TIJDREEKS B - STAP 9

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 09 Aug 2010 15:19:43 +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/Aug/09/t12813671728g5ti2vkocubkpl.htm/, Retrieved Mon, 09 Aug 2010 17:19:33 +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/2010/Aug/09/t12813671728g5ti2vkocubkpl.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Schrauwen Nathalie

Dataseries X:

» Textbox « » Textfile « » CSV «

162 161 160 158 156 155 156 158 159 159 160 162 168 177 174 169 169 160 168 172 173 175 170 177 187 201 188 179 176 170 179 183 174 177 170 166 171 178 165 162 159 149 153 156 149 150 139 131 141 150 128 124 120 113 120 121 115 119 106 98 106 116 93 94 90 93 100 99 90 91 83 83 92 104 71 69 67 75 86 81 88 87 77 70

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 137.261904761905 4.06297666951063 33.7835818236282 Geometric Mean 131.588784917565 Harmonic Mean 125.37737953966 Quadratic Mean 142.165312894799 Winsorized Mean ( 1 / 28 ) 137.130952380952 4.03167250393362 34.0134155855061 Winsorized Mean ( 2 / 28 ) 137.130952380952 4.02326780243004 34.0844704143547 Winsorized Mean ( 3 / 28 ) 137.02380952381 3.99555031442614 34.2941018735462 Winsorized Mean ( 4 / 28 ) 137.02380952381 3.93303003307888 34.8392482059293 Winsorized Mean ( 5 / 28 ) 137.142857142857 3.9106905442317 35.0687060486399 Winsorized Mean ( 6 / 28 ) 137.357142857143 3.84986617321643 35.6784201520402 Winsorized Mean ( 7 / 28 ) 137.440476190476 3.81030968478912 36.0706838972021 Winsorized Mean ( 8 / 28 ) 137.440476190476 3.81030968478912 36.0706838972021 Winsorized Mean ( 9 / 28 ) 137.761904761905 3.75595221047195 36.6782900958674 Winsorized Mean ( 10 / 28 ) 137.761904761905 3.72142465300169 37.0185930409168 Winsorized Mean ( 11 / 28 ) 137.761904761905 3.68392715600737 37.3953932659219 Winsorized Mean ( 12 / 28 ) 137.904761904762 3.6206212419618 38.0887015483673 Winsorized Mean ( 13 / 28 ) 137.904761904762 3.6206212419618 38.0887015483673 Winsorized Mean ( 14 / 28 ) 137.904761904762 3.57429221586759 38.5823971785385 Winsorized Mean ( 15 / 28 ) 137.904761904762 3.52519897867456 39.1197100472929 Winsorized Mean ( 16 / 28 ) 137.904761904762 3.47338949862883 39.7032241731605 Winsorized Mean ( 17 / 28 ) 137.702380952381 3.45036021142908 39.9095666870523 Winsorized Mean ( 18 / 28 ) 137.916666666667 3.41704446367104 40.361390708536 Winsorized Mean ( 19 / 28 ) 138.821428571429 3.27909811190607 42.3352470203262 Winsorized Mean ( 20 / 28 ) 138.821428571429 3.21638629010109 43.1606828441821 Winsorized Mean ( 21 / 28 ) 139.071428571429 3.17923130321947 43.7437277465773 Winsorized Mean ( 22 / 28 ) 139.857142857143 2.99641892102876 46.6747629564179 Winsorized Mean ( 23 / 28 ) 140.404761904762 2.91803888944335 48.1161380037487 Winsorized Mean ( 24 / 28 ) 139.833333333333 2.85391264139197 48.9970615446487 Winsorized Mean ( 25 / 28 ) 141.619047619048 2.52973735265329 55.9817197902034 Winsorized Mean ( 26 / 28 ) 141.309523809524 2.34453357640697 60.271913028468 Winsorized Mean ( 27 / 28 ) 141.630952380952 2.30123689968575 61.5455768157956 Winsorized Mean ( 28 / 28 ) 142.630952380952 2.16844975584703 65.7755394130581 Trimmed Mean ( 1 / 28 ) 137.341463414634 3.99661929976064 34.364409795764 Trimmed Mean ( 2 / 28 ) 137.5625 3.95488176742413 34.782961435936 Trimmed Mean ( 3 / 28 ) 137.794871794872 3.9103915187131 35.2381267030314 Trimmed Mean ( 4 / 28 ) 138.078947368421 3.86907501334756 35.6878444827447 Trimmed Mean ( 5 / 28 ) 138.378378378378 3.84028138155088 36.0333956368829 Trimmed Mean ( 6 / 28 ) 138.666666666667 3.81096761707624 36.3862096453738 Trimmed Mean ( 7 / 28 ) 138.928571428571 3.78967330781253 36.6597751690537 Trimmed Mean ( 8 / 28 ) 139.191176470588 3.77088898730571 36.9120323985034 Trimmed Mean ( 9 / 28 ) 139.469696969697 3.74578051327076 37.2338145482834 Trimmed Mean ( 10 / 28 ) 139.71875 3.72414824274338 37.5169678790973 Trimmed Mean ( 11 / 28 ) 139.983870967742 3.70162197611936 37.8169007723732 Trimmed Mean ( 12 / 28 ) 140.266666666667 3.67798970719772 38.1367752041744 Trimmed Mean ( 13 / 28 ) 140.551724137931 3.65720930815421 38.431413762552 Trimmed Mean ( 14 / 28 ) 140.857142857143 3.62794247540169 38.825627421655 Trimmed Mean ( 15 / 28 ) 141.185185185185 3.59624329126589 39.2590750264529 Trimmed Mean ( 16 / 28 ) 141.538461538462 3.56151093422249 39.7411278955853 Trimmed Mean ( 17 / 28 ) 141.92 3.52296720949595 40.2842239398264 Trimmed Mean ( 18 / 28 ) 142.354166666667 3.47336491244612 40.9845122107869 Trimmed Mean ( 19 / 28 ) 142.804347826087 3.4124834150778 41.8476313159843 Trimmed Mean ( 20 / 28 ) 143.204545454545 3.35931061484859 42.6291468319609 Trimmed Mean ( 21 / 28 ) 143.642857142857 3.29745289878586 43.5617616238725 Trimmed Mean ( 22 / 28 ) 144.1 3.21929280337253 44.7613835712741 Trimmed Mean ( 23 / 28 ) 144.526315789474 3.1534344983343 45.8313993411993 Trimmed Mean ( 24 / 28 ) 144.944444444444 3.07832784036544 47.0854476718885 Trimmed Mean ( 25 / 28 ) 145.470588235294 2.9809960453965 48.7993227833836 Trimmed Mean ( 26 / 28 ) 145.875 2.93228346009089 49.7479189803426 Trimmed Mean ( 27 / 28 ) 146.366666666667 2.89846702777712 50.4979581495939 Trimmed Mean ( 28 / 28 ) 146.892857142857 2.8486232104319 51.5662642236864 Median 154 Midrange 134 Midmean - Weighted Average at Xnp 143.204545454545 Midmean - Weighted Average at X(n+1)p 144.232558139535 Midmean - Empirical Distribution Function 143.204545454545 Midmean - Empirical Distribution Function - Averaging 144.232558139535 Midmean - Empirical Distribution Function - Interpolation 144.232558139535 Midmean - Closest Observation 143.204545454545 Midmean - True Basic - Statistics Graphics Toolkit 144.232558139535 Midmean - MS Excel (old versions) 143.204545454545 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/09/t12813671728g5ti2vkocubkpl/1lnp81281367179.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/09/t12813671728g5ti2vkocubkpl/1lnp81281367179.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/09/t12813671728g5ti2vkocubkpl/2lnp81281367179.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/09/t12813671728g5ti2vkocubkpl/2lnp81281367179.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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