,1,1,1])*(MeanEstimatedPower[,,,j] - TPOW[,,,j])/SDestimatedPower[,,,j] > cat("\n Z-tests for bias \n", + " Any Z with |Z|>4.61 is significant.\n\n") Z-tests for bias Any Z with |Z|>4.61 is significant. > print(round(ZforBias,2)) , , PopMeanPower = 0.25, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -41.33 2.54 39.88 Puniform 51.19 252.34 556.64 MaxLike -24.42 41.97 77.25 Zcurve 5.56 -15.76 -17.44 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 47.72 188.22 280.22 Puniform 125.12 631.42 2435.37 MaxLike -2.50 7.62 14.07 Zcurve 32.72 29.22 28.07 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 160.33 585.92 968.57 Puniform 277.02 2274.08 21432.21 MaxLike 0.96 3.20 2.31 Zcurve -22.10 43.20 83.27 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -61.84 19.82 78.61 Puniform 78.84 395.14 1059.69 MaxLike -27.65 67.79 121.27 Zcurve -16.25 -48.46 -49.63 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 85.63 319.32 487.39 Puniform 208.30 1049.74 6331.66 MaxLike 1.29 6.89 19.16 Zcurve 30.97 12.81 5.31 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 265.25 987.31 1689.30 Puniform 455.43 4351.86 90490.03 MaxLike -0.09 0.15 1.13 Zcurve -24.33 40.68 88.09 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -83.05 40.15 123.93 Puniform 111.56 566.16 1686.04 MaxLike -29.95 91.75 167.62 Zcurve -37.47 -74.61 -73.09 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 130.96 472.97 691.04 Puniform 294.93 1540.81 10747.13 MaxLike -0.27 9.30 23.90 Zcurve 24.48 -4.17 -19.32 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 392.55 1408.66 2462.31 Puniform 659.24 6476.77 191498.49 MaxLike -0.51 -0.58 2.16 Zcurve -29.35 36.98 82.62 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -103.24 68.38 185.55 Puniform 156.07 803.53 2501.94 MaxLike -30.02 121.57 221.85 Zcurve -63.18 -97.30 -98.50 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 195.07 672.10 994.13 Puniform 424.52 2230.71 17318.50 MaxLike -3.52 9.94 30.25 Zcurve 9.66 -29.98 -50.87 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 562.03 2068.78 3545.65 Puniform 940.82 9686.86 359639.60 MaxLike -0.69 0.03 0.30 Zcurve -31.90 28.70 67.63 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -129.13 110.03 278.36 Puniform 222.16 1117.70 3757.28 MaxLike -30.50 164.26 267.42 Zcurve -86.90 -113.97 -120.01 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 287.67 969.48 1440.22 Puniform 602.02 3170.82 27008.09 MaxLike -5.72 11.63 46.72 Zcurve -5.78 -57.20 -85.71 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 790.37 2953.92 5052.94 Puniform 1312.19 13958.99 600798.01 MaxLike -6.05 -1.74 0.20 Zcurve -39.30 11.51 44.82 > > # Protect the 240 tests in this table with Bonferroni > # Two-tailed at the 0.001 significance level > # 0.0005/240 = 0.000002083333, and qnorm(0.000002083333) = -4.602891 > # So any Z with |Z|>4.61 is significant. > > ###################### Is estimate close enough? ############# > > # Get table of counts in a different order, for labels > k2 = table(Method, Nstudies, PopMeanPower, SD_EffectSize) > > closeframe = + aggregate(CloseEnough,by=list(Method, Nstudies, PopMeanPower, SD_EffectSize),FUN=mean, na.rm=T) > klose = closeframe$x; dim(klose) = c(4,5,3,3) > ProportionWithin.05 = k2 > for(j in 1:3) ProportionWithin.05[,,,j] = klose[,,,j] > cat("\n Proportion of estimates within 0.05 of target \n\n") Proportion of estimates within 0.05 of target > print(round(ProportionWithin.05,3)) , , PopMeanPower = 0.25, SD_EffectSize = 0.1 Nstudies Method 100 250 500 1000 2000 Pcurve 0.443 0.611 0.726 0.851 0.946 Puniform 0.398 0.507 0.561 0.591 0.606 MaxLike 0.571 0.754 0.853 0.886 0.891 Zcurve 0.529 0.714 0.819 0.893 0.945 , , PopMeanPower = 0.5, SD_EffectSize = 0.1 Nstudies Method 100 250 500 1000 2000 Pcurve 0.417 0.503 0.529 0.512 0.469 Puniform 0.236 0.146 0.073 0.016 0.002 MaxLike 0.510 0.739 0.886 0.972 0.997 Zcurve 0.473 0.663 0.822 0.937 0.988 , , PopMeanPower = 0.75, SD_EffectSize = 0.1 Nstudies Method 100 250 500 1000 2000 Pcurve 0.298 0.206 0.109 0.033 0.006 Puniform 0.083 0.013 0.001 0.000 0.000 MaxLike 0.653 0.850 0.958 0.995 1.000 Zcurve 0.731 0.859 0.938 0.985 0.998 , , PopMeanPower = 0.25, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.385 0.569 0.696 0.792 0.851 Puniform 0.019 0.001 0.000 0.000 0.000 MaxLike 0.691 0.844 0.929 0.976 0.993 Zcurve 0.569 0.704 0.775 0.832 0.901 , , PopMeanPower = 0.5, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.092 0.021 0.001 0.000 0.000 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.617 0.832 0.947 0.992 0.999 Zcurve 0.475 0.695 0.850 0.931 0.972 , , PopMeanPower = 0.75, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.002 0.000 0.000 0.000 0.000 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.715 0.911 0.983 0.998 1.000 Zcurve 0.763 0.908 0.970 0.994 1.000 , , PopMeanPower = 0.25, SD_EffectSize = 0.3 Nstudies Method 100 250 500 1000 2000 Pcurve 0.331 0.407 0.394 0.306 0.190 Puniform 0.001 0.000 0.000 0.000 0.000 MaxLike 0.647 0.747 0.805 0.878 0.924 Zcurve 0.589 0.733 0.808 0.875 0.934 , , PopMeanPower = 0.5, SD_EffectSize = 0.3 Nstudies Method 100 250 500 1000 2000 Pcurve 0.024 0.001 0.000 0.000 0.000 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.630 0.851 0.950 0.992 1.000 Zcurve 0.481 0.719 0.852 0.930 0.967 , , PopMeanPower = 0.75, SD_EffectSize = 0.3 Nstudies Method 100 250 500 1000 2000 Pcurve 0.000 0.000 0.000 0.000 0.000 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.719 0.919 0.985 1.000 1.000 Zcurve 0.637 0.847 0.951 0.995 1.000 > > ###################### Mean Absolute Error ###################### > # Take a look at marginals to see roughly who won overall > cat(" Marginal means for method \n") Marginal means for method > print(aggregate(round(100*AbsError,2),by=list(Method),FUN=mean, na.rm=T)) Group.1 x 1 Pcurve 12.233449 2 Puniform 30.908654 3 MaxLike 2.740637 4 Zcurve 3.025925 > > errframe = aggregate(AbsError,by=list(Method, SD_EffectSize, PopMeanPower,Nstudies),FUN=mean, na.rm=T) > meanerr = 100*errframe$x; dim(meanerr) = c(4,3,3,5) > MeanAbsoluteError = kounts > for(j in 1:5) MeanAbsoluteError[,,,j] = meanerr[,,,j] > cat("\n Mean Absolute Error of Prediction \n\n") Mean Absolute Error of Prediction > print(round(MeanAbsoluteError,2)) , , PopMeanPower = 0.25, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 6.38 7.54 9.29 Puniform 7.82 41.64 65.34 MaxLike 6.19 4.02 4.27 Zcurve 5.49 5.03 4.79 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 6.99 16.50 23.87 Puniform 10.38 39.88 48.78 MaxLike 6.01 4.60 4.43 Zcurve 6.08 6.07 6.04 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 7.06 17.10 20.72 Puniform 10.62 23.84 24.96 MaxLike 4.32 3.73 3.68 Zcurve 3.64 3.40 4.12 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 4.49 5.07 7.43 Puniform 5.76 43.35 68.29 MaxLike 4.81 2.81 3.51 Zcurve 3.72 3.74 3.58 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.43 17.03 25.04 Puniform 10.14 40.70 49.33 MaxLike 3.63 2.90 2.79 Zcurve 4.09 3.86 3.70 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 7.13 17.49 21.06 Puniform 10.91 24.07 24.98 MaxLike 2.84 2.38 2.28 Zcurve 2.71 2.45 2.93 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 3.56 3.90 7.00 Puniform 4.89 44.06 69.43 MaxLike 4.09 2.31 3.37 Zcurve 3.00 3.34 3.14 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 4.98 17.64 25.40 Puniform 10.17 41.12 49.47 MaxLike 2.57 2.06 2.02 Zcurve 2.96 2.79 2.74 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 7.32 17.63 21.17 Puniform 11.02 24.13 24.99 MaxLike 2.00 1.69 1.64 Zcurve 2.13 1.89 2.19 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 2.87 3.16 7.08 Puniform 4.50 44.38 69.90 MaxLike 3.55 2.06 3.34 Zcurve 2.59 3.08 2.90 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 4.93 17.86 25.70 Puniform 10.21 41.28 49.54 MaxLike 1.80 1.49 1.50 Zcurve 2.12 2.19 2.23 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 7.45 17.75 21.23 Puniform 11.08 24.17 24.99 MaxLike 1.42 1.18 1.16 Zcurve 1.69 1.42 1.55 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 2.39 2.85 7.36 Puniform 4.46 44.52 70.25 MaxLike 3.35 1.99 3.41 Zcurve 2.40 2.78 2.64 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.13 18.07 25.91 Puniform 10.31 41.39 49.58 MaxLike 1.26 1.09 1.12 Zcurve 1.55 1.91 2.06 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 7.50 17.78 21.26 Puniform 11.08 24.19 24.99 MaxLike 1.03 0.85 0.81 Zcurve 1.30 1.08 1.06 > > > ################################################################################## > # Need to do all 6 pairwise matched t-tests for mean absolute error, for each > # combination of Nstudies and PopMeanPower, > # with a Bonferroni correction for 120 tests in the table. > # alpha = 0.001; a = alpha/120; critZ = qnorm(1-a/2); critZ # 4.456436 > # Return to simdata, multivariate format. > ###################################################################################### > > # Bonferroni correct at joint 0.001 levl for 6 pairwise comparisons within > # each combination of > # 3 values of SD(Effect size) after selection > # 5 values of k = Number of studies > # 3 values of mean power after selection > # 6*45 = 270 > a = 0.001/270; critZ = qnorm(1-a/2) # 4.627352 > > ae = simdata[,6:9] # The estimates > sdes = simdata[,2]; kk = simdata[,3]; pow = simdata[,4]; Index = 1:nlines > for(kol in 1:4) ae[,kol] = abs(ae[,kol]-pow) # Now they are absolute errors. > > nstudies = unique(Nstudies); truepower = unique(PopMeanPower) > sd_effectsize = unique(SD_EffectSize) > pairwise = matrix(0,4,4); rownames(pairwise) = colnames(pairwise) = Methods > keepscore = pairwise # Count winners in this matrix > > # This does not have to be efficient, and it isn't. > > cat("\n\n Matched Z-tests for pairwise differences in mean absolute error. \n", + "Positive value means the row method is less accurate on average. \n", + "Critical value Bonferroni protected at the 0.001 level is",critZ,".\n\n") Matched Z-tests for pairwise differences in mean absolute error. Positive value means the row method is less accurate on average. Critical value Bonferroni protected at the 0.001 level is 4.627352 . > > for(h in 1:3) # Looping over sd of effect size + { + for(i in 1:5) # Looping over Nstudies + { + for(j in 1:3) # Looping over PopMeanPower + { + cat("\n SD_EffectSize =",sd_effectsize[h]," Nstudies =",nstudies[i]," and PopMeanPower =",truepower[j],"\n\n") + In = (sdes==sd_effectsize[h]) * (kk==nstudies[i]) * (pow==truepower[j]) + pick = Index[In==1] + # Fill matrix of pairwise tests in a double loop + for(K in 1:4) + { + for(L in 1:4) + { + differ = (ae[,K]-ae[,L])[pick] + Z = 0 + if(K != L) Z = t.test(differ)$statistic + if(K < L) pairwise[K,L] = Z + if(Z < -critZ) keepscore[K,L] = keepscore[K,L]+1 + } # Next L + } # Next K + print(round(pairwise[1:3,2:4],2)) + } # Next j (PopMeanPower) + } # Next i (Nstudies) + } # Next h (SD_EffectSize) SD_EffectSize = 0.1 Nstudies = 100 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -21.06 3.26 22.08 Puniform 0.00 21.66 40.54 MaxLike 0.00 0.00 11.68 SD_EffectSize = 0.1 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -64.58 17.84 27.63 Puniform 0.00 53.01 69.04 MaxLike 0.00 0.00 -1.35 SD_EffectSize = 0.1 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -145.29 50.31 70.49 Puniform 0.00 107.86 139.63 MaxLike 0.00 0.00 16.83 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -22.4 -5.10 26.31 Puniform 0.0 13.31 42.99 MaxLike 0.0 0.00 17.60 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -140.86 47.35 44.17 Puniform 0.00 118.19 126.76 MaxLike 0.00 0.00 -17.04 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -249.57 104.22 120.86 Puniform 0.00 198.80 243.91 MaxLike 0.00 0.00 4.06 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -27.21 -8.27 23.00 Puniform 0.00 11.55 44.58 MaxLike 0.00 0.00 17.15 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -240.72 70.13 69.23 Puniform 0.00 181.82 196.07 MaxLike 0.00 0.00 -17.98 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -347.76 185.61 194.73 Puniform 0.00 323.13 368.27 MaxLike 0.00 0.00 -5.43 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -40.37 -10.75 13.40 Puniform 0.00 14.43 53.34 MaxLike 0.00 0.00 15.06 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -370.36 112.37 108.43 Puniform 0.00 287.44 298.02 MaxLike 0.00 0.00 -19.86 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -474.5 292.24 294.90 Puniform 0.0 477.60 528.72 MaxLike 0.0 0.00 -14.49 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -65.13 -14.84 -0.40 Puniform 0.00 16.55 71.13 MaxLike 0.00 0.00 14.65 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -504.45 181.20 173.22 Puniform 0.00 420.38 432.16 MaxLike 0.00 0.00 -21.04 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -647.44 464.34 421.65 Puniform 0.00 747.28 734.14 MaxLike 0.00 0.00 -20.75 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -202.43 81.32 49.99 Puniform 0.00 234.41 212.70 MaxLike 0.00 0.00 -27.21 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -359.91 146.76 136.36 Puniform 0.00 480.37 461.70 MaxLike 0.00 0.00 -54.01 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -275.54 302.49 399.20 Puniform 0.00 651.01 814.39 MaxLike 0.00 0.00 14.63 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -346.42 75.02 29.44 Puniform 0.00 387.86 333.24 MaxLike 0.00 0.00 -26.90 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -569.49 247.25 223.16 Puniform 0.00 833.43 763.08 MaxLike 0.00 0.00 -51.53 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -436.6 544.41 684.60 Puniform 0.0 1062.47 1210.39 MaxLike 0.0 0.00 -3.91 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -536.52 67.98 13.91 Puniform 0.00 576.19 467.98 MaxLike 0.00 0.00 -32.89 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -792.68 394.34 338.40 Puniform 0.00 1244.81 1109.83 MaxLike 0.00 0.00 -43.32 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -609.55 747.97 960.62 Puniform 0.00 1343.94 1600.19 MaxLike 0.00 0.00 -12.18 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -816.91 60.22 2.35 Puniform 0.00 839.09 656.04 MaxLike 0.00 0.00 -38.01 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -1107.7 581.3 452.32 Puniform 0.0 1846.3 1500.59 MaxLike 0.0 0.0 -44.99 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -874.59 1131.44 1305.97 Puniform 0.00 1957.09 2096.76 MaxLike 0.00 0.00 -19.26 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -1233.45 59.62 2.78 Puniform 0.00 1187.80 891.36 MaxLike 0.00 0.00 -34.49 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -1557.21 850.33 597.77 Puniform 0.00 2577.15 1931.83 MaxLike 0.00 0.00 -54.59 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -1233.33 1469.16 1681.41 Puniform 0.00 2368.38 2750.03 MaxLike 0.00 0.00 -20.99 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -441.8 95.14 64.33 Puniform 0.0 538.13 470.06 MaxLike 0.0 0.00 -12.61 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -328.75 224.51 210.96 Puniform 0.00 1130.77 905.01 MaxLike 0.00 0.00 -64.30 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -201.68 443.71 659.28 Puniform 0.00 776.47 833.40 MaxLike 0.00 0.00 -15.93 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -867.82 93.87 58.89 Puniform 0.00 1099.45 858.91 MaxLike 0.00 0.00 -1.65 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -505.8 423.63 370.56 Puniform 0.0 2031.34 1606.27 MaxLike 0.0 0.00 -49.31 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -317.57 811.66 1111.63 Puniform 0.00 1280.73 1195.85 MaxLike 0.00 0.00 -32.36 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -1376.56 105.00 67.64 Puniform 0.00 1836.92 1304.71 MaxLike 0.00 0.00 7.08 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -693.66 628.51 495.15 Puniform 0.00 2886.86 2204.17 MaxLike 0.00 0.00 -39.05 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -446.26 1199.09 1485.08 Puniform 0.00 1769.49 1551.79 MaxLike 0.00 0.00 -35.16 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -1951.57 134.20 92.06 Puniform 0.00 2756.69 1833.36 MaxLike 0.00 0.00 16.15 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -969.02 936.07 654.08 Puniform 0.00 3585.63 2791.53 MaxLike 0.00 0.00 -37.60 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -632.17 1859.41 1975.72 Puniform 0.00 2809.53 2154.07 MaxLike 0.00 0.00 -37.72 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -2746.34 183.70 139.69 Puniform 0.00 3856.66 2545.27 MaxLike 0.00 0.00 34.35 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -1379.65 1517.64 860.41 Puniform 0.00 5695.42 3331.06 MaxLike 0.00 0.00 -54.04 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -890.81 2673.38 2595.29 Puniform 0.00 3926.01 3028.13 MaxLike 0.00 0.00 -34.51 > > cat("\nTotal number of significant comparisons: \n") Total number of significant comparisons: > print(sum(keepscore)) [1] 262 > > cat("\n\n Number of times row method is significantly more accurate than column method \n\n"); print(addmargins(keepscore,2)) Number of times row method is significantly more accurate than column method Pcurve Puniform MaxLike Zcurve Sum Pcurve 0 45 4 0 49 Puniform 0 0 0 0 0 MaxLike 40 45 0 31 116 Zcurve 42 45 10 0 97 >