R version 3.4.3 (2017-11-30) -- "Kite-Eating Tree"
Copyright (C) 2017 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> source('/home/pw/wessanet/cretab')
>
>
>
> myrfcuid = 'account3'
>
> x <- c(1.72923686058208,0.122433126801145,0.523768788982079,-0.50175942601324,-1.86386120887019,0.0717422351702872,-0.380578531491989,-0.29851611788274,1.94316215667028,-1.24779901378139,1.35257277275093,2.84406850014719,1.12274878943606,-2.32540657982629,-2.89902363942181,0.246874012745119,-0.731094375584061,1.97769407549524,-0.089308186457892,-1.64931358279907,1.78988776616251,-0.655026882699021,-0.95518008982139,-0.501427837065876,-1.47468882156665,2.4255103110643,-0.388732570521789,-1.41970373897772,-0.435743764210552,0.588337253253952,-1.73087780677345,0.416192838768035,-0.135602934239543,1.5607508968729,-0.619488852927662,0.130061173484127,-0.485714783249833,1.19042117073251,0.504940688912012,-0.266725732456376,1.8987616014054,0.9835731579105,0.221023228988728,-0.176860990484583,-0.162198287814433,0.78911590880292,1.41209201053576,0.518161844628975,2.36462043434148,-1.24446105804486,1.09138861156198,0.422175612267996,-0.997989397904933,0.754650745534752,-1.44375392644115,0.568632265545353,1.35413305240232,-1.34288885715882,-0.0968579661829751,0.242767533935212,0.255744783559028,-0.243232899636027,0.461607264600104,0.0650797112167817,2.25999343044582,1.80462197944889,2.32548979115297,0.682758803307819,-0.335554613197298,-0.997929583796738,0.97507128242145,-1.17268516900173,-0.000337278483281606,-1.71460596672184,-1.34872342854985,-1.6521456119588,-1.48335049731373,0.925016701443022,-0.226525557050897,0.774905929042345,-0.339789522342372,0.89311055438168,-0.864578780222597,-1.95217915873499,-0.11317194501752,1.02470860347022,-1.25650654087286,-0.602130638597027,-0.83233134657693,-0.446577198612737,-4.01053303468812,0.288513333839785,-1.00798474916531,-0.572816189634855,-0.297410570159231,1.21578539483534,-0.727486991378146,-0.843943364912431,-1.20889338911855,-0.649656515850742,3.19984732249364,0.572738529480399,-0.0199646221520179,0.462316869083462,-1.28699501625665,-1.80757939159691,-2.15431670426712,0.707840316820782,1.36410372036211,0.314718394752158,-4.1002515835693,1.26992188862053,1.80144339707427,-0.42970220964945,0.529993653035631,1.18764422512472,-0.398233352310507,-0.421884162222733,-2.6898323919027,1.0140628812162,-0.542058945797581,-0.368690243263354,1.31411524584048,-0.428705333764204,-0.663582558495647,1.37204511801761,-1.27310996987184,0.810157913937622,1.5741305304336,-1.025150115941,-0.998930862337702,-0.0536208441845616,1.66337771592794,-0.178008462116163,-1.09164775518912,1.96797905166753,0.634220496887586,1.38764487483822,0.75570654001001,-2.3214750727902,1.62023993830839,0.423224828517651,-1.7051130142733,0.541981863740972,-0.593027838089475,0.213567450337977,-0.696840242545287,0.0777251570183703,-0.725328497765991,2.1315776363419,-0.33645518676905,-0.979182554450992,-0.242246084610725,-1.82980075345691,-1.14814874978528,0.496126806273696,-0.37803015357093,0.564631359789787,0.268965939275992,0.752661368724124,-2.30203173253409,2.82635859577673,-0.607627712639158,3.77405193258893,1.08426693162876,-2.2508985634727,0.290663952981133,-1.1346060583543,1.41583984485642,0.590041695581542,1.22056539827692,0.0970995178245223,-0.906020145960084,-0.597681226735446,0.437155726246844,0.742487563055592,1.22917286536281,-0.95259160353182,-0.75528682870179)
> ylimmax = ''
> ylimmin = ''
> main = 'Robustness of Central Tendency'
> #'GNU S' R Code compiled by R2WASP v. 1.2.327 (Thu, 20 Jul 2017 08:33:00 +0200)
> #Author: root
> #To cite this work: Wessa, P., (2017), Central Tendency (v1.0.7) in Free Statistics Software (v$_version), Office for Research Development and Education, URL https://www.wessa.net/rwasp_centraltendency.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #
> geomean <- function(x) {
+ return(exp(mean(log(x))))
+ }
> harmean <- function(x) {
+ return(1/mean(1/x))
+ }
> quamean <- function(x) {
+ return(sqrt(mean(x*x)))
+ }
> winmean <- function(x) {
+ x <-sort(x[!is.na(x)])
+ n<-length(x)
+ denom <- 3
+ nodenom <- n/denom
+ if (nodenom>40) denom <- n/40
+ sqrtn = sqrt(n)
+ roundnodenom = floor(nodenom)
+ win <- array(NA,dim=c(roundnodenom,2))
+ for (j in 1:roundnodenom) {
+ win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
+ win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
+ }
+ return(win)
+ }
> trimean <- function(x) {
+ x <-sort(x[!is.na(x)])
+ n<-length(x)
+ denom <- 3
+ nodenom <- n/denom
+ if (nodenom>40) denom <- n/40
+ sqrtn = sqrt(n)
+ roundnodenom = floor(nodenom)
+ tri <- array(NA,dim=c(roundnodenom,2))
+ for (j in 1:roundnodenom) {
+ tri[j,1] <- mean(x,trim=j/n)
+ tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
+ }
+ return(tri)
+ }
> midrange <- function(x) {
+ return((max(x)+min(x))/2)
+ }
> q1 <- function(data,n,p,i,f) {
+ np <- n*p;
+ i <<- floor(np)
+ f <<- np - i
+ qvalue <- (1-f)*data[i] + f*data[i+1]
+ }
> q2 <- function(data,n,p,i,f) {
+ np <- (n+1)*p
+ i <<- floor(np)
+ f <<- np - i
+ qvalue <- (1-f)*data[i] + f*data[i+1]
+ }
> q3 <- function(data,n,p,i,f) {
+ np <- n*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- data[i]
+ } else {
+ qvalue <- data[i+1]
+ }
+ }
> q4 <- function(data,n,p,i,f) {
+ np <- n*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- (data[i]+data[i+1])/2
+ } else {
+ qvalue <- data[i+1]
+ }
+ }
> q5 <- function(data,n,p,i,f) {
+ np <- (n-1)*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- data[i+1]
+ } else {
+ qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
+ }
+ }
> q6 <- function(data,n,p,i,f) {
+ np <- n*p+0.5
+ i <<- floor(np)
+ f <<- np - i
+ qvalue <- data[i]
+ }
> q7 <- function(data,n,p,i,f) {
+ np <- (n+1)*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- data[i]
+ } else {
+ qvalue <- f*data[i] + (1-f)*data[i+1]
+ }
+ }
> q8 <- function(data,n,p,i,f) {
+ np <- (n+1)*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- data[i]
+ } else {
+ if (f == 0.5) {
+ qvalue <- (data[i]+data[i+1])/2
+ } else {
+ if (f < 0.5) {
+ qvalue <- data[i]
+ } else {
+ qvalue <- data[i+1]
+ }
+ }
+ }
+ }
> midmean <- function(x,def) {
+ x <-sort(x[!is.na(x)])
+ n<-length(x)
+ if (def==1) {
+ qvalue1 <- q1(x,n,0.25,i,f)
+ qvalue3 <- q1(x,n,0.75,i,f)
+ }
+ if (def==2) {
+ qvalue1 <- q2(x,n,0.25,i,f)
+ qvalue3 <- q2(x,n,0.75,i,f)
+ }
+ if (def==3) {
+ qvalue1 <- q3(x,n,0.25,i,f)
+ qvalue3 <- q3(x,n,0.75,i,f)
+ }
+ if (def==4) {
+ qvalue1 <- q4(x,n,0.25,i,f)
+ qvalue3 <- q4(x,n,0.75,i,f)
+ }
+ if (def==5) {
+ qvalue1 <- q5(x,n,0.25,i,f)
+ qvalue3 <- q5(x,n,0.75,i,f)
+ }
+ if (def==6) {
+ qvalue1 <- q6(x,n,0.25,i,f)
+ qvalue3 <- q6(x,n,0.75,i,f)
+ }
+ if (def==7) {
+ qvalue1 <- q7(x,n,0.25,i,f)
+ qvalue3 <- q7(x,n,0.75,i,f)
+ }
+ if (def==8) {
+ qvalue1 <- q8(x,n,0.25,i,f)
+ qvalue3 <- q8(x,n,0.75,i,f)
+ }
+ midm <- 0
+ myn <- 0
+ roundno4 <- round(n/4)
+ round3no4 <- round(3*n/4)
+ for (i in 1:n) {
+ if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
+ midm = midm + x[i]
+ myn = myn + 1
+ }
+ }
+ midm = midm / myn
+ return(midm)
+ }
> (arm <- mean(x))
[1] -1.989305e-16
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 0.09684876
> (armose <- arm / armse)
[1] -2.054032e-15
> (geo <- geomean(x))
[1] NaN
Warning message:
In log(x) : NaNs produced
> (har <- harmean(x))
[1] -0.05912054
> (qua <- quamean(x))
[1] 1.292124
> (win <- winmean(x))
               [,1]       [,2]
 [1,] -0.0027066260 0.09607873
 [2,]  0.0057372910 0.09281121
 [3,]  0.0089464755 0.09216355
 [4,]  0.0081325655 0.08944528
 [5,]  0.0065415496 0.08917371
 [6,]  0.0058816400 0.08888480
 [7,]  0.0053199509 0.08822366
 [8,]  0.0038972052 0.08680475
 [9,]  0.0063233832 0.08439097
[10,]  0.0107146082 0.08368757
[11,]  0.0112826482 0.08322617
[12,]  0.0097957749 0.08265642
[13,]  0.0085293253 0.08111246
[14,]  0.0095533789 0.08092871
[15,]  0.0093805288 0.08071341
[16,]  0.0086937352 0.07948739
[17,]  0.0027079197 0.07870468
[18,]  0.0150590680 0.07628537
[19,]  0.0110841691 0.07561038
[20,]  0.0130456508 0.07505775
[21,] -0.0011335567 0.07283496
[22,]  0.0071296526 0.07184465
[23,]  0.0047380941 0.07142176
[24,]  0.0101406528 0.07040927
[25,]  0.0109707714 0.07008870
[26,]  0.0119341892 0.06968438
[27,]  0.0130122656 0.06952485
[28,]  0.0075187014 0.06882517
[29,]  0.0061212435 0.06748073
[30,]  0.0053602150 0.06615603
[31,]  0.0081188604 0.06557814
[32,]  0.0096853744 0.06525021
[33,]  0.0129289756 0.06399152
[34,]  0.0250323476 0.06273021
[35,]  0.0156996525 0.06110792
[36,]  0.0112134711 0.06029820
[37,]  0.0099359964 0.06013192
[38,] -0.0026949731 0.05887627
[39,] -0.0009298838 0.05826247
[40,] -0.0023795506 0.05709410
[41,] -0.0037340140 0.05684987
[42,] -0.0045512832 0.05470283
[43,] -0.0022606999 0.05305821
[44,] -0.0175789005 0.05069185
[45,] -0.0199495676 0.04994141
[46,] -0.0038021444 0.04782907
[47,] -0.0024911164 0.04681104
[48,] -0.0018068912 0.04670076
[49,] -0.0017605967 0.04659966
[50,]  0.0033551714 0.04565120
[51,]  0.0029592626 0.04394534
[52,] -0.0018415394 0.04308002
[53,] -0.0146231081 0.04167396
[54,] -0.0188499320 0.03974127
[55,] -0.0157291589 0.03938760
[56,] -0.0188894515 0.03882329
[57,] -0.0187801810 0.03859192
[58,] -0.0185687619 0.03835415
[59,] -0.0193722983 0.03715943
> (tri <- trimean(x))
               [,1]       [,2]
 [1,]  1.842936e-03 0.09271751
 [2,]  6.496488e-03 0.08905067
 [3,]  6.889251e-03 0.08695211
 [4,]  6.171429e-03 0.08494387
 [5,]  5.652134e-03 0.08360704
 [6,]  5.461468e-03 0.08223742
 [7,]  5.385498e-03 0.08082553
 [8,]  5.395781e-03 0.07943091
 [9,]  5.604046e-03 0.07817244
[10,]  5.514066e-03 0.07719288
[11,]  4.921138e-03 0.07623704
[12,]  4.253272e-03 0.07526703
[13,]  3.712908e-03 0.07429135
[14,]  3.273714e-03 0.07342233
[15,]  3.273714e-03 0.07250222
[16,]  2.195365e-03 0.07152871
[17,]  1.693982e-03 0.07060483
[18,]  1.619323e-03 0.06968314
[19,]  6.714454e-04 0.06892409
[20,] -3.430152e-05 0.06816286
[21,] -8.887948e-04 0.06738477
[22,] -8.733406e-04 0.06674221
[23,] -1.362929e-03 0.06612725
[24,] -1.725386e-03 0.06548973
[25,] -2.411439e-03 0.06487765
[26,] -3.165901e-03 0.06423125
[27,] -3.997568e-03 0.06355364
[28,] -4.914388e-03 0.06281953
[29,] -5.571272e-03 0.06207040
[30,] -5.571272e-03 0.06135882
[31,] -6.766155e-03 0.06068423
[32,] -7.513537e-03 0.05998396
[33,] -8.364921e-03 0.05923280
[34,] -9.405491e-03 0.05850525
[35,] -1.106884e-02 0.05779988
[36,] -1.234830e-02 0.05715331
[37,] -1.346405e-02 0.05649803
[38,] -1.456314e-02 0.05577493
[39,] -1.511665e-02 0.05507455
[40,] -1.577437e-02 0.05433838
[41,] -1.639232e-02 0.05361251
[42,] -1.697405e-02 0.05281122
[43,] -1.754335e-02 0.05210417
[44,] -1.824245e-02 0.05145194
[45,] -1.827279e-02 0.05092778
[46,] -1.819612e-02 0.05039116
[47,] -1.885508e-02 0.04996702
[48,] -1.960595e-02 0.04956345
[49,] -2.042540e-02 0.04909451
[50,] -2.128849e-02 0.04854913
[51,] -2.128849e-02 0.04800198
[52,] -2.362261e-02 0.04753310
[53,] -2.464969e-02 0.04706355
[54,] -2.512664e-02 0.04665288
[55,] -2.542818e-02 0.04636271
[56,] -2.589931e-02 0.04603151
[57,] -2.624402e-02 0.04567696
[58,] -2.661607e-02 0.04525326
[59,] -2.702322e-02 0.04474740
> (midr <- midrange(x))
[1] -0.1630998
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] -0.02744690 -0.01824245 -0.01824245 -0.01824245 -0.01827279 -0.02744690
[7] -0.01824245 -0.01824245
> postscript(file="/home/pw/wessanet/rcomp/tmp/1hdtg1516786829.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> lb <- win[,1] - 2*win[,2]
> ub <- win[,1] + 2*win[,2]
> if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
> lines(ub,lty=3)
> lines(lb,lty=3)
> grid()
> dev.off()
null device
          1
> postscript(file="/home/pw/wessanet/rcomp/tmp/25grc1516786829.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556)
> lb <- tri[,1] - 2*tri[,2]
> ub <- tri[,1] + 2*tri[,2]
> if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
> lines(ub,lty=3)
> lines(lb,lty=3)
> grid()
> dev.off()
null device
          1
>
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Measure',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.element(a,'S.E.',header=TRUE)
> a<-table.element(a,'Value/S.E.',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Arithmetic Mean',header=TRUE)
> a<-table.element(a,signif(arm,6))
> a<-table.element(a, signif(armse,6))
> a<-table.element(a,signif(armose,6))
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a, 'Geometric Mean',header=TRUE)
> a<-table.element(a,signif(geo,6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a, 'Harmonic Mean',header=TRUE)
> a<-table.element(a,signif(har,6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a, 'Quadratic Mean',header=TRUE)
> a<-table.element(a,signif(qua,6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> for (j in 1:length(win[,1])) {
+ a<-table.row.start(a)
+ mylabel <- paste('Winsorized Mean (',j)
+ mylabel <- paste(mylabel,'/')
+ mylabel <- paste(mylabel,length(win[,1]))
+ mylabel <- paste(mylabel,')')
+ a<-table.element(a, mylabel,header=TRUE)
+ a<-table.element(a,signif(win[j,1],6))
+ a<-table.element(a,signif(win[j,2],6))
+ a<-table.element(a,signif(win[j,1]/win[j,2],6))
+ a<-table.row.end(a)
+ }
> for (j in 1:length(tri[,1])) {
+ a<-table.row.start(a)
+ mylabel <- paste('Trimmed Mean (',j)
+ mylabel <- paste(mylabel,'/')
+ mylabel <- paste(mylabel,length(tri[,1]))
+ mylabel <- paste(mylabel,')')
+ a<-table.element(a, mylabel,header=TRUE)
+ a<-table.element(a,signif(tri[j,1],6))
+ a<-table.element(a,signif(tri[j,2],6))
+ a<-table.element(a,signif(tri[j,1]/tri[j,2],6))
+ a<-table.row.end(a)
+ }
> a<-table.row.start(a)
> a<-table.element(a, 'Median',header=TRUE)
> a<-table.element(a,signif(median(x),6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a, 'Midrange',header=TRUE)
> a<-table.element(a,signif(midr,6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <-  'Midmean'
> mylabel <- paste(mymid,'Weighted Average at Xnp',sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,signif(midm[1],6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <-  'Midmean'
> mylabel <- paste(mymid,'Weighted Average at X(n+1)p',sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,signif(midm[2],6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <-  'Midmean'
> mylabel <- paste(mymid,'Empirical Distribution Function',sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,signif(midm[3],6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <-  'Midmean'
> mylabel <- paste(mymid,'Empirical Distribution Function - Averaging',sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,signif(midm[4],6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <-  'Midmean'
> mylabel <- paste(mymid,'Empirical Distribution Function - Interpolation',sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,signif(midm[5],6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <-  'Midmean'
> mylabel <- paste(mymid,'Closest Observation',sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,signif(midm[6],6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <-  'Midmean'
> mylabel <- paste(mymid,'True Basic - Statistics Graphics Toolkit',sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,signif(midm[7],6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <-  'Midmean'
> mylabel <- paste(mymid,'MS Excel (old versions)',sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,signif(midm[8],6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Number of observations',header=TRUE)
> a<-table.element(a,signif(length(x),6))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.end(a)
> table.save(a,file="/home/pw/wessanet/rcomp/tmp/3d6i51516786830.tab")
>
> try(system("convert /home/pw/wessanet/rcomp/tmp/1hdtg1516786829.ps /home/pw/wessanet/rcomp/tmp/1hdtg1516786829.png",intern=TRUE))
character(0)
> try(system("convert /home/pw/wessanet/rcomp/tmp/25grc1516786829.ps /home/pw/wessanet/rcomp/tmp/25grc1516786829.png",intern=TRUE))
character(0)
>
> proc.time()
   user  system elapsed
  2.616   0.320   4.514