WS3 part 2 model 1

*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 13:00:33 -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/t1255892654obb4nummk2iysnx.htm/, Retrieved Sun, 18 Oct 2009 21:04:16 +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/t1255892654obb4nummk2iysnx.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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1885,698925 2189,892473 2618,62069 2337,682927 1663,493976 3499,176471 2975,697674 3423,058824 3229,512195 2766,049383 3423,291139 2089,534884 2152,873563 2262,528736 2327,647059 2199,880952 1258,588235 3673,103448 3391,494253 4012,325581 3195,882353 3221,204819 2961,375 2214,268293 2139,259259 2247,530864 2624,375 2200,253165 1185,696203 3890,5 3318,875 3879,873418 3232,375 3259,74026 3580,277778 2722,4 2560 2917,714286 3539,428571 2830,571429 1769,166667 4324,109589 4240,985915 4414,558824 4989,6875 4233,770492 4128,461538 2624,025974 2251,772152 2736 3263,478261 2359,393939 1667,971014 3304,805195 3011,25 3473,25 3401,948052 2810,410959 3075,540541 2349,135802 2044,698795

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 2911.08480811475 104.021130770028 27.9855139678364 Geometric Mean 2793.13315110178 Harmonic Mean 2666.37497065593 Quadratic Mean 3020.53612771591 Winsorized Mean ( 1 / 20 ) 2902.85142050820 100.941113885428 28.7578698983157 Winsorized Mean ( 2 / 20 ) 2913.16146988525 96.9759910634687 30.0400278248113 Winsorized Mean ( 3 / 20 ) 2909.29360254098 95.9600653864912 30.3177534406989 Winsorized Mean ( 4 / 20 ) 2915.45624057377 94.4636215644425 30.8632698205929 Winsorized Mean ( 5 / 20 ) 2916.37618352459 90.6243559516164 32.1809314162919 Winsorized Mean ( 6 / 20 ) 2920.59230611475 85.3065003203246 34.2364567195697 Winsorized Mean ( 7 / 20 ) 2911.75744637705 81.5423918372827 35.7085116191765 Winsorized Mean ( 8 / 20 ) 2916.88502578689 80.1883853119493 36.3754054211168 Winsorized Mean ( 9 / 20 ) 2888.38664883607 74.1005976753669 38.9792625086511 Winsorized Mean ( 10 / 20 ) 2879.23799965574 70.4979520738322 40.8414417008926 Winsorized Mean ( 11 / 20 ) 2873.67295034426 69.00171890751 41.6463965802958 Winsorized Mean ( 12 / 20 ) 2865.82772667213 67.7359178096701 42.3088343576412 Winsorized Mean ( 13 / 20 ) 2863.28924373770 66.3944180492542 43.1254513235374 Winsorized Mean ( 14 / 20 ) 2859.45730832787 63.4308442276165 45.0799188178378 Winsorized Mean ( 15 / 20 ) 2860.44312136066 63.2549023426938 45.2208922221354 Winsorized Mean ( 16 / 20 ) 2857.72726877049 61.9873013518024 46.1018177344383 Winsorized Mean ( 17 / 20 ) 2872.96164431148 58.7014525203318 48.9419174647577 Winsorized Mean ( 18 / 20 ) 2854.49441595082 55.1579191195413 51.7513071833692 Winsorized Mean ( 19 / 20 ) 2853.67930660656 53.9889155506747 52.8567628651118 Winsorized Mean ( 20 / 20 ) 2843.49281578689 51.6009785058279 55.1054049385078 Trimmed Mean ( 1 / 20 ) 2905.09812867797 97.158607453601 29.9005739668029 Trimmed Mean ( 2 / 20 ) 2907.50250057895 92.5027645729357 31.4315200632352 Trimmed Mean ( 3 / 20 ) 2904.36434487273 89.4395344658656 32.4729367412033 Trimmed Mean ( 4 / 20 ) 2902.47324601887 86.1254629491702 33.7005241728786 Trimmed Mean ( 5 / 20 ) 2898.59107607843 82.569965678938 35.1046661124846 Trimmed Mean ( 6 / 20 ) 2894.16294728571 79.4482872376594 36.428261047695 Trimmed Mean ( 7 / 20 ) 2888.44595831915 77.1619696932463 37.4335436200246 Trimmed Mean ( 8 / 20 ) 2883.93167015556 75.3081009992883 38.2951054652515 Trimmed Mean ( 9 / 20 ) 2878.0881972093 73.2162889825396 39.3093973650544 Trimmed Mean ( 10 / 20 ) 2876.38574314634 72.0906625711104 39.899560366907 Trimmed Mean ( 11 / 20 ) 2875.93962097436 71.405967084353 40.2759004380819 Trimmed Mean ( 12 / 20 ) 2876.27934310811 70.7062315062906 40.6792906626937 Trimmed Mean ( 13 / 20 ) 2877.79731597143 69.8983026545817 41.1712045454482 Trimmed Mean ( 14 / 20 ) 2879.86023533333 68.9414993442092 41.7725210900164 Trimmed Mean ( 15 / 20 ) 2882.72792783871 68.1844581984552 42.2783725793985 Trimmed Mean ( 16 / 20 ) 2885.85292368966 66.8920905627835 43.1419155749222 Trimmed Mean ( 17 / 20 ) 2889.82437033333 65.1321576315409 44.3686264269235 Trimmed Mean ( 18 / 20 ) 2892.24466748 63.3792884127469 45.6339088038469 Trimmed Mean ( 19 / 20 ) 2897.80690260870 61.5975843076129 47.0441647214168 Trimmed Mean ( 20 / 20 ) 2904.55322680952 58.802603871619 49.3949763372877 Median 2917.714286 Midrange 3087.6918515 Midmean - Weighted Average at Xnp 2864.71689796667 Midmean - Weighted Average at X(n+1)p 2882.72792783871 Midmean - Empirical Distribution Function 2882.72792783871 Midmean - Empirical Distribution Function - Averaging 2882.72792783871 Midmean - Empirical Distribution Function - Interpolation 2882.72792783871 Midmean - Closest Observation 2862.87801959375 Midmean - True Basic - Statistics Graphics Toolkit 2882.72792783871 Midmean - MS Excel (old versions) 2882.72792783871 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/18/t1255892654obb4nummk2iysnx/1htel1255892431.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255892654obb4nummk2iysnx/1htel1255892431.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255892654obb4nummk2iysnx/2vipc1255892431.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/18/t1255892654obb4nummk2iysnx/2vipc1255892431.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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