WS3 - part 3

*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: Sun, 18 Oct 2009 13:07:59 -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/18/t125589325604t6ip4v7719pou.htm/, Retrieved Sun, 18 Oct 2009 21:14:18 +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/18/t125589325604t6ip4v7719pou.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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1808,923925 2113,117473 2541,84569 2260,907927 1586,718976 3422,401471 2898,922674 3346,283824 3152,737195 2689,274383 3346,516139 2012,759884 2076,098563 2185,753736 2250,872059 2123,105952 1181,813235 3596,328448 3314,719253 3935,550581 3119,107353 3144,429819 2884,6 2137,493293 2062,484259 2170,755864 2547,6 2123,478165 1108,921203 3813,725 3242,1 3803,098418 3155,6 3182,96526 3503,502778 2645,625 2483,225 2840,939286 3462,653571 2753,796429 1692,391667 4247,334589 4164,210915 4337,783824 4912,9125 4156,995492 4051,686538 2547,250974 2174,997152 2659,225 3186,703261 2282,618939 1591,196014 3228,030195 2934,475 3396,475 3325,173052 2733,635959 2998,765541 2272,360802 1967,923795

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 3 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 2834.30980811475 104.021130770028 27.2474427756501 Geometric Mean 2712.57664689920 Harmonic Mean 2580.85216337451 Quadratic Mean 2946.61429901777 Winsorized Mean ( 1 / 20 ) 2826.0764205082 100.941113885428 27.9972779348949 Winsorized Mean ( 2 / 20 ) 2836.38646988525 96.9759910634687 29.2483370242527 Winsorized Mean ( 3 / 20 ) 2832.51860254098 95.9600653864912 29.5176810388015 Winsorized Mean ( 4 / 20 ) 2838.68124057377 94.4636215644425 30.0505230856223 Winsorized Mean ( 5 / 20 ) 2839.60118352459 90.6243559516164 31.3337529818212 Winsorized Mean ( 6 / 20 ) 2843.81730611475 85.3065003203246 33.3364666870199 Winsorized Mean ( 7 / 20 ) 2834.98244637705 81.5423918372827 34.7669768141489 Winsorized Mean ( 8 / 20 ) 2840.11002578689 80.1883853119493 35.4179724998611 Winsorized Mean ( 9 / 20 ) 2811.61164883607 74.1005976753669 37.9431710005049 Winsorized Mean ( 10 / 20 ) 2802.46299965574 70.4979520738322 39.7524029736457 Winsorized Mean ( 11 / 20 ) 2796.89795034426 69.00171890751 40.5337431389677 Winsorized Mean ( 12 / 20 ) 2789.05272667213 67.7359178096701 41.1753884328997 Winsorized Mean ( 13 / 20 ) 2786.51424373770 66.3944180492542 41.9691041146042 Winsorized Mean ( 14 / 20 ) 2782.68230832787 63.4308442276165 43.8695455217723 Winsorized Mean ( 15 / 20 ) 2783.66812136066 63.2549023426938 44.0071523038590 Winsorized Mean ( 16 / 20 ) 2780.95226877049 61.9873013518024 44.8632576047712 Winsorized Mean ( 17 / 20 ) 2796.18664431148 58.7014525203319 47.6340281927945 Winsorized Mean ( 18 / 20 ) 2777.71941595082 55.1579191195413 50.3593946307291 Winsorized Mean ( 19 / 20 ) 2776.90430660656 53.9889155506746 51.4347117048521 Winsorized Mean ( 20 / 20 ) 2766.71781578689 51.6009785058279 53.6175455563193 Trimmed Mean ( 1 / 20 ) 2828.32312867797 97.158607453601 29.1103712044109 Trimmed Mean ( 2 / 20 ) 2830.72750057895 92.5027645729357 30.601544868932 Trimmed Mean ( 3 / 20 ) 2827.58934487273 89.4395344658656 31.6145355827167 Trimmed Mean ( 4 / 20 ) 2825.69824601887 86.1254629491702 32.8090920995867 Trimmed Mean ( 5 / 20 ) 2821.81607607843 82.569965678938 34.1748486011327 Trimmed Mean ( 6 / 20 ) 2817.38794728571 79.4482872376594 35.4619091895318 Trimmed Mean ( 7 / 20 ) 2811.67095831915 77.1619696932463 36.4385586513254 Trimmed Mean ( 8 / 20 ) 2807.15667015556 75.3081009992883 37.2756268304001 Trimmed Mean ( 9 / 20 ) 2801.3131972093 73.2162889825396 38.2607919103541 Trimmed Mean ( 10 / 20 ) 2799.61074314634 72.0906625711104 38.8345819458213 Trimmed Mean ( 11 / 20 ) 2799.16462097436 71.405967084353 39.200710182493 Trimmed Mean ( 12 / 20 ) 2799.50434310811 70.7062315062906 39.593459918155 Trimmed Mean ( 13 / 20 ) 2801.02231597143 69.8983026545817 40.0728230814604 Trimmed Mean ( 14 / 20 ) 2803.08523533333 68.9414993442092 40.6588957594056 Trimmed Mean ( 15 / 20 ) 2805.95292783871 68.1844581984552 41.1523828446624 Trimmed Mean ( 16 / 20 ) 2809.07792368966 66.8920905627835 41.9941715090084 Trimmed Mean ( 17 / 20 ) 2813.04937033333 65.1321576315409 43.1898692232343 Trimmed Mean ( 18 / 20 ) 2815.46966748 63.3792884127469 44.4225509309087 Trimmed Mean ( 19 / 20 ) 2821.03190260870 61.5975843076129 45.7977684404101 Trimmed Mean ( 20 / 20 ) 2827.77822680952 58.802603871619 48.0893368767016 Median 2840.939286 Midrange 3010.9168515 Midmean - Weighted Average at Xnp 2787.94189796667 Midmean - Weighted Average at X(n+1)p 2805.95292783871 Midmean - Empirical Distribution Function 2805.95292783871 Midmean - Empirical Distribution Function - Averaging 2805.95292783871 Midmean - Empirical Distribution Function - Interpolation 2805.95292783871 Midmean - Closest Observation 2786.10301959375 Midmean - True Basic - Statistics Graphics Toolkit 2805.95292783871 Midmean - MS Excel (old versions) 2805.95292783871 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/18/t125589325604t6ip4v7719pou/1lscp1255892874.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t125589325604t6ip4v7719pou/1lscp1255892874.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t125589325604t6ip4v7719pou/2lrbf1255892874.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t125589325604t6ip4v7719pou/2lrbf1255892874.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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