Paper_MRM_output2

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

Title produced by software: Central Tendency

Date of computation: Sat, 05 Jan 2008 03:07:03 -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/Jan/05/t1199527646tntwwlm5nuljmmn.htm/, Retrieved Sat, 05 Jan 2008 11:07:28 +0100

User-defined keywords:

Dataseries X:

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Output produced by software:

Summary of compuational 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 31.1177851145833 251.522587192908 0.123717656779338 Geometric Mean NaN Harmonic Mean 294.185100175991 Quadratic Mean 2451.73641406061 Winsorized Mean ( 1 / 32 ) 25.9595909895833 249.466323832327 0.104060502398839 Winsorized Mean ( 2 / 32 ) 33.0639645729167 246.671424048548 0.134040514422981 Winsorized Mean ( 3 / 32 ) -1.64081698958334 232.204328109222 -0.00706626359182911 Winsorized Mean ( 4 / 32 ) 6.44684292708333 223.358796021626 0.0288631701187140 Winsorized Mean ( 5 / 32 ) 3.81708678124998 222.445489487493 0.017159650168877 Winsorized Mean ( 6 / 32 ) 11.05759546875 219.895936945037 0.0502855833644342 Winsorized Mean ( 7 / 32 ) -9.58859120833336 215.632221291239 -0.0444673395790082 Winsorized Mean ( 8 / 32 ) 1.51645295833331 213.55381664699 0.00710103421302953 Winsorized Mean ( 9 / 32 ) -22.2018420729167 207.390334296472 -0.107053408001061 Winsorized Mean ( 10 / 32 ) -17.1801118645834 201.853244951015 -0.0851118933894403 Winsorized Mean ( 11 / 32 ) -57.6673195 192.574652910079 -0.299454360314633 Winsorized Mean ( 12 / 32 ) -57.9213066249999 191.746846206632 -0.30207175643756 Winsorized Mean ( 13 / 32 ) -83.9460239583333 187.365778433781 -0.448032851356586 Winsorized Mean ( 14 / 32 ) -86.1037700208334 186.910722367791 -0.460667900321972 Winsorized Mean ( 15 / 32 ) -141.993155177083 176.202023192845 -0.805854283646213 Winsorized Mean ( 16 / 32 ) -147.353266510417 173.396027592529 -0.849807625678074 Winsorized Mean ( 17 / 32 ) -163.509531541667 168.250178096636 -0.971823824446436 Winsorized Mean ( 18 / 32 ) -171.629240791667 164.152600302031 -1.04554689036834 Winsorized Mean ( 19 / 32 ) -184.923668052083 160.533671151093 -1.15193072410357 Winsorized Mean ( 20 / 32 ) -196.596318260417 156.432510051766 -1.25674847380100 Winsorized Mean ( 21 / 32 ) -215.008492416667 151.525858163200 -1.41895578103305 Winsorized Mean ( 22 / 32 ) -224.857625208333 150.080312580432 -1.49824864662263 Winsorized Mean ( 23 / 32 ) -226.238978135417 148.986475961942 -1.51852023262305 Winsorized Mean ( 24 / 32 ) -190.582157385417 143.844635894694 -1.32491667972199 Winsorized Mean ( 25 / 32 ) -211.494632645833 140.823122665322 -1.50184592304822 Winsorized Mean ( 26 / 32 ) -222.849824979167 138.931479534175 -1.60402686076880 Winsorized Mean ( 27 / 32 ) -223.824769947917 137.963039278507 -1.62235313978608 Winsorized Mean ( 28 / 32 ) -184.639366989583 129.250873807935 -1.42853476769491 Winsorized Mean ( 29 / 32 ) -310.392559385417 105.652948856040 -2.93785041256492 Winsorized Mean ( 30 / 32 ) -347.856550010417 100.223440812511 -3.47081029338392 Winsorized Mean ( 31 / 32 ) -399.9408741875 93.2635979002446 -4.28828485273836 Winsorized Mean ( 32 / 32 ) -427.8141831875 89.9293867961283 -4.75722339970319 Trimmed Mean ( 1 / 32 ) 6.89502231914893 239.844845467417 0.0287478444896813 Trimmed Mean ( 2 / 32 ) -12.9984406413044 228.765246274617 -0.056819997149832 Trimmed Mean ( 3 / 32 ) -37.5650567555556 217.690476402514 -0.172561783024890 Trimmed Mean ( 4 / 32 ) -50.6284166704545 211.400030913025 -0.239491056135580 Trimmed Mean ( 5 / 32 ) -66.5563960930233 207.201328891206 -0.321216067721119 Trimmed Mean ( 6 / 32 ) -82.6417636071428 202.618738398433 -0.407868315933519 Trimmed Mean ( 7 / 32 ) -100.924565378049 197.953169287172 -0.509840614027435 Trimmed Mean ( 8 / 32 ) -116.58216095 193.542061277919 -0.602360852107453 Trimmed Mean ( 9 / 32 ) -134.751178474359 188.826697489700 -0.713623551466866 Trimmed Mean ( 10 / 32 ) -150.547576565789 184.582445572286 -0.815611560996638 Trimmed Mean ( 11 / 32 ) -167.849301716216 180.639704473204 -0.929193845869664 Trimmed Mean ( 12 / 32 ) -181.2046935 177.703834066672 -1.01970052841974 Trimmed Mean ( 13 / 32 ) -195.294223428571 174.339501041394 -1.12019492003825 Trimmed Mean ( 14 / 32 ) -207.386335588235 171.093200926493 -1.21212493813436 Trimmed Mean ( 15 / 32 ) -219.987121621212 167.265185412886 -1.31519969967560 Trimmed Mean ( 16 / 32 ) -227.786518265625 164.499449085257 -1.38472511325900 Trimmed Mean ( 17 / 32 ) -235.570381338710 161.58344986683 -1.45788681658212 Trimmed Mean ( 18 / 32 ) -242.352578966667 158.858045021436 -1.52559210289894 Trimmed Mean ( 19 / 32 ) -248.855874431034 156.156437756871 -1.59363186049680 Trimmed Mean ( 20 / 32 ) -254.624193803571 153.388771997802 -1.65999238723431 Trimmed Mean ( 21 / 32 ) -259.782227185185 150.602668106020 -1.72495102810732 Trimmed Mean ( 22 / 32 ) -263.718379692308 147.915890881430 -1.78289417128079 Trimmed Mean ( 23 / 32 ) -267.10986372 144.72549790738 -1.84563098819630 Trimmed Mean ( 24 / 32 ) -270.663853770833 140.822037413869 -1.92202767934231 Trimmed Mean ( 25 / 32 ) -277.627479543478 136.753100181717 -2.03013664168906 Trimmed Mean ( 26 / 32 ) -283.399073454545 132.083106930541 -2.14561180487355 Trimmed Mean ( 27 / 32 ) -288.722084309524 126.353303884841 -2.28503786947009 Trimmed Mean ( 28 / 32 ) -294.490734475 118.928772808267 -2.47619417506113 Trimmed Mean ( 29 / 32 ) -304.402136052632 111.137682993318 -2.73896420956459 Trimmed Mean ( 30 / 32 ) -303.851292527778 107.107011334489 -2.83689451084455 Trimmed Mean ( 31 / 32 ) -299.709621235294 102.882038726578 -2.91313843451148 Trimmed Mean ( 32 / 32 ) -290.0098225625 98.7119717143681 -2.93793972023646 Median -156.6692195 Midrange 1169.5876365 Midmean - Weighted Average at Xnp -305.819390632653 Midmean - Weighted Average at X(n+1)p -270.663853770833 Midmean - Empirical Distribution Function -305.819390632653 Midmean - Empirical Distribution Function - Averaging -270.663853770833 Midmean - Empirical Distribution Function - Interpolation -270.663853770833 Midmean - Closest Observation -305.819390632653 Midmean - True Basic - Statistics Graphics Toolkit -270.663853770833 Midmean - MS Excel (old versions) -267.10986372 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/05/t1199527646tntwwlm5nuljmmn/1owr81199527620.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/05/t1199527646tntwwlm5nuljmmn/1owr81199527620.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/05/t1199527646tntwwlm5nuljmmn/2nln71199527620.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/05/t1199527646tntwwlm5nuljmmn/2nln71199527620.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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We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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