investigating associations

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

Title produced by software: Central Tendency

Date of computation: Thu, 03 Jan 2008 02:42:12 -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/03/t1199353427v4e7g8wfdh6x9ib.htm/, Retrieved Thu, 03 Jan 2008 10:43:49 +0100

User-defined keywords:

investigating associations

Dataseries X:

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87 75 74 91 101 103 106 102 105 105 100 95 96 98 99 92 84 81 72 89 96 91 88 90 98 87 100 100 104 107 105 102 98 106 97 101 100 93 94 96 96 98 102 95 85 84 82 87 77 90 90 94 97 96 93 93 93 97 100 95 97 103 102 93 99 100 97 104 102 103 100 90 90

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 94.958904109589 0.924353070117727 102.730122481764 Geometric Mean 94.6145308224988 Harmonic Mean 94.2477808321138 Quadratic Mean 95.2822770968826 Winsorized Mean ( 1 / 24 ) 94.972602739726 0.912865219074669 104.037924498860 Winsorized Mean ( 2 / 24 ) 95 0.904285417153965 105.055326778343 Winsorized Mean ( 3 / 24 ) 95.041095890411 0.873122764744577 108.851927504392 Winsorized Mean ( 4 / 24 ) 95.2602739726027 0.814870216216743 116.90238773835 Winsorized Mean ( 5 / 24 ) 95.3287671232877 0.798603898470108 119.369273435692 Winsorized Mean ( 6 / 24 ) 95.4109589041096 0.748625228189967 127.448228180601 Winsorized Mean ( 7 / 24 ) 95.4109589041096 0.748625228189967 127.448228180601 Winsorized Mean ( 8 / 24 ) 95.4109589041096 0.70894363083682 134.581869071154 Winsorized Mean ( 9 / 24 ) 95.6575342465753 0.661285122295119 144.653994202345 Winsorized Mean ( 10 / 24 ) 95.6575342465753 0.661285122295119 144.653994202345 Winsorized Mean ( 11 / 24 ) 95.5068493150685 0.639016584056987 149.459109040199 Winsorized Mean ( 12 / 24 ) 95.6712328767123 0.609430827894382 156.984564117411 Winsorized Mean ( 13 / 24 ) 95.8493150684932 0.579216139891731 165.481084636919 Winsorized Mean ( 14 / 24 ) 96.041095890411 0.54877695624301 175.009345414063 Winsorized Mean ( 15 / 24 ) 96.041095890411 0.54877695624301 175.009345414063 Winsorized Mean ( 16 / 24 ) 95.8219178082192 0.516965764712582 185.354474800654 Winsorized Mean ( 17 / 24 ) 95.8219178082192 0.516965764712582 185.354474800654 Winsorized Mean ( 18 / 24 ) 95.5753424657534 0.484115179407459 197.42273436403 Winsorized Mean ( 19 / 24 ) 95.8356164383562 0.443545670744086 216.067076649816 Winsorized Mean ( 20 / 24 ) 95.8356164383562 0.443545670744086 216.067076649816 Winsorized Mean ( 21 / 24 ) 96.1232876712329 0.40117085367136 239.606857755367 Winsorized Mean ( 22 / 24 ) 96.4246575342466 0.359645208340787 268.110502511904 Winsorized Mean ( 23 / 24 ) 96.4246575342466 0.359645208340787 268.110502511904 Winsorized Mean ( 24 / 24 ) 96.4246575342466 0.359645208340787 268.110502511904 Trimmed Mean ( 1 / 24 ) 95.112676056338 0.876372001848302 108.530025897383 Trimmed Mean ( 2 / 24 ) 95.2608695652174 0.832434000802367 114.436543285591 Trimmed Mean ( 3 / 24 ) 95.4029850746269 0.78488079148921 121.550923540392 Trimmed Mean ( 4 / 24 ) 95.5384615384615 0.742292745963518 128.707254729332 Trimmed Mean ( 5 / 24 ) 95.6190476190476 0.713927201374591 133.933890507244 Trimmed Mean ( 6 / 24 ) 95.688524590164 0.684943850599105 139.702728196578 Trimmed Mean ( 7 / 24 ) 95.7457627118644 0.664536778035912 144.078952251293 Trimmed Mean ( 8 / 24 ) 95.8070175438596 0.639371654900139 149.845581688828 Trimmed Mean ( 9 / 24 ) 95.8727272727273 0.618488733476532 155.011275199510 Trimmed Mean ( 10 / 24 ) 95.9056603773585 0.604328935450781 158.697779886744 Trimmed Mean ( 11 / 24 ) 95.9411764705882 0.586389260197696 163.613461198526 Trimmed Mean ( 12 / 24 ) 96 0.568444589824444 168.881895823212 Trimmed Mean ( 13 / 24 ) 96.0425531914894 0.552479439266914 173.839144709038 Trimmed Mean ( 14 / 24 ) 96.0666666666667 0.538797763825195 178.298191114680 Trimmed Mean ( 15 / 24 ) 96.0697674418605 0.527636394523027 182.075702963412 Trimmed Mean ( 16 / 24 ) 96.0731707317073 0.512514418479437 187.454571554774 Trimmed Mean ( 17 / 24 ) 96.102564102564 0.499385414180183 192.441672050697 Trimmed Mean ( 18 / 24 ) 96.1351351351351 0.48111819541689 199.816045310516 Trimmed Mean ( 19 / 24 ) 96.2 0.463454329968322 207.571693216407 Trimmed Mean ( 20 / 24 ) 96.2424242424242 0.450232059336474 213.761819592014 Trimmed Mean ( 21 / 24 ) 96.2903225806452 0.430537419569624 223.651460253790 Trimmed Mean ( 22 / 24 ) 96.3103448275862 0.4155341042712 231.774826272091 Trimmed Mean ( 23 / 24 ) 96.2962962962963 0.405850430727848 237.270405561969 Trimmed Mean ( 24 / 24 ) 96.28 0.389529630879774 247.169900226964 Median 96 Midrange 89.5 Midmean - Weighted Average at Xnp 95.5365853658537 Midmean - Weighted Average at X(n+1)p 95.5365853658537 Midmean - Empirical Distribution Function 95.5365853658537 Midmean - Empirical Distribution Function - Averaging 95.5365853658537 Midmean - Empirical Distribution Function - Interpolation 95.5365853658537 Midmean - Closest Observation 95.5365853658537 Midmean - True Basic - Statistics Graphics Toolkit 95.5365853658537 Midmean - MS Excel (old versions) 95.5365853658537 Number of observations 73

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/03/t1199353427v4e7g8wfdh6x9ib/1l18p1199353329.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/03/t1199353427v4e7g8wfdh6x9ib/1l18p1199353329.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/03/t1199353427v4e7g8wfdh6x9ib/2rix41199353329.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/03/t1199353427v4e7g8wfdh6x9ib/2rix41199353329.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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