paper werkloosheid tendency

*Unverified author*

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Wed, 10 Dec 2008 02:53:25 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/10/t12289032213mart1tzkf9phta.htm/, Retrieved Wed, 10 Dec 2008 10:00:23 +0000

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/10/t12289032213mart1tzkf9phta.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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6,4 6,8 7,5 7,5 7,6 7,6 7,4 7,3 7,1 6,9 6,8 7,5 7,6 7,8 8 8,1 8,2 8,3 8,2 8 7,9 7,6 7,6 8,2 8,3 8,4 8,4 8,4 8,6 8,9 8,8 8,3 7,5 7,2 7,5 8,8 9,3 9,3 8,7 8,2 8,3 8,5 8,6 8,6 8,2 8,1 8 8,6 8,7 8,8 8,5 8,4 8,5 8,7 8,7 8,6 8,5 8,3 8,1 8,2 8,1 8,1 7,9 7,9 7,9 8 8 7,9 8 7,7 7,2 7,5 7,3 7 7 7 7,2 7,3 7,1 6,8 6,6 6,2 6,2 6,8 6,9

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 7.87058823529412 0.0756451899347014 104.046116376840 Geometric Mean 7.83913892273892 Harmonic Mean 7.80675449250949 Quadratic Mean 7.9010647085954 Winsorized Mean ( 1 / 28 ) 7.87058823529412 0.0756451899347014 104.046116376840 Winsorized Mean ( 2 / 28 ) 7.86588235294117 0.0725979091838137 108.348607299767 Winsorized Mean ( 3 / 28 ) 7.86941176470588 0.0704134156393066 111.760119762078 Winsorized Mean ( 4 / 28 ) 7.87882352941177 0.0685196432128348 114.986347855588 Winsorized Mean ( 5 / 28 ) 7.87882352941177 0.0685196432128348 114.986347855588 Winsorized Mean ( 6 / 28 ) 7.87176470588235 0.067438357883493 116.725331887257 Winsorized Mean ( 7 / 28 ) 7.87176470588235 0.067438357883493 116.725331887257 Winsorized Mean ( 8 / 28 ) 7.88117647058824 0.0657108110868314 119.937287947548 Winsorized Mean ( 9 / 28 ) 7.88117647058824 0.0657108110868314 119.937287947548 Winsorized Mean ( 10 / 28 ) 7.88117647058824 0.061981611930465 127.153460923699 Winsorized Mean ( 11 / 28 ) 7.88117647058824 0.061981611930465 127.153460923699 Winsorized Mean ( 12 / 28 ) 7.88117647058824 0.061981611930465 127.153460923699 Winsorized Mean ( 13 / 28 ) 7.8964705882353 0.059466513864648 132.788523743102 Winsorized Mean ( 14 / 28 ) 7.8964705882353 0.059466513864648 132.788523743102 Winsorized Mean ( 15 / 28 ) 7.8964705882353 0.0542957731052494 145.434352190334 Winsorized Mean ( 16 / 28 ) 7.8964705882353 0.0542957731052494 145.434352190334 Winsorized Mean ( 17 / 28 ) 7.8964705882353 0.0542957731052494 145.434352190334 Winsorized Mean ( 18 / 28 ) 7.91764705882353 0.0511540889272075 154.780335743842 Winsorized Mean ( 19 / 28 ) 7.89529411764706 0.0482438333631488 163.653954656056 Winsorized Mean ( 20 / 28 ) 7.89529411764706 0.0482438333631488 163.653954656056 Winsorized Mean ( 21 / 28 ) 7.92 0.0447150956155789 177.121392473119 Winsorized Mean ( 22 / 28 ) 7.94588235294118 0.0412532297751445 192.612369898093 Winsorized Mean ( 23 / 28 ) 7.91882352941176 0.0378517718484167 209.206151857935 Winsorized Mean ( 24 / 28 ) 7.91882352941176 0.0378517718484167 209.206151857935 Winsorized Mean ( 25 / 28 ) 7.91882352941176 0.0378517718484167 209.206151857935 Winsorized Mean ( 26 / 28 ) 7.91882352941176 0.0378517718484167 209.206151857935 Winsorized Mean ( 27 / 28 ) 7.91882352941176 0.0378517718484167 209.206151857935 Winsorized Mean ( 28 / 28 ) 7.91882352941176 0.0297277147493959 266.378482038303 Trimmed Mean ( 1 / 28 ) 7.87349397590361 0.072750511344052 108.225960621339 Trimmed Mean ( 2 / 28 ) 7.87654320987654 0.069372665235727 113.539579070693 Trimmed Mean ( 3 / 28 ) 7.88227848101266 0.0673550830848524 117.025740597525 Trimmed Mean ( 4 / 28 ) 7.88701298701299 0.0659685360012003 119.557192945277 Trimmed Mean ( 5 / 28 ) 7.88933333333333 0.0650037651947138 121.367328641678 Trimmed Mean ( 6 / 28 ) 7.89178082191781 0.0638608595185919 123.577742006749 Trimmed Mean ( 7 / 28 ) 7.89577464788732 0.0627805292105841 125.767889298967 Trimmed Mean ( 8 / 28 ) 7.9 0.061489053219367 128.478153205842 Trimmed Mean ( 9 / 28 ) 7.90298507462687 0.0603386399129766 130.977182880240 Trimmed Mean ( 10 / 28 ) 7.90615384615385 0.0589522673226841 134.111107260359 Trimmed Mean ( 11 / 28 ) 7.90952380952381 0.0580319970056902 136.295909457472 Trimmed Mean ( 12 / 28 ) 7.91311475409836 0.0568996532990516 139.071405453190 Trimmed Mean ( 13 / 28 ) 7.91694915254237 0.0555064111046322 142.631256371783 Trimmed Mean ( 14 / 28 ) 7.91929824561404 0.0542918986010292 145.865192591808 Trimmed Mean ( 15 / 28 ) 7.92181818181818 0.0527806533458572 150.089430115779 Trimmed Mean ( 16 / 28 ) 7.9245283018868 0.0518808546543089 152.744752465804 Trimmed Mean ( 17 / 28 ) 7.92745098039216 0.0507263656063377 156.278710008779 Trimmed Mean ( 18 / 28 ) 7.93061224489796 0.0492463681481982 161.039535362937 Trimmed Mean ( 19 / 28 ) 7.93191489361702 0.0480042380740354 165.233637942214 Trimmed Mean ( 20 / 28 ) 7.93555555555556 0.0469424271875469 169.048684335197 Trimmed Mean ( 21 / 28 ) 7.93953488372093 0.0455238409888717 174.403888407873 Trimmed Mean ( 22 / 28 ) 7.94146341463415 0.044444485755814 178.682760742603 Trimmed Mean ( 23 / 28 ) 7.94102564102564 0.0437324013137705 181.582199981440 Trimmed Mean ( 24 / 28 ) 7.94324324324324 0.0434165072433207 182.954450912567 Trimmed Mean ( 25 / 28 ) 7.94571428571429 0.0428683458746802 185.35154841156 Trimmed Mean ( 26 / 28 ) 7.94848484848485 0.0419959440955612 189.267916692102 Trimmed Mean ( 27 / 28 ) 7.9516129032258 0.0406588132048197 195.569232755747 Trimmed Mean ( 28 / 28 ) 7.9551724137931 0.0386299250041518 205.932898211376 Median 8 Midrange 7.75 Midmean - Weighted Average at Xnp 7.96 Midmean - Weighted Average at X(n+1)p 7.96 Midmean - Empirical Distribution Function 7.96 Midmean - Empirical Distribution Function - Averaging 7.96 Midmean - Empirical Distribution Function - Interpolation 7.96 Midmean - Closest Observation 7.91875 Midmean - True Basic - Statistics Graphics Toolkit 7.96 Midmean - MS Excel (old versions) 7.96 Number of observations 85

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t12289032213mart1tzkf9phta/12ktk1228902803.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t12289032213mart1tzkf9phta/12ktk1228902803.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t12289032213mart1tzkf9phta/2e8uq1228902803.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t12289032213mart1tzkf9phta/2e8uq1228902803.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

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)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) midm bitmap(file='test1.png') 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() bitmap(file='test2.png') 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() load(file='createtable') 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,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE) a<-table.element(a,arm) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean')) a<-table.element(a,armose) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE) a<-table.element(a,geo) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE) a<-table.element(a,har) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE) a<-table.element(a,qua) 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,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE) a<-table.element(a,win[j,1]) a<-table.element(a,win[j,2]) a<-table.element(a,win[j,1]/win[j,2]) 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,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE) a<-table.element(a,tri[j,1]) a<-table.element(a,tri[j,2]) a<-table.element(a,tri[j,1]/tri[j,2]) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE) a<-table.element(a,median(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE) a<-table.element(a,midr) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[1]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[2]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[3]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[4]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[5]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[6]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[7]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[8]) 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,length(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab')

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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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