taak 3 task 2 verbetering (2)

*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: Tue, 28 Oct 2008 13:21:48 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Oct/28/t12252217566hephbb17tt3o8n.htm/, Retrieved Tue, 28 Oct 2008 19:22:36 +0000

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@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/2008/Oct/28/t12252217566hephbb17tt3o8n.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Dataseries X:

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0.656702899 0.616182573 0.841020608 0.830508475 0.775308642 0.918690602 0.784158416 1.023765996 0.774193548 1.456449835 0.416839917 0.718002081 0.560377358 0.715809893 0.562745098 0.774594078 0.541860465 0.449511401 0.666043031 0.603019538 0.707964602 1.581521739 0.407597536 0.535051546 0.699240987 0.690360273 0.619775739 0.583732057 0.623569794 0.434927697 0.606557377 0.523724261 0.606490872 0.834881321 0.392218717 0.459793814 0.432120674 0.524781341 0.508213552 0.552962298 0.400457666 0.368801653 0.449605609 0.444242974 0.399422522 0.713582677 0.445031712 0.459854015 0.430754537 0.489299611 0.416921509 0.414398595 0.456118665 0.42737722 0.338339223 0.43720491 0.261029412 0.766373412 0.371717172 0.50347567 0.370562771

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -1.30155360390816e-16 0.0301512426258908 -4.31674946222787e-15 Geometric Mean NaN Harmonic Mean 0.279218547498116 Quadratic Mean 0.233550521115069 Winsorized Mean ( 1 / 20 ) -0.000782985131147674 0.0288703285088944 -0.0271207558620766 Winsorized Mean ( 2 / 20 ) -0.0139705723114755 0.0227539074213618 -0.613985635643383 Winsorized Mean ( 3 / 20 ) -0.0190516022786887 0.0212063834467462 -0.898389974251448 Winsorized Mean ( 4 / 20 ) -0.0240690182131149 0.0199349319770183 -1.20737899887807 Winsorized Mean ( 5 / 20 ) -0.0228917839508198 0.0195515375621072 -1.17084315635546 Winsorized Mean ( 6 / 20 ) -0.0226133289672132 0.0193481058973074 -1.16876189779177 Winsorized Mean ( 7 / 20 ) -0.027813401180328 0.0182151164379475 -1.52694061962648 Winsorized Mean ( 8 / 20 ) -0.028037650885246 0.0178461203134680 -1.57107821715663 Winsorized Mean ( 9 / 20 ) -0.0271396434262296 0.0176771973821897 -1.53529107807404 Winsorized Mean ( 10 / 20 ) -0.0268050873606559 0.0176063523739219 -1.52246682284735 Winsorized Mean ( 11 / 20 ) -0.0282005625081969 0.0173331818019513 -1.62696975260608 Winsorized Mean ( 12 / 20 ) -0.0356593730000001 0.0153066229197447 -2.32966952847591 Winsorized Mean ( 13 / 20 ) -0.0354068045245903 0.0151228699992626 -2.34127546730990 Winsorized Mean ( 14 / 20 ) -0.0356044292131149 0.0149909008703076 -2.37506935181170 Winsorized Mean ( 15 / 20 ) -0.0362956715081969 0.014658876331298 -2.47602003645412 Winsorized Mean ( 16 / 20 ) -0.0379865310491804 0.0141921199352509 -2.67659315327713 Winsorized Mean ( 17 / 20 ) -0.0385000564590165 0.0135079316259449 -2.85018147301464 Winsorized Mean ( 18 / 20 ) -0.0454428937049182 0.0123284369950312 -3.68602230138607 Winsorized Mean ( 19 / 20 ) -0.046956802180328 0.0116798312063652 -4.02033225914582 Winsorized Mean ( 20 / 20 ) -0.0577892274262296 0.010074324320041 -5.73628817083729 Trimmed Mean ( 1 / 20 ) -0.0110152641953322 0.0255683633095064 -0.430816163787717 Trimmed Mean ( 2 / 20 ) -0.0219655979306875 0.0210202520523979 -1.04497309908241 Trimmed Mean ( 3 / 20 ) -0.0263992030467960 0.0198061915622996 -1.33287628587042 Trimmed Mean ( 4 / 20 ) -0.0292180939075164 0.0190797306276272 -1.53136826078713 Trimmed Mean ( 5 / 20 ) -0.0307577685024109 0.018681613362558 -1.64641928432456 Trimmed Mean ( 6 / 20 ) -0.0327162381254602 0.0182945146198388 -1.78830861628776 Trimmed Mean ( 7 / 20 ) -0.0349016191845136 0.0178488380477149 -1.95540007092965 Trimmed Mean ( 8 / 20 ) -0.0362742582265939 0.0175977293623141 -2.06130333520619 Trimmed Mean ( 9 / 20 ) -0.0377348194121237 0.0173476107992149 -2.17521708602267 Trimmed Mean ( 10 / 20 ) -0.0394863254694124 0.0170351552409586 -2.31793164845796 Trimmed Mean ( 11 / 20 ) -0.0414698011736025 0.0166110969830184 -2.49651189298318 Trimmed Mean ( 12 / 20 ) -0.0434585568458132 0.0160940867366980 -2.70028101356745 Trimmed Mean ( 13 / 20 ) -0.0445912954519908 0.0159292536312536 -2.79933363384342 Trimmed Mean ( 14 / 20 ) -0.045897248707402 0.0157013655678324 -2.92313738630686 Trimmed Mean ( 15 / 20 ) -0.0473439353183502 0.0153685117614099 -3.08058034852992 Trimmed Mean ( 16 / 20 ) -0.0488932320825326 0.0149425934831848 -3.27207135344700 Trimmed Mean ( 17 / 20 ) -0.050433298663631 0.0144235996220269 -3.4965819896035 Trimmed Mean ( 18 / 20 ) -0.0521460698977051 0.0138303585889471 -3.77040620908984 Trimmed Mean ( 19 / 20 ) -0.0531337359550964 0.0133413557998816 -3.98263390558609 Trimmed Mean ( 20 / 20 ) -0.0540780792138955 0.0127600859857958 -4.23806542323413 Median -0.0544648167377051 Midrange 0.324950293762295 Midmean - Weighted Average at Xnp -0.0526433771710384 Midmean - Weighted Average at X(n+1)p -0.0473439353183502 Midmean - Empirical Distribution Function -0.0473439353183502 Midmean - Empirical Distribution Function - Averaging -0.0473439353183502 Midmean - Empirical Distribution Function - Interpolation -0.0473439353183502 Midmean - Closest Observation -0.0509958313314551 Midmean - True Basic - Statistics Graphics Toolkit -0.0473439353183502 Midmean - MS Excel (old versions) -0.0473439353183502 Number of observations 61

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/28/t12252217566hephbb17tt3o8n/1c8d71225221703.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/28/t12252217566hephbb17tt3o8n/1c8d71225221703.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/28/t12252217566hephbb17tt3o8n/2dwha1225221703.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/28/t12252217566hephbb17tt3o8n/2dwha1225221703.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

x <- x-0.596325281737705 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')

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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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