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Central Tendency

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

Title produced by software: Central Tendency

Date of computation: Wed, 26 Dec 2007 12:53:11 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/26/t11986976522s6u8howv41djvo.htm/, Retrieved Wed, 26 Dec 2007 20:34:15 +0100

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met voorspellingsfouten van Backward Selection...

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0.00432941450518916 0.0233604344343087 0.111529718090494 0.0426566422442822 0.00329114082772466 -0.0165654712348738 0.0328601051615075 0.0170922301110487 0.0455461538266676 -0.0173515146503020 -0.0593934315521763 0.0624774966484597 0.0770081993209697 0.053709101252903 -0.0657049095682227 -0.111187584404637 0.0176352266485562 0.037238930258372 0.0152746372627233 0.0268816086175372 -0.0529994426109983 0.0640631754196459 0.0208622686822659 0.0279464743413715 0.049900535299785 0.0090330617930574 0.0682587886333925 0.0166606038985879 0.0527302708157107 -0.0239493642811439 0.0291680288906129 0.0465178661058054 -0.00301251154084081 0.0742259190265377 -0.0576205628450657 -0.0543536659883159 0.0695743048603195 0.0248509795595009 0.101874908803837 -0.00537615556147397 -0.0499250288828526 0.079319657170796 0.0252566541924892 0.0588076942476148 -0.00257916999892505 -0.0516904353435663 -0.0335694314655619 0.0363027887384009 0.080406744001655 -0.0174791308159552 0.00764175000849487 0.093848814552608 0.0270171922041724 -0.0222662842247345 0.0504733484129973 -0.0151864590183735 -0.107353439071580 -0.0342395391363599 0.0142417646291220 0.0402140631821242 -0.0914835921955728 0.0568373013868300 0.0418639678369921 0.0523004479841136 -0.0005599725773342 0.0338304081769785 0.0495823756713341

Text written by user:

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 0.0161291955338661 0.00598736766315474 2.6938709030886 Geometric Mean NaN Harmonic Mean -0.0512080281006703 Quadratic Mean 0.0512460405280242 Winsorized Mean ( 1 / 22 ) 0.0160423199524691 0.00593594909062964 2.7025703400646 Winsorized Mean ( 2 / 22 ) 0.0162764618218655 0.00574309650364526 2.83409164577584 Winsorized Mean ( 3 / 22 ) 0.0168288474372265 0.00532615335621449 3.15966257666818 Winsorized Mean ( 4 / 22 ) 0.017140751388581 0.00522839390415616 3.27839709532127 Winsorized Mean ( 5 / 22 ) 0.0171005581689754 0.00516854063879184 3.30858541396178 Winsorized Mean ( 6 / 22 ) 0.0171439566670934 0.00506201705312334 3.38678366492569 Winsorized Mean ( 7 / 22 ) 0.0167994531518351 0.00495097840570737 3.39315823564674 Winsorized Mean ( 8 / 22 ) 0.0167986759626417 0.00489250687782115 3.4335518338858 Winsorized Mean ( 9 / 22 ) 0.0164722302793984 0.00475459183333481 3.46448882613022 Winsorized Mean ( 10 / 22 ) 0.0185766796786979 0.00424845685264271 4.37257110593991 Winsorized Mean ( 11 / 22 ) 0.0180841924842126 0.0041355431978824 4.37286992757629 Winsorized Mean ( 12 / 22 ) 0.0194542834078484 0.00376875447598624 5.1619927835064 Winsorized Mean ( 13 / 22 ) 0.0191738869748972 0.00362247326825777 5.29303753402684 Winsorized Mean ( 14 / 22 ) 0.0199696559540348 0.00342317373742293 5.83366708377138 Winsorized Mean ( 15 / 22 ) 0.0199019977452414 0.00340452311092182 5.84575198840482 Winsorized Mean ( 16 / 22 ) 0.0196533873200025 0.00331117503010378 5.93547219380501 Winsorized Mean ( 17 / 22 ) 0.0198579453014337 0.00323296319099268 6.1423357236976 Winsorized Mean ( 18 / 22 ) 0.0224080734941513 0.00280517195088371 7.98812831673014 Winsorized Mean ( 19 / 22 ) 0.0222093205784346 0.00257929807106606 8.61060643884994 Winsorized Mean ( 20 / 22 ) 0.0220486128956818 0.00251892310488411 8.75319014420497 Winsorized Mean ( 21 / 22 ) 0.0217758278602089 0.00229905701160703 9.47163456594217 Winsorized Mean ( 22 / 22 ) 0.0227800914117150 0.00208007300477556 10.9515826412896 Trimmed Mean ( 1 / 22 ) 0.0166202148782027 0.00565846646255431 2.93722954588301 Trimmed Mean ( 2 / 22 ) 0.0172348015452526 0.00531964121361503 3.23984284901434 Trimmed Mean ( 3 / 22 ) 0.0177611028687522 0.00503615266171033 3.52672050706269 Trimmed Mean ( 4 / 22 ) 0.0181139905179737 0.00489305774560195 3.70197767117202 Trimmed Mean ( 5 / 22 ) 0.0183999862270496 0.0047550058017599 3.86960331788439 Trimmed Mean ( 6 / 22 ) 0.0187165741539259 0.0046039002956624 4.06537347725794 Trimmed Mean ( 7 / 22 ) 0.0190479118005227 0.0044479513275955 4.28240113203302 Trimmed Mean ( 8 / 22 ) 0.0194698914348702 0.00428278047077411 4.54608672280395 Trimmed Mean ( 9 / 22 ) 0.0199264512222154 0.00408863684485823 4.87361729063183 Trimmed Mean ( 10 / 22 ) 0.0204735736883354 0.00387578409730096 5.28243399899207 Trimmed Mean ( 11 / 22 ) 0.0207560001297703 0.00374135210605047 5.54772700922855 Trimmed Mean ( 12 / 22 ) 0.0211344591408747 0.00359263843465470 5.8827125315509 Trimmed Mean ( 13 / 22 ) 0.0213632635598030 0.00349221638657467 6.11739399709911 Trimmed Mean ( 14 / 22 ) 0.0216525894595835 0.00339163137661548 6.38412228665919 Trimmed Mean ( 15 / 22 ) 0.0218702661871351 0.00330492638518703 6.61747453291534 Trimmed Mean ( 16 / 22 ) 0.0221214547311482 0.0031864034622581 6.94245251524786 Trimmed Mean ( 17 / 22 ) 0.0224346375276383 0.00304301919210955 7.37249294575948 Trimmed Mean ( 18 / 22 ) 0.0227622245848598 0.00285970799530254 7.95963245976505 Trimmed Mean ( 19 / 22 ) 0.0228076807593377 0.00273958526487500 8.32523121355681 Trimmed Mean ( 20 / 22 ) 0.0228858291650307 0.00263260991757520 8.69320935556983 Trimmed Mean ( 21 / 22 ) 0.0229980161451234 0.00248429554417456 9.25735917332849 Trimmed Mean ( 22 / 22 ) 0.0231675536504843 0.00233589159519474 9.91807740485183 Median 0.0248509795595009 Midrange 0.000171066842928502 Midmean - Weighted Average at Xnp 0.0212875755052115 Midmean - Weighted Average at X(n+1)p 0.0221214547311482 Midmean - Empirical Distribution Function 0.0221214547311482 Midmean - Empirical Distribution Function - Averaging 0.0221214547311482 Midmean - Empirical Distribution Function - Interpolation 0.0224346375276383 Midmean - Closest Observation 0.0212875755052115 Midmean - True Basic - Statistics Graphics Toolkit 0.0221214547311482 Midmean - MS Excel (old versions) 0.0221214547311482 Number of observations 67

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/26/t11986976522s6u8howv41djvo/1nq8w1198698788.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/26/t11986976522s6u8howv41djvo/1nq8w1198698788.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/26/t11986976522s6u8howv41djvo/2b9pd1198698788.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/26/t11986976522s6u8howv41djvo/2b9pd1198698788.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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