Mini tutorial taak 1

*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, 26 Nov 2010 17:07:37 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/26/t1290791374l6ui4rbersp4z29.htm/, Retrieved Fri, 26 Nov 2010 18:09:35 +0100

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/2010/Nov/26/t1290791374l6ui4rbersp4z29.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

cijfers van belgie

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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3.4 3.4 3.4 -3.5 -3.5 -3.5 -8.3 -8.3 -8.3 -16.7 -16.7 -16.7 -11.6 -11.6 -11.6 -8.4 -8.4 -8.4 -8.6 -8.6 -8.6 0.6 0.6 0.6 -1.5 -1.5 -1.5 9.3 9.3 9.3 2.0 2.0 2.0 -5.5 -5.5 -5.5 4.0 4.0 4.0 -0.5 -0.5 -0.5 10.9 10.9 10.9 19.4 19.4 19.4 13.9 13.9 13.9 10.6 10.6 10.6 4.8 4.8 4.8 4.7 4.7 4.7 -3.9 -3.9 -3.9 -0.2 -0.2 -0.2

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.677272727272727 1.07133621434654 0.632175705631149 Geometric Mean NaN Harmonic Mean -4.11713389870945 Quadratic Mean 8.6639010738917 Winsorized Mean ( 1 / 22 ) 0.677272727272727 1.07133621434654 0.632175705631149 Winsorized Mean ( 2 / 22 ) 0.677272727272727 1.07133621434654 0.632175705631149 Winsorized Mean ( 3 / 22 ) 0.659090909090909 0.958711687199835 0.687475617425667 Winsorized Mean ( 4 / 22 ) 0.659090909090909 0.958711687199835 0.687475617425667 Winsorized Mean ( 5 / 22 ) 0.659090909090909 0.958711687199835 0.687475617425667 Winsorized Mean ( 6 / 22 ) 0.659090909090909 0.854585812170062 0.771240172379261 Winsorized Mean ( 7 / 22 ) 0.659090909090909 0.854585812170062 0.77124017237926 Winsorized Mean ( 8 / 22 ) 0.659090909090909 0.854585812170062 0.77124017237926 Winsorized Mean ( 9 / 22 ) 0.645454545454545 0.84257121690847 0.766053399999614 Winsorized Mean ( 10 / 22 ) 0.645454545454545 0.84257121690847 0.766053399999614 Winsorized Mean ( 11 / 22 ) 0.645454545454545 0.84257121690847 0.766053399999614 Winsorized Mean ( 12 / 22 ) 0.427272727272727 0.797804520795128 0.535560674495662 Winsorized Mean ( 13 / 22 ) 0.427272727272727 0.797804520795128 0.535560674495662 Winsorized Mean ( 14 / 22 ) 0.427272727272727 0.797804520795128 0.535560674495662 Winsorized Mean ( 15 / 22 ) 0.040909090909091 0.531335026477989 0.0769930248722002 Winsorized Mean ( 16 / 22 ) 0.040909090909091 0.531335026477989 0.0769930248722002 Winsorized Mean ( 17 / 22 ) 0.0409090909090907 0.531335026477989 0.0769930248721998 Winsorized Mean ( 18 / 22 ) 0.45 0.460582634970494 0.97702337394641 Winsorized Mean ( 19 / 22 ) 0.45 0.460582634970494 0.97702337394641 Winsorized Mean ( 20 / 22 ) 0.45 0.460582634970494 0.97702337394641 Winsorized Mean ( 21 / 22 ) 0.354545454545454 0.411116971984286 0.862395567943145 Winsorized Mean ( 22 / 22 ) 0.354545454545455 0.411116971984286 0.862395567943146 Trimmed Mean ( 1 / 22 ) 0.65625 1.02925432198529 0.637597516942348 Trimmed Mean ( 2 / 22 ) 0.633870967741936 0.978180634396392 0.64801013785463 Trimmed Mean ( 3 / 22 ) 0.61 0.915357668355353 0.66640617224085 Trimmed Mean ( 4 / 22 ) 0.591379310344828 0.893677071600614 0.661737141007368 Trimmed Mean ( 5 / 22 ) 0.571428571428571 0.86688618122908 0.659173699848802 Trimmed Mean ( 6 / 22 ) 0.55 0.8336005860764 0.659788403687125 Trimmed Mean ( 7 / 22 ) 0.526923076923077 0.823372362082395 0.639957206713174 Trimmed Mean ( 8 / 22 ) 0.502 0.809880263258913 0.619844713809891 Trimmed Mean ( 9 / 22 ) 0.475 0.792241299476204 0.599564804705397 Trimmed Mean ( 10 / 22 ) 0.447826086956522 0.772302781168955 0.579858182407027 Trimmed Mean ( 11 / 22 ) 0.418181818181818 0.746119437406662 0.560475705652866 Trimmed Mean ( 12 / 22 ) 0.385714285714286 0.711524278856799 0.542095747363688 Trimmed Mean ( 13 / 22 ) 0.38 0.677894553482343 0.560559157833531 Trimmed Mean ( 14 / 22 ) 0.373684210526316 0.632215776615028 0.591070682429144 Trimmed Mean ( 15 / 22 ) 0.366666666666667 0.568386745151127 0.645100663931166 Trimmed Mean ( 16 / 22 ) 0.408823529411765 0.560849362992384 0.728936424623016 Trimmed Mean ( 17 / 22 ) 0.45625 0.548695988965157 0.831516922258698 Trimmed Mean ( 18 / 22 ) 0.51 0.529830812293106 0.962571425003997 Trimmed Mean ( 19 / 22 ) 0.517857142857143 0.523547463305944 0.98913122334149 Trimmed Mean ( 20 / 22 ) 0.526923076923077 0.511725818783328 1.02969804841171 Trimmed Mean ( 21 / 22 ) 0.5375 0.491220474275886 1.09421334848132 Trimmed Mean ( 22 / 22 ) 0.563636363636364 0.476483577643419 1.18290826815896 Median 0.2 Midrange 1.35 Midmean - Weighted Average at Xnp 0.366666666666667 Midmean - Weighted Average at X(n+1)p 0.366666666666667 Midmean - Empirical Distribution Function 0.366666666666667 Midmean - Empirical Distribution Function - Averaging 0.366666666666667 Midmean - Empirical Distribution Function - Interpolation 0.366666666666667 Midmean - Closest Observation 0.366666666666667 Midmean - True Basic - Statistics Graphics Toolkit 0.366666666666667 Midmean - MS Excel (old versions) 0.366666666666667 Number of observations 66

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/26/t1290791374l6ui4rbersp4z29/17rlw1290791253.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290791374l6ui4rbersp4z29/17rlw1290791253.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290791374l6ui4rbersp4z29/27rlw1290791253.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290791374l6ui4rbersp4z29/27rlw1290791253.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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