# Study 3.3 Results: Chi-squared test with 3 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("Study3.3.Data.txt") # .1=1df, .3=3df, .5=5df Read 4135860 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 10212 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 0.2407744 0.2112948 0.1881801 0.1915394 0.2327253 [2,] 2 0.1 100 0.25 0.2719835 0.2659209 0.3213982 0.0343041 0.3252723 [3,] 3 0.1 100 0.25 0.2246977 0.2071305 0.2781097 0.2348975 0.2199698 [4,] 4 0.1 100 0.25 0.2476130 0.1966433 0.2967587 0.2416603 0.2996223 [5,] 5 0.1 100 0.25 0.2152430 0.1882453 0.2059751 0.2098379 0.2538724 [6,] 6 0.1 100 0.25 0.2503883 0.1647550 0.2058198 0.2077913 0.1617308 Simulation SD_EffectSize Nstudies PopMeanPower SampleMeanPower Pcurve Puniform MaxLike Zcurve [459535,] 32 0.3 2000 0.75 0.7608894 0.9662650 1 0.7645505 0.7709847 [459536,] 33 0.3 2000 0.75 0.7561271 0.9643148 1 0.7588026 0.7782781 [459537,] 34 0.3 2000 0.75 0.7584853 0.9656247 1 0.7647574 0.7654560 [459538,] 35 0.3 2000 0.75 0.7373174 0.9594863 1 0.7491482 0.7647449 [459539,] 36 0.3 2000 0.75 0.7493126 0.9563267 1 0.7377462 0.7481902 [459540,] 37 0.3 2000 0.75 0.7559025 0.9606933 1 0.7493764 0.7728264 > # 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 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 10212 10212 10212 Puniform 10212 10212 10212 MaxLike 10212 10212 10212 Zcurve 10212 10212 10212 > > ###################### 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 0.228 0.254 0.300 Puniform 0.288 0.676 0.959 MaxLike 0.231 0.266 0.279 Zcurve 0.263 0.247 0.246 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.546 0.649 0.728 Puniform 0.628 0.901 0.993 MaxLike 0.504 0.505 0.506 Zcurve 0.536 0.531 0.524 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.830 0.918 0.956 Puniform 0.881 0.991 1.000 MaxLike 0.752 0.751 0.751 Zcurve 0.755 0.776 0.789 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.230 0.262 0.309 Puniform 0.289 0.744 0.992 MaxLike 0.230 0.264 0.276 Zcurve 0.253 0.235 0.235 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.552 0.658 0.738 Puniform 0.632 0.920 0.998 MaxLike 0.502 0.502 0.505 Zcurve 0.525 0.515 0.507 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.834 0.922 0.959 Puniform 0.884 0.994 1.000 MaxLike 0.750 0.750 0.751 Zcurve 0.755 0.770 0.781 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.230 0.267 0.317 Puniform 0.288 0.813 0.999 MaxLike 0.228 0.264 0.277 Zcurve 0.246 0.231 0.232 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.555 0.662 0.743 Puniform 0.633 0.935 1.000 MaxLike 0.501 0.501 0.504 Zcurve 0.518 0.506 0.499 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.836 0.924 0.961 Puniform 0.885 0.995 1.000 MaxLike 0.750 0.749 0.750 Zcurve 0.755 0.766 0.773 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.232 0.270 0.320 Puniform 0.288 0.899 1.000 MaxLike 0.229 0.263 0.276 Zcurve 0.242 0.229 0.229 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.558 0.665 0.745 Puniform 0.634 0.954 1.000 MaxLike 0.500 0.501 0.504 Zcurve 0.512 0.500 0.493 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.837 0.924 0.961 Puniform 0.885 0.997 1.000 MaxLike 0.750 0.749 0.750 Zcurve 0.755 0.762 0.767 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.234 0.273 0.323 Puniform 0.288 0.966 1.000 MaxLike 0.230 0.263 0.276 Zcurve 0.239 0.229 0.229 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.560 0.667 0.747 Puniform 0.634 0.976 1.000 MaxLike 0.500 0.501 0.504 Zcurve 0.508 0.496 0.489 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.837 0.925 0.961 Puniform 0.885 0.998 1.000 MaxLike 0.748 0.749 0.750 Zcurve 0.754 0.759 0.762 > > > ########################## 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 0.067 0.087 0.105 Puniform 0.079 0.195 0.093 MaxLike 0.082 0.048 0.044 Zcurve 0.069 0.062 0.060 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.073 0.083 0.085 Puniform 0.075 0.069 0.017 MaxLike 0.066 0.057 0.054 Zcurve 0.070 0.071 0.072 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.040 0.029 0.022 Puniform 0.035 0.010 0.001 MaxLike 0.058 0.046 0.046 Zcurve 0.042 0.037 0.038 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.043 0.058 0.069 Puniform 0.051 0.171 0.030 MaxLike 0.075 0.030 0.028 Zcurve 0.046 0.042 0.040 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.047 0.053 0.053 Puniform 0.048 0.050 0.005 MaxLike 0.043 0.036 0.036 Zcurve 0.047 0.047 0.046 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.025 0.018 0.013 Puniform 0.022 0.005 0.000 MaxLike 0.041 0.033 0.030 Zcurve 0.031 0.026 0.026 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.031 0.041 0.050 Puniform 0.036 0.165 0.006 MaxLike 0.072 0.022 0.020 Zcurve 0.035 0.032 0.030 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.034 0.038 0.037 Puniform 0.034 0.045 0.001 MaxLike 0.029 0.026 0.028 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 0.004 0.000 MaxLike 0.034 0.031 0.021 Zcurve 0.025 0.021 0.020 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.022 0.030 0.036 Puniform 0.027 0.136 0.001 MaxLike 0.068 0.016 0.015 Zcurve 0.027 0.027 0.024 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.024 0.026 0.026 Puniform 0.024 0.042 0.000 MaxLike 0.021 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 0.026 0.026 0.018 Zcurve 0.019 0.016 0.016 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.016 0.021 0.025 Puniform 0.021 0.078 0.000 MaxLike 0.066 0.012 0.013 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 0.018 Puniform 0.018 0.034 0.000 MaxLike 0.018 0.018 0.015 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 0.027 0.022 0.017 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 0.499 0.498 0.498 Puniform 0.499 0.498 0.498 MaxLike 0.499 0.498 0.498 Zcurve 0.499 0.498 0.498 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.750 0.749 0.748 Puniform 0.750 0.749 0.748 MaxLike 0.750 0.749 0.748 Zcurve 0.750 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 0.500 0.499 0.498 Puniform 0.500 0.499 0.498 MaxLike 0.500 0.499 0.498 Zcurve 0.500 0.499 0.498 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.750 0.749 0.749 Puniform 0.750 0.749 0.749 MaxLike 0.750 0.749 0.749 Zcurve 0.750 0.749 0.749 , , 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 0.500 0.499 0.499 Puniform 0.500 0.499 0.499 MaxLike 0.500 0.499 0.499 Zcurve 0.500 0.499 0.499 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.750 0.749 0.749 Puniform 0.750 0.749 0.749 MaxLike 0.750 0.749 0.749 Zcurve 0.750 0.749 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 0.500 0.499 0.499 Puniform 0.500 0.499 0.499 MaxLike 0.500 0.499 0.499 Zcurve 0.500 0.499 0.499 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.750 0.750 0.749 Puniform 0.750 0.750 0.749 MaxLike 0.750 0.750 0.749 Zcurve 0.750 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 0.500 0.500 0.500 Puniform 0.500 0.500 0.500 MaxLike 0.500 0.500 0.500 Zcurve 0.500 0.500 0.500 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.750 0.750 0.750 Puniform 0.750 0.750 0.750 MaxLike 0.750 0.750 0.750 Zcurve 0.750 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 -0.022 0.004 0.050 Puniform 0.038 0.426 0.709 MaxLike -0.019 0.016 0.029 Zcurve 0.013 -0.003 -0.004 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.046 0.149 0.228 Puniform 0.128 0.401 0.493 MaxLike 0.004 0.005 0.006 Zcurve 0.036 0.031 0.024 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.080 0.168 0.206 Puniform 0.131 0.241 0.250 MaxLike 0.002 0.001 0.001 Zcurve 0.005 0.026 0.039 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.020 0.012 0.059 Puniform 0.039 0.494 0.742 MaxLike -0.020 0.014 0.026 Zcurve 0.003 -0.015 -0.015 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.052 0.158 0.238 Puniform 0.132 0.420 0.498 MaxLike 0.002 0.002 0.005 Zcurve 0.025 0.015 0.007 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.084 0.172 0.209 Puniform 0.134 0.244 0.250 MaxLike 0.000 0.000 0.001 Zcurve 0.005 0.020 0.031 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.020 0.017 0.067 Puniform 0.038 0.563 0.749 MaxLike -0.022 0.014 0.027 Zcurve -0.004 -0.019 -0.018 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.055 0.162 0.243 Puniform 0.133 0.435 0.500 MaxLike 0.001 0.001 0.004 Zcurve 0.018 0.006 -0.001 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.086 0.174 0.211 Puniform 0.135 0.245 0.250 MaxLike 0.000 -0.001 0.000 Zcurve 0.005 0.016 0.023 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.018 0.020 0.070 Puniform 0.038 0.649 0.750 MaxLike -0.021 0.013 0.026 Zcurve -0.008 -0.021 -0.021 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.058 0.165 0.245 Puniform 0.134 0.454 0.500 MaxLike 0.000 0.001 0.004 Zcurve 0.012 0.000 -0.007 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.087 0.174 0.211 Puniform 0.135 0.247 0.250 MaxLike 0.000 -0.001 0.000 Zcurve 0.005 0.012 0.017 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -0.016 0.023 0.073 Puniform 0.038 0.716 0.750 MaxLike -0.020 0.013 0.026 Zcurve -0.011 -0.021 -0.021 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.060 0.167 0.247 Puniform 0.134 0.476 0.500 MaxLike 0.000 0.001 0.004 Zcurve 0.008 -0.004 -0.011 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 0.087 0.175 0.211 Puniform 0.135 0.248 0.250 MaxLike -0.002 -0.001 0.000 Zcurve 0.004 0.009 0.012 > > ########################## 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 -31.57 5.99 48.69 Puniform 49.89 221.74 774.95 MaxLike -22.29 36.10 68.40 Zcurve 20.31 -3.06 -5.38 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 64.11 184.90 273.80 Puniform 173.76 589.89 2888.28 MaxLike 7.48 12.21 16.16 Zcurve 53.15 46.56 37.51 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 203.24 580.11 934.22 Puniform 375.15 2451.49 27695.27 MaxLike 2.97 5.24 5.04 Zcurve 10.93 73.70 105.59 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -46.77 22.01 87.43 Puniform 78.82 292.80 2505.37 MaxLike -26.63 51.52 98.12 Zcurve 6.98 -33.07 -36.17 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 111.96 305.57 458.67 Puniform 277.35 850.14 11048.07 MaxLike 6.21 9.47 17.98 Zcurve 55.34 35.45 18.42 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 339.67 973.12 1652.32 Puniform 613.88 4723.09 270869.56 MaxLike 0.32 2.23 4.50 Zcurve 15.82 80.42 120.67 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -65.07 41.04 136.52 Puniform 108.37 345.84 12781.83 MaxLike -29.97 63.42 133.95 Zcurve -10.59 -58.11 -60.41 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 166.43 436.38 663.98 Puniform 394.98 984.71 34903.80 MaxLike 5.59 8.48 19.54 Zcurve 53.58 21.47 0.15 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 488.71 1392.01 2394.04 Puniform 874.42 6289.70 1487941.57 MaxLike -1.11 -0.13 4.39 Zcurve 18.96 79.74 119.98 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -80.43 68.69 201.05 Puniform 144.97 483.05 76229.37 MaxLike -30.22 87.37 174.12 Zcurve -30.16 -76.37 -84.82 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 246.81 633.90 948.12 Puniform 557.64 1086.16 172012.50 MaxLike 3.00 7.38 25.59 Zcurve 47.56 2.61 -26.40 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 703.17 1970.71 3400.38 Puniform 1219.45 7665.45 15672843.26 MaxLike -0.59 -1.57 3.08 Zcurve 24.35 75.46 113.56 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve -101.44 108.42 294.32 Puniform 185.90 924.35 8263376763.18 MaxLike -30.32 108.46 202.47 Zcurve -54.05 -94.60 -105.96 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 357.01 904.10 1376.60 Puniform 770.69 1402.17 38241635.28 MaxLike 1.57 5.67 31.04 Zcurve 42.51 -18.10 -54.20 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 999.64 2812.41 4854.98 Puniform 1703.56 10013.94 213248242.69 MaxLike -6.37 -1.40 0.63 Zcurve 28.41 68.73 100.14 > > # 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 0.502 0.688 0.819 0.928 0.986 Puniform 0.458 0.567 0.635 0.688 0.752 MaxLike 0.589 0.764 0.858 0.891 0.898 Zcurve 0.528 0.716 0.849 0.928 0.978 , , PopMeanPower = 0.5, SD_EffectSize = 0.1 Nstudies Method 100 250 500 1000 2000 Pcurve 0.407 0.454 0.435 0.359 0.275 Puniform 0.139 0.047 0.010 0.000 0.000 MaxLike 0.557 0.779 0.920 0.987 0.998 Zcurve 0.446 0.629 0.790 0.915 0.975 , , PopMeanPower = 0.75, SD_EffectSize = 0.1 Nstudies Method 100 250 500 1000 2000 Pcurve 0.206 0.092 0.029 0.003 0.000 Puniform 0.023 0.001 0.000 0.000 0.000 MaxLike 0.684 0.888 0.976 0.997 0.998 Zcurve 0.767 0.884 0.955 0.989 0.999 , , PopMeanPower = 0.25, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.417 0.604 0.743 0.835 0.901 Puniform 0.021 0.001 0.000 0.000 0.000 MaxLike 0.697 0.875 0.956 0.991 0.996 Zcurve 0.577 0.726 0.809 0.868 0.934 , , PopMeanPower = 0.5, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.109 0.026 0.002 0.000 0.000 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.623 0.846 0.950 0.995 0.998 Zcurve 0.473 0.686 0.843 0.947 0.986 , , PopMeanPower = 0.75, SD_EffectSize = 0.2 Nstudies Method 100 250 500 1000 2000 Pcurve 0.002 0.000 0.000 0.000 0.000 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.733 0.927 0.985 0.998 0.999 Zcurve 0.702 0.866 0.950 0.989 0.999 , , PopMeanPower = 0.25, SD_EffectSize = 0.3 Nstudies Method 100 250 500 1000 2000 Pcurve 0.340 0.406 0.372 0.288 0.176 Puniform 0.001 0.000 0.000 0.000 0.000 MaxLike 0.668 0.805 0.886 0.946 0.984 Zcurve 0.601 0.753 0.843 0.898 0.953 , , PopMeanPower = 0.5, SD_EffectSize = 0.3 Nstudies Method 100 250 500 1000 2000 Pcurve 0.030 0.001 0.000 0.000 0.000 Puniform 0.000 0.000 0.000 0.000 0.000 MaxLike 0.640 0.855 0.954 0.994 0.999 Zcurve 0.480 0.710 0.867 0.948 0.984 , , 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 0.734 0.926 0.988 0.999 0.999 Zcurve 0.545 0.758 0.910 0.986 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 12.008570 2 Puniform 33.951576 3 MaxLike 2.555084 4 Zcurve 3.050326 > > 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 5.70 7.00 9.22 Puniform 6.83 42.69 70.87 MaxLike 5.97 3.95 4.12 Zcurve 5.57 5.00 4.77 , , PopMeanPower = 0.5, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 7.10 15.30 22.84 Puniform 13.10 40.10 49.27 MaxLike 5.15 4.51 4.37 Zcurve 6.40 6.23 6.11 , , PopMeanPower = 0.75, Nstudies = 100 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.15 16.80 20.59 Puniform 13.08 24.07 24.98 MaxLike 4.08 3.58 3.62 Zcurve 3.38 3.76 4.71 , , PopMeanPower = 0.25, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 3.86 4.68 7.34 Puniform 5.15 49.44 74.24 MaxLike 4.73 2.60 3.11 Zcurve 3.70 3.63 3.44 , , PopMeanPower = 0.5, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.90 15.84 23.83 Puniform 13.21 41.97 49.84 MaxLike 3.26 2.84 2.78 Zcurve 4.35 3.97 3.76 , , PopMeanPower = 0.75, Nstudies = 250 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.39 17.20 20.94 Puniform 13.39 24.38 25.00 MaxLike 2.61 2.29 2.27 Zcurve 2.52 2.75 3.46 , , PopMeanPower = 0.25, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 2.99 3.55 7.02 Puniform 4.31 56.35 74.94 MaxLike 4.02 2.00 2.82 Zcurve 2.81 3.11 2.91 , , PopMeanPower = 0.5, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.70 16.24 24.31 Puniform 13.32 43.54 49.97 MaxLike 2.28 2.05 2.02 Zcurve 3.18 2.82 2.68 , , PopMeanPower = 0.75, Nstudies = 500 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.56 17.36 21.06 Puniform 13.47 24.53 25.00 MaxLike 1.87 1.68 1.59 Zcurve 2.00 2.17 2.63 , , PopMeanPower = 0.25, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 2.33 2.84 7.09 Puniform 3.96 64.88 75.00 MaxLike 3.38 1.63 2.66 Zcurve 2.30 2.84 2.72 , , PopMeanPower = 0.5, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 5.85 16.51 24.52 Puniform 13.41 45.43 50.00 MaxLike 1.62 1.46 1.45 Zcurve 2.33 2.06 2.08 , , PopMeanPower = 0.75, Nstudies = 1000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.69 17.43 21.11 Puniform 13.53 24.68 25.00 MaxLike 1.31 1.20 1.14 Zcurve 1.59 1.64 1.95 , , PopMeanPower = 0.25, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 1.88 2.55 7.31 Puniform 3.82 71.61 75.00 MaxLike 2.96 1.42 2.67 Zcurve 1.99 2.55 2.45 , , PopMeanPower = 0.5, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 6.02 16.72 24.67 Puniform 13.45 47.60 50.00 MaxLike 1.17 1.07 1.04 Zcurve 1.71 1.63 1.76 , , PopMeanPower = 0.75, Nstudies = 2000 SD_EffectSize Method 0.1 0.2 0.3 Pcurve 8.75 17.49 21.15 Puniform 13.55 24.84 25.00 MaxLike 0.96 0.85 0.82 Zcurve 1.26 1.23 1.37 > > > ################################################################################## > # 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 -18.73 -4.59 3.33 Puniform 0.00 11.96 24.74 MaxLike 0.00 0.00 6.87 SD_EffectSize = 0.1 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -105.07 45.26 19.18 Puniform 0.00 102.63 97.99 MaxLike 0.00 0.00 -32.56 SD_EffectSize = 0.1 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -199.08 74.89 109.34 Puniform 0.00 163.54 219.70 MaxLike 0.00 0.00 18.72 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -26.09 -14.17 5.50 Puniform 0.00 5.85 35.30 MaxLike 0.00 0.00 16.78 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -216.38 66.90 48.15 Puniform 0.00 181.98 182.57 MaxLike 0.00 0.00 -38.50 SD_EffectSize = 0.1 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -320.67 142.78 195.09 Puniform 0.00 277.03 379.92 MaxLike 0.00 0.00 3.05 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -31.68 -16.38 7.79 Puniform 0.00 4.12 41.93 MaxLike 0.00 0.00 19.07 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -339.31 103.72 87.19 Puniform 0.00 290.01 284.79 MaxLike 0.00 0.00 -44.26 SD_EffectSize = 0.1 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -436.97 198.69 301.82 Puniform 0.00 356.83 545.71 MaxLike 0.00 0.00 -4.43 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -45.22 -16.90 1.53 Puniform 0.00 8.57 51.29 MaxLike 0.00 0.00 17.24 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -471.82 158.16 145.27 Puniform 0.00 425.77 418.76 MaxLike 0.00 0.00 -44.01 SD_EffectSize = 0.1 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -583.63 292.05 457.86 Puniform 0.00 498.19 768.93 MaxLike 0.00 0.00 -12.30 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -66.56 -17.31 -7.22 Puniform 0.00 13.18 67.97 MaxLike 0.00 0.00 15.48 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -609.36 228.46 226.21 Puniform 0.00 563.21 587.56 MaxLike 0.00 0.00 -35.76 SD_EffectSize = 0.1 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -795.63 296.44 655.43 Puniform 0.00 486.82 1035.04 MaxLike 0.00 0.00 -11.51 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -184.26 80.92 42.45 Puniform 0.00 203.98 192.06 MaxLike 0.00 0.00 -32.18 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -351.05 138.74 132.19 Puniform 0.00 457.90 438.42 MaxLike 0.00 0.00 -54.61 SD_EffectSize = 0.2 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -287.05 301.45 440.21 Puniform 0.00 669.30 826.91 MaxLike 0.00 0.00 -6.29 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -263.54 78.76 24.99 Puniform 0.00 278.70 263.42 MaxLike 0.00 0.00 -33.75 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -480.73 234.49 228.07 Puniform 0.00 714.44 675.01 MaxLike 0.00 0.00 -52.00 SD_EffectSize = 0.2 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -441.04 489.26 768.57 Puniform 0.00 918.58 1152.14 MaxLike 0.00 0.00 -17.86 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -323.93 76.73 11.98 Puniform 0.00 333.91 321.29 MaxLike 0.00 0.00 -39.45 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -550.89 348.12 329.99 Puniform 0.00 876.27 837.39 MaxLike 0.00 0.00 -46.23 SD_EffectSize = 0.2 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -604.94 538.76 1049.95 Puniform 0.00 875.41 1464.09 MaxLike 0.00 0.00 -17.75 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -460.47 76.77 -0.23 Puniform 0.00 470.23 456.12 MaxLike 0.00 0.00 -50.15 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -630.9 521.72 466.87 Puniform 0.0 1004.93 967.38 MaxLike 0.0 0.00 -40.76 SD_EffectSize = 0.2 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -821.23 668.70 1430.98 Puniform 0.00 1041.01 1891.10 MaxLike 0.00 0.00 -18.62 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -875.76 86.75 0.07 Puniform 0.00 899.55 872.36 MaxLike 0.00 0.00 -53.29 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -823.19 671.97 627.82 Puniform 0.00 1258.62 1270.47 MaxLike 0.00 0.00 -33.19 SD_EffectSize = 0.2 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -1143.33 774.46 1877.75 Puniform 0.00 1165.63 2507.72 MaxLike 0.00 0.00 -17.60 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -564.72 98.92 64.73 Puniform 0.00 707.97 652.20 MaxLike 0.00 0.00 -17.37 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -336.86 213.41 204.80 Puniform 0.00 1196.18 915.00 MaxLike 0.00 0.00 -65.71 SD_EffectSize = 0.3 Nstudies = 100 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -199.8 426.52 638.24 Puniform 0.0 742.65 751.85 MaxLike 0.0 0.00 -33.25 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -1135.35 107.60 61.95 Puniform 0.00 2002.31 1772.92 MaxLike 0.00 0.00 -9.62 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -504.22 380.81 352.47 Puniform 0.00 2035.83 1644.47 MaxLike 0.00 0.00 -50.05 SD_EffectSize = 0.3 Nstudies = 250 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -319.12 749.73 1087.80 Puniform 0.00 1128.38 1048.95 MaxLike 0.00 0.00 -46.02 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -1543.12 127.12 75.40 Puniform 0.00 3901.52 3503.81 MaxLike 0.00 0.00 -2.90 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -699.9 575.81 507.24 Puniform 0.0 2463.33 2360.10 MaxLike 0.0 0.00 -33.68 SD_EffectSize = 0.3 Nstudies = 500 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -446.7 1158.57 1427.75 Puniform 0.0 1712.21 1377.13 MaxLike 0.0 0.00 -54.98 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -1987.46 172.63 101.01 Puniform 0.00 5130.97 4354.88 MaxLike 0.00 0.00 -2.05 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -982.31 867.68 667.66 Puniform 0.00 3758.92 3148.78 MaxLike 0.00 0.00 -37.41 SD_EffectSize = 0.3 Nstudies = 1000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -625.34 1337.58 1862.27 Puniform 0.00 1803.73 1832.51 MaxLike 0.00 0.00 -47.77 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.25 Puniform MaxLike Zcurve Pcurve -2726.32 232.43 150.57 Puniform 0.00 6018.35 4979.76 MaxLike 0.00 0.00 9.90 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.5 Puniform MaxLike Zcurve Pcurve -1410.58 1273.67 887.50 Puniform 0.00 4545.01 3832.52 MaxLike 0.00 0.00 -44.83 SD_EffectSize = 0.3 Nstudies = 2000 and PopMeanPower = 0.75 Puniform MaxLike Zcurve Pcurve -882.8 1278.83 2489.52 Puniform 0.0 1592.78 2540.03 MaxLike 0.0 0.00 -32.21 > > cat("\nTotal number of significant comparisons: \n") Total number of significant comparisons: > print(sum(keepscore)) [1] 260 > > cat("\n\n Number of times row method is significantly more accurate than column method \n\n"); print(addmargins(keepscore,2)) Number of times row method is significantly more accurate than column method Pcurve Puniform MaxLike Zcurve Sum Pcurve 0 45 4 1 50 Puniform 0 0 0 0 0 MaxLike 40 44 0 34 118 Zcurve 40 45 7 0 92 > > ############################################################################### > >