# Study 3.5 Results: Chi-squared test with 5 df, heterogeneity in sample size and effect size. > ################################################################################## > # AnalyzeStudy3.txt > ################################################################################## > # Analysis of small sample size data from Study 3, Poisson heterogeneity in > # sample size, Gamma in effect size, chi-squared tests > > rm(list=ls()) > options(scipen=999) # To avoid scientific notation! > # read.table chokes on large data sets > # simdata = scan("Testoutput.txt") > simdata = scan("Study3.5.Data.txt") # .1=1df, .3=3df, .5=5df Read 4082400 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 10080 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 0.2567243 0.1399594 0.2394531 0.20165900 0.1576562 [2,] 2 0.1 100 0.25 0.2393523 0.1357969 0.1889578 0.17119350 0.1139472 [3,] 3 0.1 100 0.25 0.2166795 0.2499094 0.1994473 0.05004668 0.2692122 [4,] 4 0.1 100 0.25 0.2509516 0.1626304 0.2684917 0.19573090 0.1414204 [5,] 5 0.1 100 0.25 0.2769295 0.2501902 0.4422071 0.30038460 0.3288151 [6,] 6 0.1 100 0.25 0.2856275 0.1738934 0.2391460 0.20823290 0.1727590 Simulation SD_EffectSize Nstudies PopMeanPower SampleMeanPower Pcurve Puniform MaxLike Zcurve [453595,] 31 0.3 2000 0.75 0.7645023 0.9640001 1 0.7576723 0.7689995 [453596,] 32 0.3 2000 0.75 0.7495755 0.9581617 1 0.7482157 0.7519308 [453597,] 33 0.3 2000 0.75 0.7503583 0.9605029 1 0.7492727 0.7647293 [453598,] 34 0.3 2000 0.75 0.7521836 0.9592991 1 0.7553161 0.7675510 [453599,] 35 0.3 2000 0.75 0.7602415 0.9644001 1 0.7618939 0.7763901 [453600,] 36 0.3 2000 0.75 0.7514840 0.9580978 1 0.7491472 0.7691215 > # 50 MLEs out of 1.8 million were bizarre. > simdata[,8][simdata[,8]>1] = NA # Temporary fix-up. I'm re-running the job. > # But this should not affect the results. > > # 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 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10080 10080 10080 Puniform 10080 10080 10080 MaxLike 10080 10080 10080 Zcurve 10080 10080 10080 > > ###################### 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 0.231 0.251 0.298 Puniform 0.282 0.619 0.945 MaxLike 0.233 0.264 0.277 Zcurve 0.263 0.247 0.246 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.549 0.642 0.722 Puniform 0.640 0.885 0.990 MaxLike 0.503 0.505 0.507 Zcurve 0.532 0.530 0.526 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.833 0.914 0.954 Puniform 0.888 0.989 1.000 MaxLike 0.750 0.751 0.750 Zcurve 0.754 0.775 0.788 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.232 0.259 0.309 Puniform 0.284 0.673 0.989 MaxLike 0.235 0.262 0.275 Zcurve 0.252 0.235 0.235 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.555 0.650 0.731 Puniform 0.644 0.902 0.997 MaxLike 0.501 0.502 0.505 Zcurve 0.522 0.515 0.508 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.838 0.918 0.957 Puniform 0.892 0.992 1.000 MaxLike 0.749 0.750 0.751 Zcurve 0.754 0.770 0.780 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.232 0.263 0.314 Puniform 0.282 0.734 0.999 MaxLike 0.234 0.261 0.274 Zcurve 0.245 0.230 0.231 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.559 0.655 0.735 Puniform 0.645 0.917 0.999 MaxLike 0.500 0.501 0.504 Zcurve 0.514 0.506 0.499 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.840 0.920 0.958 Puniform 0.893 0.994 1.000 MaxLike 0.749 0.750 0.750 Zcurve 0.754 0.766 0.773 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.234 0.267 0.319 Puniform 0.282 0.816 1.000 MaxLike 0.235 0.260 0.274 Zcurve 0.240 0.229 0.229 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.561 0.658 0.738 Puniform 0.646 0.936 1.000 MaxLike 0.499 0.501 0.504 Zcurve 0.508 0.500 0.493 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.841 0.921 0.959 Puniform 0.893 0.995 1.000 MaxLike 0.748 0.749 0.750 Zcurve 0.753 0.761 0.766 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.236 0.269 0.321 Puniform 0.282 0.913 1.000 MaxLike 0.235 0.260 0.274 Zcurve 0.238 0.229 0.229 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.564 0.659 0.739 Puniform 0.646 0.962 1.000 MaxLike 0.499 0.500 0.503 Zcurve 0.504 0.496 0.489 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.842 0.921 0.960 Puniform 0.894 0.998 1.000 MaxLike 0.747 0.749 0.750 Zcurve 0.753 0.758 0.761 > > > ########################## 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 0.065 0.083 0.102 Puniform 0.074 0.187 0.106 MaxLike 0.079 0.049 0.044 Zcurve 0.069 0.064 0.060 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.073 0.082 0.082 Puniform 0.075 0.073 0.021 MaxLike 0.063 0.057 0.054 Zcurve 0.069 0.071 0.071 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.039 0.031 0.022 Puniform 0.034 0.011 0.001 MaxLike 0.055 0.048 0.047 Zcurve 0.041 0.037 0.038 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.042 0.056 0.067 Puniform 0.048 0.171 0.038 MaxLike 0.068 0.030 0.029 Zcurve 0.046 0.043 0.039 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.047 0.052 0.052 Puniform 0.048 0.052 0.007 MaxLike 0.040 0.036 0.035 Zcurve 0.047 0.047 0.046 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.024 0.019 0.013 Puniform 0.021 0.006 0.000 MaxLike 0.036 0.035 0.029 Zcurve 0.031 0.027 0.026 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.030 0.040 0.048 Puniform 0.034 0.178 0.011 MaxLike 0.063 0.023 0.023 Zcurve 0.034 0.033 0.030 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.033 0.037 0.037 Puniform 0.035 0.049 0.002 MaxLike 0.029 0.026 0.026 Zcurve 0.035 0.035 0.034 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.017 0.013 0.009 Puniform 0.015 0.005 0.000 MaxLike 0.027 0.032 0.025 Zcurve 0.024 0.021 0.020 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.021 0.029 0.035 Puniform 0.024 0.175 0.001 MaxLike 0.059 0.017 0.017 Zcurve 0.026 0.027 0.024 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.024 0.026 0.025 Puniform 0.025 0.049 0.001 MaxLike 0.023 0.020 0.020 Zcurve 0.026 0.026 0.024 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.012 0.009 0.006 Puniform 0.011 0.004 0.000 MaxLike 0.024 0.027 0.022 Zcurve 0.019 0.017 0.015 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.015 0.021 0.025 Puniform 0.017 0.132 0.000 MaxLike 0.057 0.015 0.016 Zcurve 0.021 0.022 0.020 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.017 0.018 0.018 Puniform 0.018 0.044 0.000 MaxLike 0.018 0.017 0.017 Zcurve 0.020 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 0.003 0.000 MaxLike 0.022 0.030 0.018 Zcurve 0.015 0.013 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 0.249 0.249 0.249 Puniform 0.249 0.249 0.249 MaxLike 0.249 0.249 0.249 Zcurve 0.249 0.249 0.249 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.498 0.498 0.498 Puniform 0.498 0.498 0.498 MaxLike 0.498 0.498 0.498 Zcurve 0.498 0.498 0.498 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.748 0.749 0.748 Puniform 0.748 0.749 0.748 MaxLike 0.748 0.749 0.748 Zcurve 0.748 0.749 0.748 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.250 0.249 0.249 Puniform 0.250 0.249 0.249 MaxLike 0.250 0.249 0.249 Zcurve 0.250 0.249 0.249 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.498 0.499 0.499 Puniform 0.498 0.499 0.499 MaxLike 0.498 0.499 0.499 Zcurve 0.498 0.499 0.499 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.749 0.750 0.749 Puniform 0.749 0.750 0.749 MaxLike 0.749 0.750 0.749 Zcurve 0.749 0.750 0.749 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.250 0.249 0.249 Puniform 0.250 0.249 0.249 MaxLike 0.250 0.249 0.249 Zcurve 0.250 0.249 0.249 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.498 0.499 0.499 Puniform 0.498 0.499 0.499 MaxLike 0.498 0.499 0.499 Zcurve 0.498 0.499 0.499 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.749 0.750 0.749 Puniform 0.749 0.750 0.749 MaxLike 0.749 0.750 0.749 Zcurve 0.749 0.750 0.749 , , 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 0.498 0.499 0.499 Puniform 0.498 0.499 0.499 MaxLike 0.498 0.499 0.499 Zcurve 0.498 0.499 0.499 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.749 0.750 0.749 Puniform 0.749 0.750 0.749 MaxLike 0.749 0.750 0.749 Zcurve 0.749 0.750 0.749 , , 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 0.499 Puniform 0.499 0.500 0.499 MaxLike 0.499 0.500 0.499 Zcurve 0.499 0.500 0.499 , , 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 -0.019 0.001 0.048 Puniform 0.032 0.369 0.695 MaxLike -0.017 0.014 0.027 Zcurve 0.013 -0.003 -0.004 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.049 0.142 0.222 Puniform 0.140 0.385 0.490 MaxLike 0.003 0.005 0.007 Zcurve 0.032 0.030 0.026 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.083 0.164 0.204 Puniform 0.138 0.239 0.250 MaxLike 0.000 0.001 0.000 Zcurve 0.004 0.025 0.038 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.018 0.009 0.059 Puniform 0.034 0.423 0.739 MaxLike -0.015 0.012 0.025 Zcurve 0.002 -0.015 -0.015 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.055 0.150 0.231 Puniform 0.144 0.402 0.497 MaxLike 0.001 0.002 0.005 Zcurve 0.022 0.015 0.008 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.088 0.168 0.207 Puniform 0.142 0.242 0.250 MaxLike -0.001 0.000 0.001 Zcurve 0.004 0.020 0.030 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.018 0.013 0.064 Puniform 0.032 0.484 0.749 MaxLike -0.016 0.011 0.024 Zcurve -0.005 -0.020 -0.019 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.059 0.155 0.235 Puniform 0.145 0.417 0.499 MaxLike 0.000 0.001 0.004 Zcurve 0.014 0.006 -0.001 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.090 0.170 0.208 Puniform 0.143 0.244 0.250 MaxLike -0.001 0.000 0.000 Zcurve 0.004 0.016 0.023 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.016 0.017 0.069 Puniform 0.032 0.566 0.750 MaxLike -0.015 0.010 0.024 Zcurve -0.010 -0.021 -0.021 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.061 0.158 0.238 Puniform 0.146 0.436 0.500 MaxLike -0.001 0.001 0.004 Zcurve 0.008 0.000 -0.007 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.091 0.171 0.209 Puniform 0.143 0.245 0.250 MaxLike -0.002 -0.001 0.000 Zcurve 0.003 0.011 0.016 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.014 0.019 0.071 Puniform 0.032 0.663 0.750 MaxLike -0.015 0.010 0.024 Zcurve -0.012 -0.021 -0.021 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.064 0.159 0.239 Puniform 0.146 0.462 0.500 MaxLike -0.001 0.000 0.003 Zcurve 0.004 -0.004 -0.011 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.092 0.171 0.210 Puniform 0.144 0.248 0.250 MaxLike -0.003 -0.001 0.000 Zcurve 0.003 0.008 0.011 > > ########################## 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 -27.85 1.73 48.96 Puniform 44.36 198.70 659.01 MaxLike -20.15 29.33 63.96 Zcurve 20.09 -3.14 -5.34 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 70.41 175.14 275.35 Puniform 189.79 531.04 2368.49 MaxLike 7.68 11.43 17.88 Zcurve 50.13 45.04 39.81 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 218.27 544.80 918.68 Puniform 412.23 2115.06 30476.17 MaxLike 2.77 4.95 5.23 Zcurve 14.44 71.28 106.14 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -42.05 16.46 89.86 Puniform 71.22 248.67 1948.48 MaxLike -21.58 41.05 90.62 Zcurve 6.01 -33.41 -36.14 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 121.22 294.32 447.43 Puniform 301.82 771.36 7217.26 MaxLike 6.69 8.52 17.74 Zcurve 50.81 33.64 20.25 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 364.92 916.30 1606.70 Puniform 671.03 3969.55 188840.95 MaxLike 1.56 0.94 6.19 Zcurve 17.50 75.55 118.74 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -59.66 33.88 135.02 Puniform 93.58 272.46 6910.61 MaxLike -25.35 50.92 110.37 Zcurve -13.93 -58.91 -61.61 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 183.59 426.17 640.36 Puniform 425.72 855.85 21873.28 MaxLike 4.15 8.61 21.22 Zcurve 45.40 21.58 0.26 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 527.89 1343.77 2330.10 Puniform 957.46 5289.95 1003343.05 MaxLike 2.89 -0.58 2.06 Zcurve 22.56 74.85 117.33 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -75.09 59.36 200.25 Puniform 136.24 324.46 94893.97 MaxLike -25.47 66.07 141.30 Zcurve -36.15 -77.85 -86.15 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 260.63 611.42 940.27 Puniform 594.70 897.68 81699.06 MaxLike 1.63 5.83 23.14 Zcurve 37.45 3.35 -26.86 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 759.18 1880.04 3353.91 Puniform 1365.11 6008.24 6234551.53 MaxLike -1.23 -1.50 1.01 Zcurve 24.56 70.32 110.03 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -90.67 95.36 291.33 Puniform 190.07 506.04 62125095.61 MaxLike -26.01 70.12 157.88 Zcurve -60.20 -95.10 -104.63 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 382.20 872.38 1316.28 Puniform 845.92 1045.73 838911.50 MaxLike 1.03 3.22 21.33 Zcurve 29.15 -19.19 -55.76 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 1066.08 2719.40 4750.79 Puniform 1882.99 7486.57 94447659.11 MaxLike -5.36 -3.21 0.59 Zcurve 28.28 64.20 97.44 > > # 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 0.517 0.708 0.841 0.942 0.992 Puniform 0.480 0.613 0.702 0.779 0.856 MaxLike 0.594 0.784 0.878 0.914 0.919 Zcurve 0.523 0.726 0.850 0.930 0.976 , , PopMeanPower = 0.5, SD_EffectSize = 0.1 Nstudies Method 100 250 500 1000 2000 Pcurve 0.397 0.430 0.386 0.317 0.208 Puniform 0.107 0.029 0.004 0.000 0.000 MaxLike 0.589 0.797 0.928 0.986 0.997 Zcurve 0.465 0.654 0.818 0.929 0.983 , , PopMeanPower = 0.75, SD_EffectSize = 0.1 Nstudies Method 100 250 500 1000 2000 Pcurve 0.190 0.070 0.015 0.001 0.000 Puniform 0.012 0.000 0.000 0.000 0.000 MaxLike 0.694 0.898 0.978 0.997 0.999 Zcurve 0.772 0.892 0.956 0.991 0.999 , , PopMeanPower = 0.25, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.441 0.630 0.770 0.868 0.931 Puniform 0.031 0.002 0.000 0.000 0.000 MaxLike 0.699 0.881 0.963 0.991 0.994 Zcurve 0.562 0.722 0.798 0.862 0.922 , , PopMeanPower = 0.5, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.120 0.035 0.004 0.000 0.000 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.614 0.832 0.954 0.993 0.997 Zcurve 0.456 0.679 0.843 0.948 0.986 , , 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 0.733 0.923 0.984 0.998 0.998 Zcurve 0.697 0.870 0.948 0.989 0.999 , , PopMeanPower = 0.25, SD_EffectSize = 0.3 Nstudies Method 100 250 500 1000 2000 Pcurve 0.358 0.412 0.385 0.303 0.190 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.676 0.818 0.902 0.958 0.988 Zcurve 0.591 0.758 0.828 0.892 0.952 , , PopMeanPower = 0.5, SD_EffectSize = 0.3 Nstudies Method 100 250 500 1000 2000 Pcurve 0.027 0.001 0.000 0.000 0.000 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.645 0.849 0.952 0.993 0.997 Zcurve 0.474 0.710 0.863 0.952 0.986 , , 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 0.737 0.929 0.989 0.999 0.999 Zcurve 0.551 0.768 0.914 0.988 0.999 > > ###################### 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 11.784929 2 Puniform 33.090386 3 MaxLike 2.473863 4 Zcurve 3.030728 > > 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 5.53 6.68 8.88 Puniform 6.31 37.02 69.50 MaxLike 5.79 3.93 4.05 Zcurve 5.60 5.10 4.79 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 7.19 14.65 22.31 Puniform 14.28 38.46 49.02 MaxLike 4.95 4.59 4.32 Zcurve 6.21 6.29 6.15 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.42 16.45 20.38 Puniform 13.83 23.88 24.98 MaxLike 3.98 3.64 3.61 Zcurve 3.30 3.73 4.67 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 3.70 4.47 7.19 Puniform 4.63 42.34 73.86 MaxLike 4.28 2.57 3.04 Zcurve 3.65 3.66 3.39 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 6.10 15.04 23.08 Puniform 14.38 40.16 49.73 MaxLike 3.16 2.88 2.79 Zcurve 4.18 3.99 3.75 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.77 16.84 20.73 Puniform 14.18 24.21 25.00 MaxLike 2.48 2.31 2.22 Zcurve 2.47 2.73 3.39 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 2.85 3.35 6.76 Puniform 3.79 48.38 74.86 MaxLike 3.51 1.91 2.66 Zcurve 2.77 3.17 3.00 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.99 15.51 23.48 Puniform 14.53 41.73 49.94 MaxLike 2.22 2.06 2.00 Zcurve 2.99 2.83 2.69 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.99 17.02 20.85 Puniform 14.30 24.38 25.00 MaxLike 1.78 1.70 1.59 Zcurve 1.97 2.16 2.60 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 2.20 2.64 6.92 Puniform 3.37 56.56 75.00 MaxLike 2.86 1.50 2.52 Zcurve 2.29 2.89 2.72 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 6.14 15.77 23.77 Puniform 14.56 43.59 49.99 MaxLike 1.62 1.49 1.43 Zcurve 2.21 2.07 2.05 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 9.09 17.08 20.91 Puniform 14.33 24.55 25.00 MaxLike 1.26 1.23 1.15 Zcurve 1.54 1.62 1.89 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 1.71 2.30 7.14 Puniform 3.24 66.29 75.00 MaxLike 2.46 1.28 2.49 Zcurve 2.00 2.60 2.46 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 6.37 15.93 23.85 Puniform 14.63 46.15 50.00 MaxLike 1.16 1.11 1.07 Zcurve 1.60 1.64 1.79 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 9.18 17.14 20.95 Puniform 14.37 24.76 25.00 MaxLike 0.95 0.92 0.82 Zcurve 1.22 1.21 1.34 > > > ################################################################################## > # 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 -14.5 -4.73 -1.66 Puniform 0.0 8.00 15.15 MaxLike 0.0 0.00 3.43 SD_EffectSize = 0.1 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -120.41 50.25 25.58 Puniform 0.00 117.30 112.27 MaxLike 0.00 0.00 -34.85 SD_EffectSize = 0.1 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -214.84 82.92 114.62 Puniform 0.00 188.63 243.51 MaxLike 0.00 0.00 20.44 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -21.01 -10.64 1.79 Puniform 0.00 5.55 25.79 MaxLike 0.00 0.00 11.26 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -236.61 71.91 55.09 Puniform 0.00 204.30 201.38 MaxLike 0.00 0.00 -37.57 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -341.98 171.87 208.36 Puniform 0.00 342.57 412.28 MaxLike 0.00 0.00 0.70 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -24.55 -11.90 3.79 Puniform 0.00 4.68 30.42 MaxLike 0.00 0.00 13.20 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -365.75 106.26 96.50 Puniform 0.00 309.20 310.52 MaxLike 0.00 0.00 -36.58 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -465.1 261.97 322.22 Puniform 0.0 482.96 592.25 MaxLike 0.0 0.00 -8.74 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -36.86 -12.37 -5.35 Puniform 0.00 8.79 36.86 MaxLike 0.00 0.00 10.40 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -500.14 154.75 150.97 Puniform 0.00 430.25 446.48 MaxLike 0.00 0.00 -32.65 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -646.8 323.16 482.27 Puniform 0.0 565.23 839.26 MaxLike 0.0 0.00 -12.82 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -60.2 -14.00 -19.77 Puniform 0.0 13.61 50.93 MaxLike 0.0 0.00 8.50 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -671.2 234.32 238.58 Puniform 0.0 601.30 637.94 MaxLike 0.0 0.00 -29.39 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -856.33 375.29 676.71 Puniform 0.00 632.81 1119.85 MaxLike 0.00 0.00 -13.13 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -161.68 75.98 34.68 Puniform 0.00 180.25 168.47 MaxLike 0.00 0.00 -35.63 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -335.08 129.79 121.02 Puniform 0.00 411.34 397.96 MaxLike 0.00 0.00 -53.44 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -286.14 277.10 412.44 Puniform 0.00 593.39 779.36 MaxLike 0.00 0.00 -3.06 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -221.26 77.48 20.15 Puniform 0.00 234.48 220.37 MaxLike 0.00 0.00 -37.36 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -453.11 219.01 210.56 Puniform 0.00 651.88 619.07 MaxLike 0.00 0.00 -51.29 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -445.28 444.40 746.26 Puniform 0.00 820.53 1149.75 MaxLike 0.00 0.00 -15.24 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -253.61 73.82 5.09 Puniform 0.00 261.96 249.99 MaxLike 0.00 0.00 -45.44 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -506.98 337.93 317.42 Puniform 0.00 763.01 736.23 MaxLike 0.00 0.00 -45.10 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -616.13 504.63 1020.10 Puniform 0.00 820.05 1427.43 MaxLike 0.00 0.00 -15.62 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -309.41 74.86 -8.55 Puniform 0.00 315.39 304.61 MaxLike 0.00 0.00 -57.57 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -547.35 493.43 446.55 Puniform 0.00 830.61 811.77 MaxLike 0.00 0.00 -36.81 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -814.9 601.85 1362.12 Puniform 0.0 939.50 1850.49 MaxLike 0.0 0.00 -15.40 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -486.84 70.37 -12.14 Puniform 0.00 494.36 480.97 MaxLike 0.00 0.00 -58.74 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -651.12 659.96 590.14 Puniform 0.00 975.82 967.68 MaxLike 0.00 0.00 -34.33 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -1120.38 558.31 1802.64 Puniform 0.00 837.51 2478.88 MaxLike 0.00 0.00 -9.91 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -511.45 95.77 59.31 Puniform 0.00 612.31 569.37 MaxLike 0.00 0.00 -20.09 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -354.49 216.47 207.07 Puniform 0.00 1127.12 876.07 MaxLike 0.00 0.00 -66.74 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -207.35 414.74 646.0 Puniform 0.00 718.30 757.0 MaxLike 0.00 0.00 -31.5 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -1083.09 103.07 60.67 Puniform 0.00 1648.76 1517.32 MaxLike 0.00 0.00 -9.71 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -523.87 374.82 347.96 Puniform 0.00 2030.94 1599.42 MaxLike 0.00 0.00 -49.70 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -329.32 793.97 1068.65 Puniform 0.00 1255.25 1054.97 MaxLike 0.00 0.00 -48.75 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -1564.69 123.17 70.03 Puniform 0.00 3221.06 3114.98 MaxLike 0.00 0.00 -10.52 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -721.01 561.28 480.29 Puniform 0.00 2869.77 2328.45 MaxLike 0.00 0.00 -41.25 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -462.73 906.15 1394.31 Puniform 0.00 1249.94 1379.17 MaxLike 0.00 0.00 -43.98 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -2025.43 167.45 97.61 Puniform 0.00 4584.34 4269.11 MaxLike 0.00 0.00 -7.28 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -1034.72 828.94 655.47 Puniform 0.00 3377.21 3164.96 MaxLike 0.00 0.00 -34.25 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -653.9 976.07 1871.62 Puniform 0.0 1248.66 1870.06 MaxLike 0.0 0.00 -34.18 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -2759.37 216.89 145.21 Puniform 0.00 4890.17 4902.65 MaxLike 0.00 0.00 1.10 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -1439.46 1083.31 840.70 Puniform 0.00 3476.35 3797.18 MaxLike 0.00 0.00 -38.50 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -916.31 1233.3 2502.99 Puniform 0.00 1542.7 2552.78 MaxLike 0.00 0.0 -30.13 > > cat("\nTotal number of significant comparisons: \n") Total number of significant comparisons: > print(sum(keepscore)) [1] 263 > > 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 0 0 0 MaxLike 40 45 0 36 121 Zcurve 38 45 5 0 88 > > ############################################################################### > >