Central Tendency voor 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: Tue, 20 Oct 2009 13:21:07 -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/20/t1256066883gx6ezk4xu0ipiuy.htm/, Retrieved Tue, 20 Oct 2009 21:28:04 +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/20/t1256066883gx6ezk4xu0ipiuy.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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23.97 23.81 24.23 25.66 26.79 27.82 28.67 29.44 30.59 30.88 30.88 30.16 30.40 30.97 31.84 31.97 32.02 32.47 33.50 34.99 36.25 37.07 36.72 35.72 33.59 34.82 36.27 37.07 38.43 38.78 39.37 40.66 41.08 39.72 41.85 42.89 42.28 41.86 38.59 39.49 40.76 37.77 38.01 35.66 34.71 34.53 36.50 36.10 33.37 28.99 29.30 28.76 21.63 20.10 18.82 19.42 18.59 17.25 19.36 21.40 21.23

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 4 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 32.0627868852459 0.895313210486392 35.8118103359910 Geometric Mean 31.2184653737359 Harmonic Mean 30.2787989554709 Quadratic Mean 32.8042291106038 Winsorized Mean ( 1 / 20 ) 32.0747540983607 0.887535933438873 36.1391047842794 Winsorized Mean ( 2 / 20 ) 32.0685245901639 0.883046262335303 36.3157922274146 Winsorized Mean ( 3 / 20 ) 32.0945901639344 0.876418711649595 36.6201562533119 Winsorized Mean ( 4 / 20 ) 32.0480327868852 0.866392805186111 36.9901880475577 Winsorized Mean ( 5 / 20 ) 32.0775409836066 0.84854866953866 37.8028298613048 Winsorized Mean ( 6 / 20 ) 32.1788524590164 0.821432245737071 39.1740799390488 Winsorized Mean ( 7 / 20 ) 32.0904918032787 0.79921913482913 40.1523066763655 Winsorized Mean ( 8 / 20 ) 32.0904918032787 0.78775781368261 40.7364944477822 Winsorized Mean ( 9 / 20 ) 32.3944262295082 0.71709643453701 45.1744349425242 Winsorized Mean ( 10 / 20 ) 32.3239344262295 0.696541780790895 46.4063108885256 Winsorized Mean ( 11 / 20 ) 32.3365573770492 0.681945941371696 47.4180655903693 Winsorized Mean ( 12 / 20 ) 32.5863934426229 0.623074565650002 52.2993478455155 Winsorized Mean ( 13 / 20 ) 32.7377049180328 0.565656173612114 57.8756255924503 Winsorized Mean ( 14 / 20 ) 32.9190163934426 0.51686606613647 63.6896452489316 Winsorized Mean ( 15 / 20 ) 32.9559016393443 0.456878179471294 72.1327984573071 Winsorized Mean ( 16 / 20 ) 32.9795081967213 0.453201147529252 72.770133916293 Winsorized Mean ( 17 / 20 ) 32.9460655737705 0.428803219462297 76.8325984471003 Winsorized Mean ( 18 / 20 ) 32.9726229508197 0.405390919858585 81.33537614094 Winsorized Mean ( 19 / 20 ) 32.9445901639344 0.388514374678365 84.796322378568 Winsorized Mean ( 20 / 20 ) 33.1740983606557 0.352982327229028 93.9823209311301 Trimmed Mean ( 1 / 20 ) 32.1303389830508 0.871137193390268 36.8832133753891 Trimmed Mean ( 2 / 20 ) 32.1898245614035 0.850756941868297 37.8366875158413 Trimmed Mean ( 3 / 20 ) 32.2570909090909 0.828331643301622 38.9422415163549 Trimmed Mean ( 4 / 20 ) 32.3194339622641 0.80348729288812 40.2239515774948 Trimmed Mean ( 5 / 20 ) 32.4005882352941 0.776056467106878 41.7502973154554 Trimmed Mean ( 6 / 20 ) 32.4810204081633 0.747521712929362 43.4516079551426 Trimmed Mean ( 7 / 20 ) 32.5463829787234 0.71993841765188 45.2071763094339 Trimmed Mean ( 8 / 20 ) 32.6346666666667 0.69067955118437 47.2500837916876 Trimmed Mean ( 9 / 20 ) 32.7311627906977 0.655514575525766 49.932013738131 Trimmed Mean ( 10 / 20 ) 32.7868292682927 0.630644602383283 51.9893917182312 Trimmed Mean ( 11 / 20 ) 32.8592307692308 0.602732014965544 54.5171485060558 Trimmed Mean ( 12 / 20 ) 32.9375675675676 0.568741089809809 57.9131139945984 Trimmed Mean ( 13 / 20 ) 32.9885714285714 0.54049186171582 61.0343536419725 Trimmed Mean ( 14 / 20 ) 33.0242424242424 0.518554778947715 63.6851568338785 Trimmed Mean ( 15 / 20 ) 33.0390322580645 0.501979169948403 65.8175363361402 Trimmed Mean ( 16 / 20 ) 33.0506896551724 0.495053346141337 66.7618750843398 Trimmed Mean ( 17 / 20 ) 33.0607407407407 0.483982153942706 68.3098343015649 Trimmed Mean ( 18 / 20 ) 33.0772 0.473405576646495 69.87074430832 Trimmed Mean ( 19 / 20 ) 33.0926086956522 0.463018630222718 71.4714409649871 Trimmed Mean ( 20 / 20 ) 33.1152380952381 0.44995058937601 73.5974990968724 Median 33.37 Midrange 30.07 Midmean - Weighted Average at Xnp 33.0390322580645 Midmean - Weighted Average at X(n+1)p 33.0390322580645 Midmean - Empirical Distribution Function 33.0390322580645 Midmean - Empirical Distribution Function - Averaging 33.0390322580645 Midmean - Empirical Distribution Function - Interpolation 33.0390322580645 Midmean - Closest Observation 32.8759375 Midmean - True Basic - Statistics Graphics Toolkit 33.0390322580645 Midmean - MS Excel (old versions) 33.0390322580645 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/20/t1256066883gx6ezk4xu0ipiuy/12zei1256066460.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256066883gx6ezk4xu0ipiuy/12zei1256066460.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256066883gx6ezk4xu0ipiuy/2dvej1256066460.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/20/t1256066883gx6ezk4xu0ipiuy/2dvej1256066460.ps (open in new window)

Parameters (Session):

par1 = Y[t] / X[t] = c + e[t] ; par3 = Y[t] - X[t] = c + e[t] ;

Parameters (R input):

par1 = Y[t] / X[t] = c + e[t] ; par3 = Y[t] - X[t] = c + e[t] ;

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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