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ws3 part3 percentiles

*The author of this computation has been verified*
R Software Module: rwasp_percentiles.wasp (opens new window with default values)
Title produced by software: Percentiles
Date of computation: Tue, 20 Oct 2009 15:12:39 -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/t1256073254ovlhkj1orft64d3.htm/, Retrieved Tue, 20 Oct 2009 23:14:15 +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/t1256073254ovlhkj1orft64d3.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:
» Textbox « » Textfile « » CSV «
165420174 168482695 174292040 170818956 167671299 181759548 182033308 188786285 197365400 206818784 205116596 198756428 195529152 196370080 216058096 216533548 211999410 214466142 213243366 221850324 233687748 241477992 232417350 228092760 220634858 219848754 221762645 218504292 220512853 226019388 234074223 240433024 249327920 253974132 237810524 228116330 228334883 212354640 226385037 220926592 227229489 225545628 229337603 241295944 252074644 251546033 234127032 228846076 231548590 223860522 228157303 212953011 231495500 232837280 237721260 246177408 260552015 257570872 239352080 239076089
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Percentiles - Ungrouped Data
pWeighted Average at XnpWeighted Average at X(n+1)pEmpirical Distribution FunctionEmpirical Distribution Function - AveragingEmpirical Distribution Function - InterpolationClosest ObservationTrue Basic - Statistics Graphics ToolkitMS Excel (old versions)
0.02165870399165915421.5167671299167671299167817350.28165420174167176051.5165420174
0.04167995857.4168028313.24168482695168482695169323748.96167671299168125680.76167671299
0.06169884451.6170024627.26170818956170818956172694421.36170818956169277023.74170818956
0.08173597423.2173875269.92174292040174292040179668645.76174292040171235726.08174292040
0.1181759548181786924181759548181896428182005932181759548182005932181759548
0.12183383903.4184194260.64188786285188786285189325714.36182033308186625332.36182033308
0.14191483431.8192427433.18195529152195529152195747793.28188786285191888003.82195529152
0.16196033708.8196168257.28196370080196370080196808020.8196370080195730974.72196370080
0.18197166336197345493.6197365400197365400198227837.36197365400196389986.4197365400
0.2198756428200028461.6198756428201936512203844562.4198756428203844562.4198756428
0.22205457033.6205831514.96206818784206818784206784740.24205116596206103865.04205116596
0.24208891034.4210134384.64211999410211999410212056246.8206818784208683809.36211999410
0.26212212548212304907.8212354640212354640212558086.14212354640212049142.2212354640
0.28212833336.8212976239.4212953011212953011213103995.6212953011213220137.6212953011
0.3213243366213610198.8213243366213854754214099309.2213243366214099309.2213243366
0.32214784532.8215293958.08216058096216058096215867061.52214466142215230279.92216058096
0.34216248276.8216409930.48216533548216533548216651792.64216058096216181713.52216533548
0.36217715994.4218425462.24218504292218504292218826962.88218504292216612377.76218504292
0.38219579861.6219968291.82219848754219848754220127675.58219848754220393315.18219848754
0.4220512853220561655220512853220573855.5220586056220512853220586056220512853
0.42220693204.8220815733.08220926592220926592220862410.52220634858220745716.92220926592
0.44221261013.2221628876.52221762645221762645221729202.88220926592221060360.48221762645
0.46221815252.4221970935.88221850324221850324222131751.72221850324223739910.12221850324
0.48223458482.4224332351.68223860522223860522224399755.92223860522225073798.32223860522
0.5225545628225782508225545628225782508225782508225545628225782508225782508
0.52226092517.8226282655.28226385037226385037226268029.32226019388226121769.72226385037
0.54226722817.8227178821.88227229489227229489227111265.72226385037226435704.12227229489
0.56227747451.6228096531.2228092760228092760228093702.8228092760228112558.8228092760
0.58228111616228131899.74228116330228116330228125344.06228116330228141733.26228116330
0.6228157303228263851228157303228246093228228335228157303228228335228334883
0.62228437121.6228754061.26228846076228846076228631374.94228334883228426897.74228846076
0.64229042686.8229423918.88229337603229337603229219636.52228846076231409184.12229337603
0.66230632341.2231509303.4231495500231495500231366026.18231495500231534786.6231495500
0.68231537972231965594.8231548590231548590231652841.2231548590232000345.2231548590
0.7232417350232711301232417350232627315232543329232417350232543329232837280
0.72233007373.6233619710.56233687748233687748233245504.64232837280232905317.44233687748
0.74233842338234081616.26234074223234074223233942821.5233687748234119638.74234074223
0.76234105908.4235420954.08234127032234127032234118582.56234127032236427337.92234127032
0.78237002414.4237773033.12237721260237721260237723045.28237721260237758750.88237810524
0.8237810524238822976237810524238443306.5238063637237810524238063637239076089
0.82239131287.2239373698.88239352080239352080239180965.58239076089240411405.12239352080
0.84239784457.6240640124.8240433024240433024239957408.64239352080241088843.2240433024
0.86240950776241379686.08241295944241295944241071584.8241295944241394249.92241295944
0.88241441582.4244673594.88241477992241477992241463428.16241477992242981805.12246177408
0.9246177408249012868.8246177408247752664246492459.2246177408246492459.2249327920
0.92249771542.6251609466.32251546033251546033249948991.64249327920252011210.68251546033
0.94251757477.4252720469.92252074644252074644251789194.06251546033253328306.08252074644
0.96253214336.8255988306.4253974132253974132253290316.32253974132255556697.6257570872
0.98256851524259896163.54257570872257570872256923458.8257570872258226723.46260552015
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Oct/20/t1256073254ovlhkj1orft64d3/1jn941256073158.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Oct/20/t1256073254ovlhkj1orft64d3/1jn941256073158.ps (open in new window)


 
Parameters (Session):
 
Parameters (R input):
 
R code (references can be found in the software module):
x <-sort(x[!is.na(x)])
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]
}
}
}
}
lx <- length(x)
qval <- array(NA,dim=c(99,8))
mystep <- 25
mystart <- 25
if (lx>10){
mystep=10
mystart=10
}
if (lx>20){
mystep=5
mystart=5
}
if (lx>50){
mystep=2
mystart=2
}
if (lx>=100){
mystep=1
mystart=1
}
for (perc in seq(mystart,99,mystep)) {
qval[perc,1] <- q1(x,lx,perc/100,i,f)
qval[perc,2] <- q2(x,lx,perc/100,i,f)
qval[perc,3] <- q3(x,lx,perc/100,i,f)
qval[perc,4] <- q4(x,lx,perc/100,i,f)
qval[perc,5] <- q5(x,lx,perc/100,i,f)
qval[perc,6] <- q6(x,lx,perc/100,i,f)
qval[perc,7] <- q7(x,lx,perc/100,i,f)
qval[perc,8] <- q8(x,lx,perc/100,i,f)
}
bitmap(file='test1.png')
myqqnorm <- qqnorm(x,col=2)
qqline(x)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Percentiles - Ungrouped Data',9,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p',1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_1.htm', 'Weighted Average at Xnp',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),1,TRUE)
a<-table.element(a,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),1,TRUE)
a<-table.row.end(a)
for (perc in seq(mystart,99,mystep)) {
a<-table.row.start(a)
a<-table.element(a,round(perc/100,2),1,TRUE)
for (j in 1:8) {
a<-table.element(a,round(qval[perc,j],6))
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
 




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Software written by Ed van Stee & Patrick Wessa


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