workshop 3 review

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Fri, 23 Oct 2009 08:17:25 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/23/t1256307516cmbzdu2076dpoi8.htm/, Retrieved Fri, 23 Oct 2009 16:18:38 +0200

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/2009/Oct/23/t1256307516cmbzdu2076dpoi8.htm/}, year = {2009}, } @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 = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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-1,6 -1,8 -1 -0,9 -2 -0,4 -0,4 -0,2 -0,5 -0,8 0,3 -1,3 -1,6 -0,4 0,2 0,6 -0,1 0,4 0,9 0,2 0,5 0,6 0,5 0,3 -0,3 0,6 0,6 0,9 -0,7 1,2 0,8 0,7 0,1 -0,4 0 -0,6 -1 0,2 0,9 1,1 -0,6 1,2 0,3 0,7 0,9 0,7 0,2 0,3 -0,2 0,8 1,2 1,2 -0,5 1,4 0,4 1,1 1 0,7 0,7 0,4 0 0,9 1,1 1,7 -0,2 1,6 1,3 1,3 1 0,7 0,4 0,3

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 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.244444444444444 0.0983209765628508 2.48618812576771 Geometric Mean NaN Harmonic Mean 0 Quadratic Mean 0.863777234656663 Winsorized Mean ( 1 / 24 ) 0.245833333333333 0.097181273513742 2.52963687802024 Winsorized Mean ( 2 / 24 ) 0.245833333333333 0.0945696433806287 2.59949519259464 Winsorized Mean ( 3 / 24 ) 0.241666666666667 0.0938806470996206 2.57419046558365 Winsorized Mean ( 4 / 24 ) 0.258333333333333 0.0895290669789192 2.88546884325469 Winsorized Mean ( 5 / 24 ) 0.272222222222222 0.083619747758929 3.25547767743839 Winsorized Mean ( 6 / 24 ) 0.272222222222222 0.083619747758929 3.25547767743839 Winsorized Mean ( 7 / 24 ) 0.281944444444444 0.0815855779491648 3.45581230815232 Winsorized Mean ( 8 / 24 ) 0.293055555555556 0.079373682604347 3.69209977337634 Winsorized Mean ( 9 / 24 ) 0.293055555555556 0.0750411047737744 3.90526707248017 Winsorized Mean ( 10 / 24 ) 0.306944444444444 0.072522361477518 4.23241105489371 Winsorized Mean ( 11 / 24 ) 0.306944444444444 0.072522361477518 4.23241105489371 Winsorized Mean ( 12 / 24 ) 0.306944444444444 0.0671440183885027 4.57143393873792 Winsorized Mean ( 13 / 24 ) 0.306944444444444 0.0671440183885027 4.57143393873792 Winsorized Mean ( 14 / 24 ) 0.306944444444444 0.0611677696517229 5.01807481606939 Winsorized Mean ( 15 / 24 ) 0.306944444444444 0.0611677696517229 5.01807481606939 Winsorized Mean ( 16 / 24 ) 0.306944444444444 0.0611677696517229 5.01807481606939 Winsorized Mean ( 17 / 24 ) 0.306944444444444 0.0611677696517229 5.01807481606939 Winsorized Mean ( 18 / 24 ) 0.331944444444444 0.0571844060435839 5.80480706910637 Winsorized Mean ( 19 / 24 ) 0.331944444444444 0.0495214338796173 6.70304590233343 Winsorized Mean ( 20 / 24 ) 0.331944444444444 0.0495214338796173 6.70304590233343 Winsorized Mean ( 21 / 24 ) 0.302777777777778 0.045792116431947 6.61200663716308 Winsorized Mean ( 22 / 24 ) 0.333333333333333 0.0411588776345725 8.09869832440087 Winsorized Mean ( 23 / 24 ) 0.365277777777778 0.0365341032087834 9.99826862288927 Winsorized Mean ( 24 / 24 ) 0.365277777777778 0.0365341032087834 9.99826862288927 Trimmed Mean ( 1 / 24 ) 0.255714285714286 0.0935306044682572 2.73401724674057 Trimmed Mean ( 2 / 24 ) 0.266176470588235 0.0891529324524502 2.9856165497439 Trimmed Mean ( 3 / 24 ) 0.277272727272727 0.0856020895586588 3.23908830616484 Trimmed Mean ( 4 / 24 ) 0.290625 0.0816107300538393 3.5611126111514 Trimmed Mean ( 5 / 24 ) 0.3 0.0784905185474709 3.82211769716569 Trimmed Mean ( 6 / 24 ) 0.306666666666667 0.0766482414607192 4.00096154618012 Trimmed Mean ( 7 / 24 ) 0.313793103448276 0.0743777687589104 4.21890987971703 Trimmed Mean ( 8 / 24 ) 0.319642857142857 0.0721389191415876 4.43093493701357 Trimmed Mean ( 9 / 24 ) 0.324074074074074 0.0699373376906125 4.63377767549155 Trimmed Mean ( 10 / 24 ) 0.328846153846154 0.0682321771855529 4.81951723381006 Trimmed Mean ( 11 / 24 ) 0.332 0.0666663945572678 4.98002032665506 Trimmed Mean ( 12 / 24 ) 0.335416666666667 0.0646519310823072 5.18803786757203 Trimmed Mean ( 13 / 24 ) 0.339130434782609 0.0632820739069668 5.35902845537547 Trimmed Mean ( 14 / 24 ) 0.343181818181818 0.0614653451986421 5.58333833597993 Trimmed Mean ( 15 / 24 ) 0.347619047619048 0.0604126436872559 5.75407772946673 Trimmed Mean ( 16 / 24 ) 0.3525 0.0589423338352726 5.98042149103121 Trimmed Mean ( 17 / 24 ) 0.357894736842105 0.0569034493285053 6.28950865132917 Trimmed Mean ( 18 / 24 ) 0.363888888888889 0.0540653305245296 6.73054035476194 Trimmed Mean ( 19 / 24 ) 0.367647058823529 0.0513143797165231 7.16460105051505 Trimmed Mean ( 20 / 24 ) 0.371875 0.0496427509488968 7.4910232187337 Trimmed Mean ( 21 / 24 ) 0.376666666666667 0.0471445157360289 7.98961789692984 Trimmed Mean ( 22 / 24 ) 0.385714285714286 0.0444586145211458 8.6758053499582 Trimmed Mean ( 23 / 24 ) 0.392307692307692 0.0422166853354223 9.2927165927573 Trimmed Mean ( 24 / 24 ) 0.395833333333333 0.0405930522838553 9.75125818490779 Median 0.4 Midrange -0.15 Midmean - Weighted Average at Xnp 0.343181818181818 Midmean - Weighted Average at X(n+1)p 0.4175 Midmean - Empirical Distribution Function 0.343181818181818 Midmean - Empirical Distribution Function - Averaging 0.4175 Midmean - Empirical Distribution Function - Interpolation 0.4175 Midmean - Closest Observation 0.343181818181818 Midmean - True Basic - Statistics Graphics Toolkit 0.4175 Midmean - MS Excel (old versions) 0.343181818181818 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/23/t1256307516cmbzdu2076dpoi8/1o2uq1256307442.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/23/t1256307516cmbzdu2076dpoi8/1o2uq1256307442.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/23/t1256307516cmbzdu2076dpoi8/2wz5u1256307442.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/23/t1256307516cmbzdu2076dpoi8/2wz5u1256307442.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')

Copyright

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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