# Study4.5.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("Study4.5.Data.txt") # Numerator df: .1=1df, .3=3df, .5=5df Read 4093740 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 10108 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 0.2015612 0.2131542 0.2013781 0.04950733 0.2279888 [2,] 1 0.1 100 0.50 0.5282570 0.6033826 0.6400402 0.54945620 0.5207212 [3,] 1 0.1 100 0.75 0.7559727 0.8327545 0.9035344 0.75364930 0.7620908 [4,] 1 0.1 250 0.25 0.2599075 0.2594262 0.3045927 0.24751720 0.2488253 [5,] 1 0.1 250 0.50 0.4868753 0.6105112 0.6673294 0.54861190 0.5267055 [6,] 1 0.1 250 0.75 0.7558263 0.8497307 0.8891075 0.76949250 0.7431604 Simulation SD_EffectSize Nstudies PopMeanPower SampleMeanPower Pcurve Puniform MaxLike Zcurve [454855,] 36 0.3 1000 0.25 0.2475196 0.3172095 0.8757080 0.2580358 0.2142192 [454856,] 36 0.3 1000 0.50 0.4820124 0.7292819 0.9791740 0.4998046 0.4753013 [454857,] 36 0.3 1000 0.75 0.7662786 0.9635578 0.9998948 0.7696717 0.8160973 [454858,] 36 0.3 2000 0.25 0.2377813 0.3125758 0.8649105 0.2478926 0.1950752 [454859,] 36 0.3 2000 0.50 0.4998253 0.7258125 0.9801077 0.4932342 0.4779134 [454860,] 36 0.3 2000 0.75 0.7500496 0.9548505 0.9995739 0.7559125 0.7641793 > 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 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10108 10108 10108 Puniform 10108 10108 10108 MaxLike 10108 10108 10108 Zcurve 10108 10108 10108 > > ###################### 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 0.233 0.247 0.292 Puniform 0.274 0.510 0.832 MaxLike 0.217 0.251 0.260 Zcurve 0.247 0.239 0.237 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.547 0.631 0.711 Puniform 0.624 0.837 0.968 MaxLike 0.492 0.502 0.502 Zcurve 0.514 0.514 0.514 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.828 0.908 0.949 Puniform 0.876 0.979 0.999 MaxLike 0.751 0.751 0.751 Zcurve 0.739 0.760 0.776 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.232 0.254 0.307 Puniform 0.274 0.518 0.861 MaxLike 0.217 0.253 0.260 Zcurve 0.236 0.228 0.230 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.551 0.642 0.723 Puniform 0.626 0.847 0.977 MaxLike 0.493 0.500 0.502 Zcurve 0.502 0.500 0.499 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.833 0.912 0.953 Puniform 0.880 0.982 0.999 MaxLike 0.750 0.750 0.750 Zcurve 0.740 0.755 0.768 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.233 0.260 0.314 Puniform 0.274 0.519 0.870 MaxLike 0.218 0.253 0.259 Zcurve 0.231 0.224 0.226 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.555 0.647 0.727 Puniform 0.628 0.850 0.979 MaxLike 0.493 0.500 0.501 Zcurve 0.495 0.493 0.490 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.835 0.914 0.954 Puniform 0.881 0.983 1.000 MaxLike 0.749 0.750 0.750 Zcurve 0.739 0.752 0.762 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.234 0.263 0.318 Puniform 0.274 0.520 0.876 MaxLike 0.217 0.252 0.259 Zcurve 0.227 0.221 0.224 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.557 0.650 0.730 Puniform 0.628 0.851 0.980 MaxLike 0.496 0.499 0.501 Zcurve 0.489 0.486 0.484 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.836 0.914 0.955 Puniform 0.881 0.983 1.000 MaxLike 0.748 0.750 0.750 Zcurve 0.739 0.749 0.756 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.236 0.267 0.322 Puniform 0.274 0.521 0.879 MaxLike 0.215 0.253 0.259 Zcurve 0.224 0.222 0.225 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.560 0.652 0.732 Puniform 0.629 0.852 0.981 MaxLike 0.497 0.499 0.501 Zcurve 0.485 0.483 0.480 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.837 0.915 0.955 Puniform 0.882 0.983 1.000 MaxLike 0.748 0.750 0.750 Zcurve 0.739 0.746 0.751 > > > ########################## 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 0.068 0.084 0.103 Puniform 0.075 0.149 0.144 MaxLike 0.092 0.064 0.048 Zcurve 0.069 0.064 0.059 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.075 0.084 0.085 Puniform 0.077 0.076 0.035 MaxLike 0.101 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 0.032 0.023 Puniform 0.036 0.015 0.002 MaxLike 0.054 0.046 0.045 Zcurve 0.046 0.039 0.037 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.044 0.056 0.069 Puniform 0.048 0.097 0.089 MaxLike 0.084 0.044 0.033 Zcurve 0.045 0.043 0.040 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.048 0.052 0.053 Puniform 0.048 0.046 0.018 MaxLike 0.072 0.038 0.037 Zcurve 0.048 0.048 0.047 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.025 0.019 0.014 Puniform 0.022 0.009 0.001 MaxLike 0.033 0.029 0.029 Zcurve 0.033 0.029 0.027 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.031 0.040 0.049 Puniform 0.034 0.069 0.062 MaxLike 0.081 0.032 0.023 Zcurve 0.034 0.032 0.030 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.035 0.037 0.037 Puniform 0.035 0.032 0.012 MaxLike 0.061 0.028 0.027 Zcurve 0.036 0.035 0.034 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.018 0.013 0.010 Puniform 0.016 0.006 0.000 MaxLike 0.024 0.021 0.021 Zcurve 0.026 0.022 0.021 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.022 0.029 0.035 Puniform 0.024 0.050 0.044 MaxLike 0.079 0.026 0.022 Zcurve 0.026 0.026 0.025 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.025 0.026 0.026 Puniform 0.025 0.023 0.008 MaxLike 0.039 0.021 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 0.007 Puniform 0.011 0.004 0.000 MaxLike 0.018 0.015 0.014 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 0.025 Puniform 0.017 0.035 0.031 MaxLike 0.080 0.023 0.019 Zcurve 0.020 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 0.016 0.005 MaxLike 0.032 0.018 0.016 Zcurve 0.020 0.021 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 0.003 0.000 MaxLike 0.015 0.011 0.013 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 0.499 0.500 0.500 Puniform 0.499 0.500 0.500 MaxLike 0.499 0.500 0.500 Zcurve 0.499 0.500 0.500 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.748 0.750 0.750 Puniform 0.748 0.750 0.750 MaxLike 0.748 0.750 0.750 Zcurve 0.748 0.750 0.750 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.250 0.251 0.250 Puniform 0.250 0.251 0.250 MaxLike 0.250 0.251 0.250 Zcurve 0.250 0.251 0.250 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.499 0.500 0.500 Puniform 0.499 0.500 0.500 MaxLike 0.499 0.500 0.500 Zcurve 0.499 0.500 0.500 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.749 0.750 0.750 Puniform 0.749 0.750 0.750 MaxLike 0.749 0.750 0.750 Zcurve 0.749 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 0.499 0.500 0.500 Puniform 0.499 0.500 0.500 MaxLike 0.499 0.500 0.500 Zcurve 0.499 0.500 0.500 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.749 0.750 0.750 Puniform 0.749 0.750 0.750 MaxLike 0.749 0.750 0.750 Zcurve 0.749 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 0.499 0.500 0.500 Puniform 0.499 0.500 0.500 MaxLike 0.499 0.500 0.500 Zcurve 0.499 0.500 0.500 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.748 0.750 0.750 Puniform 0.748 0.750 0.750 MaxLike 0.748 0.750 0.750 Zcurve 0.748 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 0.499 0.500 0.500 Puniform 0.499 0.500 0.500 MaxLike 0.499 0.500 0.500 Zcurve 0.499 0.500 0.500 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.749 0.750 0.750 Puniform 0.749 0.750 0.750 MaxLike 0.749 0.750 0.750 Zcurve 0.749 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 -0.017 -0.003 0.042 Puniform 0.024 0.260 0.582 MaxLike -0.033 0.001 0.010 Zcurve -0.003 -0.011 -0.013 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.047 0.131 0.211 Puniform 0.124 0.337 0.468 MaxLike -0.008 0.002 0.002 Zcurve 0.014 0.014 0.014 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.078 0.158 0.199 Puniform 0.126 0.229 0.249 MaxLike 0.001 0.001 0.001 Zcurve -0.011 0.010 0.026 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.018 0.004 0.057 Puniform 0.024 0.268 0.611 MaxLike -0.033 0.003 0.010 Zcurve -0.014 -0.022 -0.020 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.051 0.142 0.223 Puniform 0.126 0.347 0.477 MaxLike -0.007 0.000 0.002 Zcurve 0.002 0.000 -0.001 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.083 0.162 0.203 Puniform 0.130 0.232 0.249 MaxLike 0.000 0.000 0.000 Zcurve -0.010 0.005 0.018 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.017 0.010 0.064 Puniform 0.024 0.269 0.620 MaxLike -0.032 0.003 0.009 Zcurve -0.019 -0.026 -0.024 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.055 0.147 0.227 Puniform 0.128 0.350 0.479 MaxLike -0.007 0.000 0.001 Zcurve -0.005 -0.007 -0.010 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.085 0.164 0.204 Puniform 0.131 0.233 0.250 MaxLike -0.001 0.000 0.000 Zcurve -0.011 0.002 0.012 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.016 0.013 0.068 Puniform 0.024 0.270 0.626 MaxLike -0.033 0.002 0.009 Zcurve -0.023 -0.029 -0.026 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.057 0.150 0.230 Puniform 0.128 0.351 0.480 MaxLike -0.004 -0.001 0.001 Zcurve -0.011 -0.014 -0.016 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.086 0.164 0.205 Puniform 0.131 0.233 0.250 MaxLike -0.002 0.000 0.000 Zcurve -0.011 -0.001 0.006 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.014 0.017 0.072 Puniform 0.024 0.271 0.629 MaxLike -0.035 0.003 0.009 Zcurve -0.026 -0.028 -0.025 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.060 0.152 0.232 Puniform 0.129 0.352 0.481 MaxLike -0.003 -0.001 0.001 Zcurve -0.015 -0.017 -0.020 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.087 0.165 0.205 Puniform 0.132 0.233 0.250 MaxLike -0.002 0.000 0.000 Zcurve -0.011 -0.004 0.001 > > ########################## 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 -25.99 -4.06 41.30 Puniform 31.99 175.61 407.52 MaxLike -36.16 0.49 21.86 Zcurve -4.66 -18.59 -20.65 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 64.49 156.79 247.98 Puniform 164.21 444.03 1332.40 MaxLike -7.15 4.00 3.77 Zcurve 21.63 20.70 19.70 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 196.07 495.08 859.87 Puniform 355.46 1508.86 10499.52 MaxLike 4.82 2.12 0.49 Zcurve -20.14 24.12 69.42 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -42.95 7.14 83.24 Puniform 50.00 277.75 687.77 MaxLike -39.93 4.71 29.86 Zcurve -31.06 -51.98 -51.53 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 108.97 273.97 421.30 Puniform 265.38 761.70 2674.02 MaxLike -7.83 1.19 4.99 Zcurve 7.53 1.28 -2.14 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 334.42 842.50 1457.77 Puniform 592.30 2714.02 30242.12 MaxLike 3.31 1.67 0.25 Zcurve -27.19 19.18 66.88 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -55.95 24.38 131.18 Puniform 71.56 389.82 1003.53 MaxLike -40.18 8.13 37.21 Zcurve -58.45 -81.85 -79.07 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 162.27 402.45 616.94 Puniform 373.01 1082.32 4102.99 MaxLike -8.57 -0.98 4.72 Zcurve -10.41 -21.43 -30.66 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 484.67 1231.96 2074.82 Puniform 847.95 4063.39 58097.67 MaxLike 2.89 1.53 1.53 Zcurve -35.12 9.21 57.25 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -72.31 46.72 194.57 Puniform 100.73 542.72 1428.56 MaxLike -41.42 9.16 40.22 Zcurve -90.72 -111.82 -103.68 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 240.61 577.77 875.03 Puniform 530.59 1552.61 6052.60 MaxLike -6.51 -4.43 5.53 Zcurve -36.45 -51.66 -64.33 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 685.74 1750.85 3050.28 Puniform 1192.99 5776.65 97685.85 MaxLike -0.83 -0.92 0.75 Zcurve -48.72 -7.38 37.85 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -89.65 81.15 289.19 Puniform 138.93 771.90 2062.50 MaxLike -43.25 12.75 45.11 Zcurve -127.65 -130.08 -122.86 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 351.63 812.69 1278.68 Puniform 760.77 2151.21 9045.10 MaxLike -6.73 -5.24 6.86 Zcurve -69.99 -83.29 -103.94 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 1000.66 2489.76 4335.06 Puniform 1738.31 8393.24 146789.96 MaxLike -1.70 1.34 -0.84 Zcurve -61.77 -29.79 5.72 > > # 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 0.493 0.700 0.831 0.938 0.989 Puniform 0.480 0.659 0.775 0.863 0.939 MaxLike 0.514 0.691 0.785 0.828 0.832 Zcurve 0.525 0.700 0.792 0.852 0.895 , , PopMeanPower = 0.5, SD_EffectSize = 0.1 Nstudies Method 100 250 500 1000 2000 Pcurve 0.397 0.461 0.441 0.379 0.288 Puniform 0.151 0.060 0.014 0.001 0.000 MaxLike 0.541 0.753 0.896 0.978 0.991 Zcurve 0.503 0.705 0.836 0.920 0.961 , , PopMeanPower = 0.75, SD_EffectSize = 0.1 Nstudies Method 100 250 500 1000 2000 Pcurve 0.224 0.103 0.033 0.005 0.000 Puniform 0.030 0.001 0.000 0.000 0.000 MaxLike 0.667 0.878 0.968 0.998 0.999 Zcurve 0.733 0.854 0.926 0.973 0.994 , , PopMeanPower = 0.25, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.430 0.630 0.776 0.881 0.945 Puniform 0.070 0.010 0.001 0.000 0.000 MaxLike 0.644 0.853 0.946 0.981 0.985 Zcurve 0.542 0.677 0.741 0.775 0.835 , , PopMeanPower = 0.5, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.152 0.045 0.006 0.000 0.000 Puniform 0.002 0.000 0.000 0.000 0.000 MaxLike 0.593 0.817 0.940 0.988 0.998 Zcurve 0.494 0.698 0.836 0.908 0.949 , , PopMeanPower = 0.75, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.006 0.000 0.000 0.000 0.000 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.722 0.913 0.985 0.999 1.000 Zcurve 0.789 0.917 0.972 0.995 1.000 , , PopMeanPower = 0.25, SD_EffectSize = 0.3 Nstudies Method 100 250 500 1000 2000 Pcurve 0.361 0.415 0.389 0.304 0.187 Puniform 0.003 0.000 0.000 0.000 0.000 MaxLike 0.714 0.886 0.966 0.990 0.993 Zcurve 0.580 0.709 0.787 0.844 0.910 , , PopMeanPower = 0.5, SD_EffectSize = 0.3 Nstudies Method 100 250 500 1000 2000 Pcurve 0.040 0.003 0.000 0.000 0.000 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.621 0.828 0.945 0.990 0.997 Zcurve 0.490 0.707 0.845 0.907 0.946 , , 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 0.732 0.919 0.984 1.000 1.000 Zcurve 0.688 0.874 0.970 0.997 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 11.403315 2 Puniform 27.592027 3 MaxLike 2.733732 4 Zcurve 3.092625 > > 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 5.74 6.81 8.73 Puniform 6.22 26.33 58.17 MaxLike 7.11 4.68 3.83 Zcurve 5.52 5.22 4.87 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 7.28 13.68 21.20 Puniform 12.82 33.66 46.82 MaxLike 6.38 4.82 4.55 Zcurve 5.75 5.89 5.94 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.01 15.78 19.94 Puniform 12.61 22.89 24.88 MaxLike 4.14 3.68 3.60 Zcurve 3.67 3.24 3.84 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 3.83 4.46 7.20 Puniform 4.23 26.83 61.06 MaxLike 5.80 2.97 2.56 Zcurve 3.80 3.95 3.69 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.87 14.22 22.26 Puniform 12.65 34.67 47.67 MaxLike 4.03 3.06 2.94 Zcurve 3.84 3.83 3.76 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.28 16.20 20.28 Puniform 12.98 23.17 24.94 MaxLike 2.59 2.34 2.30 Zcurve 2.74 2.32 2.69 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 2.91 3.29 6.81 Puniform 3.32 26.89 62.05 MaxLike 5.10 2.14 1.87 Zcurve 3.17 3.51 3.25 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.66 14.73 22.72 Puniform 12.76 34.97 47.91 MaxLike 2.96 2.18 2.07 Zcurve 2.88 2.84 2.81 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.50 16.38 20.39 Puniform 13.12 23.26 24.95 MaxLike 1.89 1.65 1.64 Zcurve 2.26 1.79 1.97 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 2.22 2.53 6.91 Puniform 2.78 27.00 62.57 MaxLike 4.65 1.63 1.50 Zcurve 2.89 3.41 3.04 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.75 14.97 22.98 Puniform 12.84 35.08 48.04 MaxLike 1.91 1.61 1.52 Zcurve 2.28 2.39 2.44 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.56 16.44 20.46 Puniform 13.11 23.30 24.96 MaxLike 1.37 1.18 1.15 Zcurve 1.87 1.41 1.38 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 1.77 2.14 7.23 Puniform 2.48 27.09 62.89 MaxLike 4.57 1.34 1.26 Zcurve 2.82 3.11 2.79 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.98 15.16 23.20 Puniform 12.94 35.17 48.12 MaxLike 1.41 1.22 1.12 Zcurve 2.03 2.21 2.33 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.66 16.51 20.50 Puniform 13.17 23.32 24.96 MaxLike 1.02 0.85 0.82 Zcurve 1.56 1.17 0.99 > > > ################################################################################## > # 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 -9.72 -20.75 6.51 Puniform 0.00 -12.47 15.43 MaxLike 0.00 0.00 24.09 SD_EffectSize = 0.1 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -97.61 10.96 36.04 Puniform 0.00 59.07 94.49 MaxLike 0.00 0.00 8.66 SD_EffectSize = 0.1 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -186.13 75.35 81.99 Puniform 0.00 163.76 177.01 MaxLike 0.00 0.00 15.63 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -10.28 -28.35 1.11 Puniform 0.00 -21.38 11.21 MaxLike 0.00 0.00 28.41 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -198.8 26.87 48.74 Puniform 0.0 106.54 159.35 MaxLike 0.0 0.00 3.28 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -303.6 167.26 146.57 Puniform 0.0 331.78 306.96 MaxLike 0.0 0.00 -6.89 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -12.13 -30.86 -12.01 Puniform 0.00 -24.05 4.36 MaxLike 0.00 0.00 26.64 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -320.34 42.74 70.38 Puniform 0.00 144.84 229.78 MaxLike 0.00 0.00 1.59 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -418.46 266.39 217.59 Puniform 0.00 493.19 433.54 MaxLike 0.00 0.00 -20.44 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -18.99 -33.57 -35.64 Puniform 0.00 -25.15 -3.59 MaxLike 0.00 0.00 23.92 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -470.75 89.10 102.33 Puniform 0.00 249.19 318.63 MaxLike 0.00 0.00 -10.72 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -572.1 381.4 297.10 Puniform 0.0 679.9 576.17 MaxLike 0.0 0.0 -32.70 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -29.34 -37.57 -63.50 Puniform 0.00 -27.50 -12.45 MaxLike 0.00 0.00 23.05 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -630.32 131.69 142.76 Puniform 0.00 331.78 415.90 MaxLike 0.00 0.00 -20.68 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -790.55 531.35 412.30 Puniform 0.00 908.43 785.07 MaxLike 0.00 0.00 -39.87 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -131.46 45.83 34.68 Puniform 0.00 142.40 138.55 MaxLike 0.00 0.00 -12.52 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -306.52 112.94 103.32 Puniform 0.00 334.29 325.60 MaxLike 0.00 0.00 -38.75 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -287.89 262.45 312.82 Puniform 0.00 583.40 683.35 MaxLike 0.00 0.00 21.45 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -226.88 42.64 12.21 Puniform 0.00 232.60 212.74 MaxLike 0.00 0.00 -25.76 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -508.52 198.31 176.28 Puniform 0.00 610.41 568.61 MaxLike 0.00 0.00 -38.35 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -456.57 507.36 550.24 Puniform 0.00 1056.20 1086.56 MaxLike 0.00 0.00 1.38 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -348.09 42.98 -6.18 Puniform 0.00 337.58 292.91 MaxLike 0.00 0.00 -43.20 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -706.64 304.69 257.66 Puniform 0.00 876.27 791.10 MaxLike 0.00 0.00 -34.54 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -647.38 786.87 763.74 Puniform 0.00 1572.80 1449.62 MaxLike 0.00 0.00 -11.79 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -531.37 38.12 -28.77 Puniform 0.00 472.25 397.59 MaxLike 0.00 0.00 -63.39 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -993.67 445.55 342.82 Puniform 0.00 1253.56 1041.00 MaxLike 0.00 0.00 -43.11 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -910.21 1137.46 996.91 Puniform 0.00 2241.05 1885.10 MaxLike 0.00 0.00 -22.69 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -819.25 35.60 -38.33 Puniform 0.00 651.09 551.15 MaxLike 0.00 0.00 -67.60 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -1368.54 598.02 448.41 Puniform 0.00 1595.53 1325.45 MaxLike 0.00 0.00 -53.67 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -1283.3 1679.17 1248.28 Puniform 0.0 3190.11 2374.07 MaxLike 0.0 0.00 -37.29 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -347.96 91.64 55.26 Puniform 0.00 371.05 347.01 MaxLike 0.00 0.00 -30.33 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -368.58 186.96 177.05 Puniform 0.00 826.22 736.26 MaxLike 0.00 0.00 -53.78 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -222.93 419.57 605.06 Puniform 0.00 782.06 864.43 MaxLike 0.00 0.00 -9.51 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -653.77 101.94 54.37 Puniform 0.00 650.18 579.06 MaxLike 0.00 0.00 -34.83 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -560.02 336.60 301.40 Puniform 0.00 1554.66 1286.56 MaxLike 0.00 0.00 -43.77 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -344.38 743.96 979.39 Puniform 0.00 1254.13 1215.02 MaxLike 0.00 0.00 -21.05 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -1017.46 127.79 63.99 Puniform 0.00 971.33 823.78 MaxLike 0.00 0.00 -49.09 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -787.09 517.83 419.82 Puniform 0.00 2245.01 1787.76 MaxLike 0.00 0.00 -38.86 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -474.12 1121.79 1315.79 Puniform 0.00 1880.04 1646.27 MaxLike 0.00 0.00 -26.46 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -1472.49 160.78 87.77 Puniform 0.00 1344.81 1142.84 MaxLike 0.00 0.00 -55.33 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -1093.76 752.62 541.50 Puniform 0.00 3238.89 2207.31 MaxLike 0.00 0.00 -51.07 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -683.48 1718.56 1765.69 Puniform 0.00 2777.58 2299.64 MaxLike 0.00 0.00 -26.19 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -2122.35 226.87 135.45 Puniform 0.00 1866.89 1587.06 MaxLike 0.00 0.00 -61.15 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -1564.94 1049.16 724.59 Puniform 0.00 3757.09 2737.40 MaxLike 0.00 0.00 -67.07 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -961.37 1766.00 2199.80 Puniform 0.00 2414.24 3190.73 MaxLike 0.00 0.00 -16.53 > > 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 6 56 Puniform 0 0 5 1 6 MaxLike 40 40 0 34 114 Zcurve 38 42 8 0 88 > > ###############################################################################