# ::Free Statistics and Forecasting Software::

v1.2.1

### :: Bootstrap Plot - Central Tendency - Free Statistics Software (Calculator) ::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the Bootstrap Plot for three measures of Central Tendency: mean, median, and midrange. This method can be applied to univariate data series.
The following charts are generated by this module: sequences of simulated values (mean, median, midrange, and mode), density trace of each eastimation, and notched boxplots of simulated values.

For more information about the bootstrap: Davison, A.C. and Hinkley, D.V. (1997), Bootstrap Methods and Their Application,. Cambridge University Press.

Enter (or paste) your data delimited by hard returns.

 Send output to: Browser Blue - Charts White Browser Black/White CSV Data[reset data] 112 118 132 129 121 135 148 148 136 119 104 118 115 126 141 135 125 149 170 170 158 133 114 140 145 150 178 163 172 178 199 199 184 162 146 166 171 180 193 181 183 218 230 242 209 191 172 194 196 196 236 235 229 243 264 272 237 211 180 201 204 188 235 227 234 264 302 293 259 229 203 229 242 233 267 269 270 315 364 347 312 274 237 278 284 277 317 313 318 374 413 405 355 306 271 306 315 301 356 348 355 422 465 467 404 347 305 336 340 318 362 348 363 435 491 505 404 359 310 337 360 342 406 396 420 472 548 559 463 407 362 405 417 391 419 461 472 535 622 606 508 461 390 432 # simulations Significant digits Bandwidth (?) Quantiles P1 P5 Q1 Q3 P95 P99P0.5 P2.5 Q1 Q3 P97.5 P99.5P10 P20 Q1 Q3 P80 P90 Chart options Width: Height:

 Source code of R module par1 <- as.numeric(par1) par2 <- as.numeric(par2) if (par3 == "0") bw <- 0.4 if (par3 != "0") bw <- as.numeric(par3) if(bw<0) bw=0.1 if (par1 < 10) par1 = 10 if (par1 > 5000) par1 = 5000 library(modeest) library(lattice) library(boot) boot.stat <- function(s,i) { s.mean <- mean(s[i]) s.median <- median(s[i]) s.midrange <- (max(s[i]) + min(s[i])) / 2 s.mode <- hrm(s[i], bw=bw) s.kernelmode <- mlv(s[i], method="parzen", kernel="gaussian") c(s.mean, s.median, s.midrange, s.mode, s.kernelmode) } x<-na.omit(x) (r <- boot(x,boot.stat, R=par1, stype="i")) bitmap(file="plot1.png") plot(r\$t[,1],type="p",ylab="simulated values",main="Simulation of Mean") grid() dev.off() bitmap(file="plot2.png") plot(r\$t[,2],type="p",ylab="simulated values",main="Simulation of Median") grid() dev.off() bitmap(file="plot3.png") plot(r\$t[,3],type="p",ylab="simulated values",main="Simulation of Midrange") grid() dev.off() bitmap(file="plot7.png") plot(r\$t[,4],type="p",ylab="simulated values",main="Simulation of Mode") grid() dev.off() bitmap(file="plot8.png") plot(r\$t[,5],type="p",ylab="simulated values",main="Simulation of Mode of Kernel Density") grid() dev.off() bitmap(file="plot4.png") densityplot(~r\$t[,1],col="black",main="Density Plot",xlab="mean") dev.off() bitmap(file="plot5.png") densityplot(~r\$t[,2],col="black",main="Density Plot",xlab="median") dev.off() bitmap(file="plot6.png") densityplot(~r\$t[,3],col="black",main="Density Plot",xlab="midrange") dev.off() bitmap(file="plot9.png") densityplot(~r\$t[,4],col="black",main="Density Plot",xlab="mode") dev.off() bitmap(file="plot10.png") densityplot(~r\$t[,5],col="black",main="Density Plot",xlab="mode of kernel dens.") dev.off() z <- data.frame(cbind(r\$t[,1],r\$t[,2],r\$t[,3],r\$t[,4],r\$t[,5])) colnames(z) <- list("mean","median","midrange","mode","mode k.dens") bitmap(file="plot11.png") boxplot(z,notch=TRUE,ylab="simulated values",main="Bootstrap Simulation - Central Tendency") grid() dev.off() load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Estimation Results of Bootstrap",10,TRUE) a<-table.row.end(a) if (par4 == "P1 P5 Q1 Q3 P95 P99") { myq.1 <- 0.01 myq.2 <- 0.05 myq.3 <- 0.95 myq.4 <- 0.99 myl.1 <- "P1" myl.2 <- "P5" myl.3 <- "P95" myl.4 <- "P99" } if (par4 == "P0.5 P2.5 Q1 Q3 P97.5 P99.5") { myq.1 <- 0.005 myq.2 <- 0.025 myq.3 <- 0.975 myq.4 <- 0.995 myl.1 <- "P0.5" myl.2 <- "P2.5" myl.3 <- "P97.5" myl.4 <- "P99.5" } if (par4 == "P10 P20 Q1 Q3 P80 P90") { myq.1 <- 0.10 myq.2 <- 0.20 myq.3 <- 0.80 myq.4 <- 0.90 myl.1 <- "P10" myl.2 <- "P20" myl.3 <- "P80" myl.4 <- "P90" } a<-table.row.start(a) a<-table.element(a,"statistic",header=TRUE) a<-table.element(a,myl.1,header=TRUE) a<-table.element(a,myl.2,header=TRUE) a<-table.element(a,"Q1",header=TRUE) a<-table.element(a,"Estimate",header=TRUE) a<-table.element(a,"Q3",header=TRUE) a<-table.element(a,myl.3,header=TRUE) a<-table.element(a,myl.4,header=TRUE) a<-table.element(a,"S.D.",header=TRUE) a<-table.element(a,"IQR",header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"mean",header=TRUE) q1 <- quantile(r\$t[,1],0.25)[] q3 <- quantile(r\$t[,1],0.75)[] p01 <- quantile(r\$t[,1],myq.1)[] p05 <- quantile(r\$t[,1],myq.2)[] p95 <- quantile(r\$t[,1],myq.3)[] p99 <- quantile(r\$t[,1],myq.4)[] a<-table.element(a,signif(p01,par2)) a<-table.element(a,signif(p05,par2)) a<-table.element(a,signif(q1,par2)) a<-table.element(a,signif(r\$t0,par2)) a<-table.element(a,signif(q3,par2)) a<-table.element(a,signif(p95,par2)) a<-table.element(a,signif(p99,par2)) a<-table.element( a,signif( sqrt(var(r\$t[,1])),par2 ) ) a<-table.element(a,signif(q3-q1,par2)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"median",header=TRUE) q1 <- quantile(r\$t[,2],0.25)[] q3 <- quantile(r\$t[,2],0.75)[] p01 <- quantile(r\$t[,2],myq.1)[] p05 <- quantile(r\$t[,2],myq.2)[] p95 <- quantile(r\$t[,2],myq.3)[] p99 <- quantile(r\$t[,2],myq.4)[] a<-table.element(a,signif(p01,par2)) a<-table.element(a,signif(p05,par2)) a<-table.element(a,signif(q1,par2)) a<-table.element(a,signif(r\$t0,par2)) a<-table.element(a,signif(q3,par2)) a<-table.element(a,signif(p95,par2)) a<-table.element(a,signif(p99,par2)) a<-table.element(a,signif(sqrt(var(r\$t[,2])),par2)) a<-table.element(a,signif(q3-q1,par2)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"midrange",header=TRUE) q1 <- quantile(r\$t[,3],0.25)[] q3 <- quantile(r\$t[,3],0.75)[] p01 <- quantile(r\$t[,3],myq.1)[] p05 <- quantile(r\$t[,3],myq.2)[] p95 <- quantile(r\$t[,3],myq.3)[] p99 <- quantile(r\$t[,3],myq.4)[] a<-table.element(a,signif(p01,par2)) a<-table.element(a,signif(p05,par2)) a<-table.element(a,signif(q1,par2)) a<-table.element(a,signif(r\$t0,par2)) a<-table.element(a,signif(q3,par2)) a<-table.element(a,signif(p95,par2)) a<-table.element(a,signif(p99,par2)) a<-table.element(a,signif(sqrt(var(r\$t[,3])),par2)) a<-table.element(a,signif(q3-q1,par2)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"mode",header=TRUE) q1 <- quantile(r\$t[,4],0.25)[] q3 <- quantile(r\$t[,4],0.75)[] p01 <- quantile(r\$t[,4],myq.1)[] p05 <- quantile(r\$t[,4],myq.2)[] p95 <- quantile(r\$t[,4],myq.3)[] p99 <- quantile(r\$t[,4],myq.4)[] a<-table.element(a,signif(p01,par2)) a<-table.element(a,signif(p05,par2)) a<-table.element(a,signif(q1,par2)) a<-table.element(a,signif(r\$t0,par2)) a<-table.element(a,signif(q3,par2)) a<-table.element(a,signif(p95,par2)) a<-table.element(a,signif(p99,par2)) a<-table.element(a,signif(sqrt(var(r\$t[,4])),par2)) a<-table.element(a,signif(q3-q1,par2)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"mode k.dens",header=TRUE) q1 <- quantile(r\$t[,5],0.25)[] q3 <- quantile(r\$t[,5],0.75)[] p01 <- quantile(r\$t[,5],myq.1)[] p05 <- quantile(r\$t[,5],myq.2)[] p95 <- quantile(r\$t[,5],myq.3)[] p99 <- quantile(r\$t[,5],myq.4)[] a<-table.element(a,signif(p01,par2)) a<-table.element(a,signif(p05,par2)) a<-table.element(a,signif(q1,par2)) a<-table.element(a,signif(r\$t0,par2)) a<-table.element(a,signif(q3,par2)) a<-table.element(a,signif(p95,par2)) a<-table.element(a,signif(p99,par2)) a<-table.element(a,signif(sqrt(var(r\$t[,5])),par2)) a<-table.element(a,signif(q3-q1,par2)) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab")
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 Cite this software as: Wessa P., (2019), Bootstrap Plot for Central Tendency (v1.0.16) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL https://www.wessa.net/rwasp_bootstrapplot1.wasp/ The R code is based on : Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988), The New S Language, Wadsworth & Brooks/Cole. Chambers, J. M., Cleveland, W. S., Kleiner, B. and Tukey, P. A., (1983), Graphical Methods for Data Analysis., Wadsworth & Brooks/Cole. Murrell, P. (2005), R Graphics, Chapman & Hall/CRC Press. NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, 2006-10-03. Scott, D. W. (1992), Multivariate Density Estimation. Theory, Practice and Visualization, New York: Wiley. Sheather, S. J. and Jones M. C. (1991), A reliable data-based bandwidth selection method for kernel density estimation., J. Roy. Statist. Soc. B, 683-690. Silverman, B. W. (1986), Density Estimation, London: Chapman and Hall. Venables, W. N. and Ripley, B. D. (2002), Modern Applied Statistics with S, New York: Springer. S original by Angelo Canty R port by Brian Ripley, boot: Bootstrap R (S-Plus) Functions (Canty), 2005 P. PONCET (2010). modeest: Mode Estimation. R package version 1.14. URL: CRAN.R-project.org/package=modeest
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