# Study4.3.Results.txt > ################################################################################## > # 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("Study4.3.Data.txt") # Numerator df: .1=1df, .3=3df, .5=5df Read 4140720 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 10224 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 0.2092671 0.2802883 0.3443695 0.29228990 0.3034813 [2,] 1 0.1 100 0.50 0.4937154 0.6738365 0.7306071 0.58627140 0.5487513 [3,] 1 0.1 100 0.75 0.7449431 0.8254046 0.8692227 0.78296960 0.7258643 [4,] 1 0.1 250 0.25 0.2515074 0.2015541 0.2645996 0.01524195 0.1744627 [5,] 1 0.1 250 0.50 0.5160434 0.5741617 0.6526564 0.52285250 0.5371707 [6,] 1 0.1 250 0.75 0.7527758 0.8530425 0.8904014 0.76074950 0.7558569 Simulation SD_EffectSize Nstudies PopMeanPower SampleMeanPower Pcurve Puniform MaxLike Zcurve [460075,] 36 0.3 1000 0.25 0.2426988 0.2971049 0.9247915 0.2492333 0.2131140 [460076,] 36 0.3 1000 0.50 0.5307063 0.7752949 0.9939335 0.5342833 0.5057195 [460077,] 36 0.3 1000 0.75 0.7492058 0.9509626 0.9998852 0.7342033 0.7286093 [460078,] 36 0.3 2000 0.25 0.2509468 0.3198070 0.8845248 0.2650719 0.2653253 [460079,] 36 0.3 2000 0.50 0.4978422 0.7188979 0.9850028 0.4906897 0.4639227 [460080,] 36 0.3 2000 0.75 0.7529183 0.9549404 0.9997697 0.7431084 0.7439622 > 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 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10224 10224 10224 Puniform 10224 10224 10224 MaxLike 10224 10224 10224 Zcurve 10224 10224 10224 > > ###################### 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 0.230 0.248 0.295 Puniform 0.281 0.567 0.864 MaxLike 0.220 0.256 0.266 Zcurve 0.252 0.239 0.240 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.543 0.642 0.722 Puniform 0.613 0.860 0.978 MaxLike 0.496 0.503 0.504 Zcurve 0.519 0.518 0.518 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.825 0.913 0.953 Puniform 0.870 0.983 0.999 MaxLike 0.751 0.751 0.751 Zcurve 0.741 0.763 0.779 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.229 0.257 0.307 Puniform 0.279 0.577 0.893 MaxLike 0.220 0.256 0.264 Zcurve 0.241 0.229 0.230 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.548 0.652 0.732 Puniform 0.618 0.870 0.985 MaxLike 0.497 0.501 0.502 Zcurve 0.509 0.504 0.501 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.829 0.917 0.956 Puniform 0.873 0.986 1.000 MaxLike 0.751 0.751 0.750 Zcurve 0.742 0.759 0.771 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.230 0.264 0.316 Puniform 0.280 0.582 0.906 MaxLike 0.221 0.257 0.264 Zcurve 0.235 0.225 0.227 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.552 0.656 0.737 Puniform 0.619 0.873 0.987 MaxLike 0.498 0.500 0.502 Zcurve 0.502 0.495 0.492 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.831 0.919 0.957 Puniform 0.874 0.987 1.000 MaxLike 0.750 0.750 0.750 Zcurve 0.742 0.756 0.765 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.232 0.268 0.320 Puniform 0.279 0.582 0.911 MaxLike 0.221 0.257 0.264 Zcurve 0.230 0.223 0.226 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.555 0.660 0.739 Puniform 0.620 0.875 0.988 MaxLike 0.499 0.500 0.501 Zcurve 0.496 0.490 0.486 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.832 0.920 0.958 Puniform 0.875 0.987 1.000 MaxLike 0.750 0.750 0.750 Zcurve 0.743 0.752 0.759 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.234 0.270 0.324 Puniform 0.280 0.583 0.913 MaxLike 0.221 0.256 0.264 Zcurve 0.229 0.224 0.226 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.557 0.661 0.742 Puniform 0.621 0.876 0.989 MaxLike 0.499 0.500 0.502 Zcurve 0.492 0.487 0.482 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.833 0.920 0.958 Puniform 0.875 0.987 1.000 MaxLike 0.749 0.750 0.750 Zcurve 0.743 0.749 0.754 > > > ########################## 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 0.069 0.086 0.106 Puniform 0.077 0.157 0.134 MaxLike 0.092 0.058 0.049 Zcurve 0.069 0.063 0.060 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.075 0.085 0.086 Puniform 0.075 0.072 0.028 MaxLike 0.090 0.060 0.057 Zcurve 0.070 0.072 0.072 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.041 0.030 0.023 Puniform 0.037 0.013 0.002 MaxLike 0.055 0.047 0.046 Zcurve 0.046 0.039 0.037 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.045 0.059 0.069 Puniform 0.050 0.105 0.080 MaxLike 0.083 0.038 0.033 Zcurve 0.046 0.042 0.040 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.048 0.053 0.052 Puniform 0.048 0.044 0.014 MaxLike 0.062 0.037 0.036 Zcurve 0.048 0.047 0.046 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.026 0.019 0.014 Puniform 0.023 0.007 0.001 MaxLike 0.035 0.030 0.029 Zcurve 0.033 0.028 0.027 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.031 0.042 0.050 Puniform 0.035 0.075 0.055 MaxLike 0.079 0.027 0.026 Zcurve 0.034 0.033 0.031 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.034 0.038 0.037 Puniform 0.034 0.031 0.008 MaxLike 0.044 0.027 0.026 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 0.016 0.005 0.000 MaxLike 0.027 0.022 0.023 Zcurve 0.026 0.022 0.021 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.023 0.030 0.036 Puniform 0.025 0.054 0.038 MaxLike 0.077 0.022 0.021 Zcurve 0.026 0.026 0.025 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.025 0.027 0.026 Puniform 0.024 0.022 0.006 MaxLike 0.027 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 0.011 0.003 0.000 MaxLike 0.019 0.016 0.016 Zcurve 0.020 0.018 0.016 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.016 0.021 0.026 Puniform 0.018 0.038 0.027 MaxLike 0.077 0.020 0.020 Zcurve 0.021 0.022 0.020 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.017 0.019 0.019 Puniform 0.017 0.015 0.004 MaxLike 0.022 0.014 0.014 Zcurve 0.019 0.020 0.019 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.009 0.007 0.005 Puniform 0.008 0.002 0.000 MaxLike 0.013 0.011 0.012 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 0.25 0.25 0.25 Puniform 0.25 0.25 0.25 MaxLike 0.25 0.25 0.25 Zcurve 0.25 0.25 0.25 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.50 0.50 0.50 Puniform 0.50 0.50 0.50 MaxLike 0.50 0.50 0.50 Zcurve 0.50 0.50 0.50 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.75 0.75 0.75 Puniform 0.75 0.75 0.75 MaxLike 0.75 0.75 0.75 Zcurve 0.75 0.75 0.75 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.25 0.25 0.25 Puniform 0.25 0.25 0.25 MaxLike 0.25 0.25 0.25 Zcurve 0.25 0.25 0.25 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.50 0.50 0.50 Puniform 0.50 0.50 0.50 MaxLike 0.50 0.50 0.50 Zcurve 0.50 0.50 0.50 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.75 0.75 0.75 Puniform 0.75 0.75 0.75 MaxLike 0.75 0.75 0.75 Zcurve 0.75 0.75 0.75 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.25 0.25 0.25 Puniform 0.25 0.25 0.25 MaxLike 0.25 0.25 0.25 Zcurve 0.25 0.25 0.25 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.50 0.50 0.50 Puniform 0.50 0.50 0.50 MaxLike 0.50 0.50 0.50 Zcurve 0.50 0.50 0.50 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.75 0.75 0.75 Puniform 0.75 0.75 0.75 MaxLike 0.75 0.75 0.75 Zcurve 0.75 0.75 0.75 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.25 0.25 0.25 Puniform 0.25 0.25 0.25 MaxLike 0.25 0.25 0.25 Zcurve 0.25 0.25 0.25 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.50 0.50 0.50 Puniform 0.50 0.50 0.50 MaxLike 0.50 0.50 0.50 Zcurve 0.50 0.50 0.50 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.75 0.75 0.75 Puniform 0.75 0.75 0.75 MaxLike 0.75 0.75 0.75 Zcurve 0.75 0.75 0.75 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.25 0.25 0.25 Puniform 0.25 0.25 0.25 MaxLike 0.25 0.25 0.25 Zcurve 0.25 0.25 0.25 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.50 0.50 0.50 Puniform 0.50 0.50 0.50 MaxLike 0.50 0.50 0.50 Zcurve 0.50 0.50 0.50 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.75 0.75 0.75 Puniform 0.75 0.75 0.75 MaxLike 0.75 0.75 0.75 Zcurve 0.75 0.75 0.75 > > ###################### 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 -0.020 -0.002 0.045 Puniform 0.031 0.317 0.614 MaxLike -0.030 0.006 0.016 Zcurve 0.002 -0.011 -0.010 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.043 0.142 0.222 Puniform 0.113 0.360 0.478 MaxLike -0.004 0.003 0.004 Zcurve 0.019 0.018 0.018 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.075 0.163 0.203 Puniform 0.120 0.233 0.249 MaxLike 0.001 0.001 0.001 Zcurve -0.009 0.013 0.029 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.021 0.007 0.057 Puniform 0.029 0.327 0.643 MaxLike -0.030 0.006 0.014 Zcurve -0.009 -0.021 -0.020 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.048 0.152 0.232 Puniform 0.118 0.370 0.485 MaxLike -0.003 0.001 0.002 Zcurve 0.009 0.004 0.001 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.079 0.167 0.206 Puniform 0.123 0.236 0.250 MaxLike 0.001 0.001 0.000 Zcurve -0.008 0.009 0.021 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.020 0.014 0.066 Puniform 0.030 0.332 0.656 MaxLike -0.029 0.007 0.014 Zcurve -0.015 -0.025 -0.023 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.052 0.156 0.237 Puniform 0.119 0.373 0.487 MaxLike -0.002 0.000 0.002 Zcurve 0.002 -0.005 -0.008 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.081 0.169 0.207 Puniform 0.124 0.237 0.250 MaxLike 0.000 0.000 0.000 Zcurve -0.008 0.006 0.015 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.018 0.018 0.070 Puniform 0.029 0.332 0.661 MaxLike -0.029 0.007 0.014 Zcurve -0.020 -0.027 -0.024 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.055 0.160 0.239 Puniform 0.120 0.375 0.488 MaxLike -0.001 0.000 0.001 Zcurve -0.004 -0.010 -0.014 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.082 0.170 0.208 Puniform 0.125 0.237 0.250 MaxLike 0.000 0.000 0.000 Zcurve -0.007 0.002 0.009 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.016 0.020 0.074 Puniform 0.030 0.333 0.663 MaxLike -0.029 0.006 0.014 Zcurve -0.021 -0.026 -0.024 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.057 0.161 0.242 Puniform 0.121 0.376 0.489 MaxLike -0.001 0.000 0.002 Zcurve -0.008 -0.013 -0.018 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.083 0.170 0.208 Puniform 0.125 0.237 0.250 MaxLike -0.001 0.000 0.000 Zcurve -0.007 -0.001 0.004 > > ########################## 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 -29.32 -2.20 43.41 Puniform 39.58 203.87 462.75 MaxLike -34.01 10.78 32.62 Zcurve 2.33 -16.87 -16.70 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 57.58 169.06 260.08 Puniform 151.76 503.91 1697.40 MaxLike -4.70 4.58 6.72 Zcurve 27.47 25.35 24.60 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 182.44 540.98 908.22 Puniform 327.49 1827.39 13339.64 MaxLike 2.76 1.64 0.85 Zcurve -19.38 35.07 79.39 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -47.71 12.20 83.68 Puniform 60.29 314.55 813.32 MaxLike -36.06 17.06 43.45 Zcurve -20.48 -49.79 -50.58 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 101.82 290.51 448.45 Puniform 249.93 848.48 3582.48 MaxLike -4.33 3.47 5.94 Zcurve 19.73 9.05 1.99 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 308.34 894.76 1525.65 Puniform 541.48 3234.47 47099.82 MaxLike 2.13 1.83 0.85 Zcurve -23.97 33.61 80.20 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -63.45 33.88 132.20 Puniform 85.50 446.23 1212.95 MaxLike -36.73 24.89 54.31 Zcurve -44.59 -76.87 -73.53 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 152.81 421.00 646.31 Puniform 353.51 1213.80 5828.06 MaxLike -3.90 0.93 6.78 Zcurve 5.88 -13.54 -25.65 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 453.33 1301.62 2232.15 Puniform 779.19 4758.65 90185.64 MaxLike 0.05 0.62 -0.34 Zcurve -29.14 26.67 72.10 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -80.65 60.61 198.85 Puniform 117.28 620.93 1741.11 MaxLike -37.86 30.36 66.05 Zcurve -75.86 -103.65 -97.68 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 224.80 607.63 925.65 Puniform 501.14 1724.38 8822.28 MaxLike -2.31 0.23 7.68 Zcurve -13.79 -38.02 -57.73 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 645.46 1864.15 3235.86 Puniform 1109.94 6987.58 159164.39 MaxLike -0.29 0.97 -0.19 Zcurve -35.13 13.35 55.40 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -98.24 96.55 290.64 Puniform 169.93 887.69 2518.66 MaxLike -38.59 32.55 70.38 Zcurve -104.63 -120.06 -117.67 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 332.80 880.98 1316.25 Puniform 715.31 2503.54 12939.78 MaxLike -3.27 -1.66 10.80 Zcurve -40.44 -67.07 -94.35 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 929.46 2625.45 4612.24 Puniform 1594.85 10104.49 252120.81 MaxLike -4.66 0.48 -0.41 Zcurve -43.90 -5.52 30.62 > > # 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 0.490 0.666 0.815 0.920 0.983 Puniform 0.473 0.620 0.703 0.796 0.874 MaxLike 0.536 0.712 0.808 0.852 0.857 Zcurve 0.526 0.709 0.815 0.873 0.931 , , PopMeanPower = 0.5, SD_EffectSize = 0.1 Nstudies Method 100 250 500 1000 2000 Pcurve 0.411 0.480 0.473 0.424 0.347 Puniform 0.178 0.081 0.024 0.002 0.000 MaxLike 0.540 0.754 0.904 0.978 0.996 Zcurve 0.492 0.693 0.846 0.938 0.986 , , PopMeanPower = 0.75, SD_EffectSize = 0.1 Nstudies Method 100 250 500 1000 2000 Pcurve 0.242 0.128 0.053 0.010 0.000 Puniform 0.043 0.003 0.000 0.000 0.000 MaxLike 0.656 0.871 0.967 0.997 1.000 Zcurve 0.730 0.863 0.936 0.980 0.997 , , PopMeanPower = 0.25, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.424 0.597 0.744 0.846 0.921 Puniform 0.039 0.004 0.000 0.000 0.000 MaxLike 0.679 0.863 0.955 0.987 0.992 Zcurve 0.550 0.687 0.749 0.810 0.874 , , PopMeanPower = 0.5, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.126 0.034 0.005 0.000 0.000 Puniform 0.001 0.000 0.000 0.000 0.000 MaxLike 0.600 0.826 0.942 0.992 0.999 Zcurve 0.483 0.705 0.846 0.928 0.968 , , PopMeanPower = 0.75, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.003 0.000 0.000 0.000 0.000 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.717 0.917 0.985 0.999 1.000 Zcurve 0.772 0.912 0.973 0.996 1.000 , , PopMeanPower = 0.25, SD_EffectSize = 0.3 Nstudies Method 100 250 500 1000 2000 Pcurve 0.338 0.422 0.379 0.287 0.179 Puniform 0.001 0.000 0.000 0.000 0.000 MaxLike 0.706 0.885 0.955 0.989 0.995 Zcurve 0.586 0.721 0.794 0.856 0.924 , , PopMeanPower = 0.5, SD_EffectSize = 0.3 Nstudies Method 100 250 500 1000 2000 Pcurve 0.033 0.001 0.000 0.000 0.000 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.622 0.842 0.948 0.993 0.999 Zcurve 0.488 0.715 0.852 0.917 0.961 , , 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 0.733 0.919 0.984 0.999 1.000 Zcurve 0.661 0.853 0.956 0.996 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 11.708721 2 Puniform 28.919130 3 MaxLike 2.659198 4 Zcurve 3.037223 > > 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 5.82 6.95 9.15 Puniform 6.50 31.91 61.40 MaxLike 6.94 4.30 3.90 Zcurve 5.51 5.18 4.86 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 7.06 14.67 22.25 Puniform 11.89 36.02 47.81 MaxLike 6.02 4.75 4.54 Zcurve 5.86 5.98 5.98 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 7.71 16.30 20.28 Puniform 12.05 23.31 24.92 MaxLike 4.20 3.72 3.62 Zcurve 3.65 3.31 4.00 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 4.02 4.73 7.19 Puniform 4.60 32.69 64.33 MaxLike 5.53 2.76 2.58 Zcurve 3.76 3.87 3.62 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.68 15.23 23.24 Puniform 11.86 36.96 48.48 MaxLike 3.78 2.94 2.86 Zcurve 3.90 3.79 3.71 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 7.92 16.73 20.60 Puniform 12.33 23.57 24.96 MaxLike 2.68 2.35 2.30 Zcurve 2.72 2.40 2.86 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 3.01 3.52 6.98 Puniform 3.75 33.18 65.55 MaxLike 4.81 1.97 2.05 Zcurve 3.01 3.44 3.22 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.37 15.62 23.74 Puniform 11.91 37.28 48.72 MaxLike 2.60 2.12 2.06 Zcurve 2.80 2.84 2.76 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.09 16.88 20.71 Puniform 12.42 23.65 24.97 MaxLike 1.91 1.66 1.66 Zcurve 2.15 1.80 2.08 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 2.40 2.79 7.11 Puniform 3.19 33.19 66.09 MaxLike 4.30 1.52 1.68 Zcurve 2.72 3.20 2.95 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.48 15.96 23.95 Puniform 12.00 37.46 48.81 MaxLike 1.77 1.52 1.50 Zcurve 2.14 2.24 2.31 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.23 16.98 20.79 Puniform 12.50 23.70 24.98 MaxLike 1.38 1.19 1.15 Zcurve 1.73 1.41 1.46 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 1.89 2.40 7.36 Puniform 3.02 33.31 66.32 MaxLike 4.13 1.24 1.54 Zcurve 2.53 2.92 2.68 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.69 16.14 24.15 Puniform 12.07 37.57 48.87 MaxLike 1.27 1.11 1.10 Zcurve 1.69 1.99 2.15 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.32 17.03 20.82 Puniform 12.54 23.72 24.98 MaxLike 0.99 0.86 0.81 Zcurve 1.38 1.09 1.00 > > > ################################################################################## > # 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 -12.47 -16.85 8.82 Puniform 0.00 -5.94 20.89 MaxLike 0.00 0.00 21.62 SD_EffectSize = 0.1 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -87.57 15.14 31.79 Puniform 0.00 61.01 87.63 MaxLike 0.00 0.00 2.61 SD_EffectSize = 0.1 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -172.84 70.14 79.50 Puniform 0.00 151.27 166.99 MaxLike 0.00 0.00 18.55 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -13.05 -22.13 10.13 Puniform 0.00 -12.79 20.96 MaxLike 0.00 0.00 25.83 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -183.3 33.36 49.02 Puniform 0.0 114.28 154.20 MaxLike 0.0 0.00 -2.55 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -292.45 151.61 142.56 Puniform 0.00 293.10 290.87 MaxLike 0.00 0.00 -1.66 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -19.48 -26.13 -0.16 Puniform 0.00 -14.59 20.34 MaxLike 0.00 0.00 25.59 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -302.76 60.81 74.22 Puniform 0.00 184.49 232.14 MaxLike 0.00 0.00 -5.86 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -402.32 227.29 216.47 Puniform 0.00 406.10 418.40 MaxLike 0.00 0.00 -11.25 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -24.49 -27.44 -17.59 Puniform 0.00 -15.40 14.45 MaxLike 0.00 0.00 22.42 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -447.28 118.07 109.69 Puniform 0.00 317.58 327.42 MaxLike 0.00 0.00 -18.48 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -551.48 376.45 312.45 Puniform 0.00 651.23 582.18 MaxLike 0.00 0.00 -24.20 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -42.8 -31.51 -39.29 Puniform 0.0 -15.27 17.91 MaxLike 0.0 0.00 22.18 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -586.61 176.06 164.64 Puniform 0.00 431.52 448.05 MaxLike 0.00 0.00 -21.82 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -750.68 573.91 442.27 Puniform 0.00 977.00 808.37 MaxLike 0.00 0.00 -34.81 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -158.36 61.29 37.07 Puniform 0.00 175.19 166.11 MaxLike 0.00 0.00 -21.98 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -331.55 124.95 116.42 Puniform 0.00 379.53 371.99 MaxLike 0.00 0.00 -43.12 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -289.31 280.66 360.65 Puniform 0.00 603.58 754.29 MaxLike 0.00 0.00 17.75 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -265.71 62.71 19.81 Puniform 0.00 280.76 252.21 MaxLike 0.00 0.00 -31.91 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -536.28 217.55 198.08 Puniform 0.00 681.90 641.72 MaxLike 0.00 0.00 -44.60 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -447.77 519.84 616.31 Puniform 0.00 1057.19 1148.47 MaxLike 0.00 0.00 -2.87 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -411.43 64.11 2.11 Puniform 0.00 416.31 353.90 MaxLike 0.00 0.00 -49.48 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -741.42 329.88 279.57 Puniform 0.00 997.94 885.16 MaxLike 0.00 0.00 -42.92 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -642.67 745.94 871.99 Puniform 0.00 1390.19 1532.24 MaxLike 0.00 0.00 -9.48 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -627.09 60.51 -13.03 Puniform 0.00 587.68 482.76 MaxLike 0.00 0.00 -62.55 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -1036.46 499.17 389.91 Puniform 0.00 1438.93 1204.68 MaxLike 0.00 0.00 -44.93 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -896.43 1074.40 1155.18 Puniform 0.00 1910.95 2015.55 MaxLike 0.00 0.00 -18.35 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -967.2 57.49 -19.93 Puniform 0.0 812.69 672.85 MaxLike 0.0 0.00 -67.55 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -1460.7 734.41 523.46 Puniform 0.0 2096.08 1603.21 MaxLike 0.0 0.00 -60.36 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -1255.45 1745.39 1473.72 Puniform 0.00 3365.82 2664.66 MaxLike 0.00 0.00 -30.04 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -389.99 95.47 60.84 Puniform 0.00 425.59 393.25 MaxLike 0.00 0.00 -25.53 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -352.35 198.76 190.84 Puniform 0.00 953.79 818.27 MaxLike 0.00 0.00 -54.97 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -215.15 426.74 646.91 Puniform 0.00 754.73 849.05 MaxLike 0.00 0.00 -13.67 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -753.89 101.48 55.13 Puniform 0.00 773.71 677.19 MaxLike 0.00 0.00 -30.21 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -544.84 363.78 330.96 Puniform 0.00 1747.09 1446.51 MaxLike 0.00 0.00 -45.33 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -329.22 777.59 1053.56 Puniform 0.00 1300.77 1195.81 MaxLike 0.00 0.00 -28.62 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -1169.22 127.59 67.42 Puniform 0.00 1166.72 980.36 MaxLike 0.00 0.00 -36.46 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -753.71 549.93 452.20 Puniform 0.00 2550.04 2005.10 MaxLike 0.00 0.00 -40.13 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -466.05 996.12 1418.48 Puniform 0.00 1456.20 1575.46 MaxLike 0.00 0.00 -24.61 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -1732.37 173.44 94.23 Puniform 0.00 1694.27 1361.89 MaxLike 0.00 0.00 -44.92 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -1059.84 794.33 588.10 Puniform 0.00 3509.57 2497.54 MaxLike 0.00 0.00 -45.28 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -660.64 1511.64 1924.08 Puniform 0.00 2160.42 2211.52 MaxLike 0.00 0.00 -25.96 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -2420.76 226.55 141.13 Puniform 0.00 2228.55 1888.30 MaxLike 0.00 0.00 -43.17 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -1484.33 1172.52 775.97 Puniform 0.00 4867.13 3043.08 MaxLike 0.00 0.00 -64.49 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -931.82 1912.25 2490.82 Puniform 0.00 2594.86 3190.14 MaxLike 0.00 0.00 -19.59 > > cat("\nTotal number of significant comparisons: \n") Total number of significant comparisons: > print(sum(keepscore)) [1] 264 > > 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 5 4 54 Puniform 0 0 5 0 5 MaxLike 40 40 0 34 114 Zcurve 39 45 7 0 91 > > ###############################################################################