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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_percentiles.wasp
Title produced by softwarePercentiles
Date of computationFri, 02 Sep 2016 12:45:08 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Sep/02/t14728179406lmgp9bocb6io81.htm/, Retrieved Thu, 07 Jul 2022 14:58:31 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Thu, 07 Jul 2022 14:58:31 +0200
QR Codes:

Original text written by user:Verteilungsfunktion
IsPrivate?No (this computation is public)
User-defined keywordsVera ohne
Estimated Impact0
Dataseries X:
0.41544
0.85038
0.85652
1.07204
1.07858
1.22992
1.23474
1.33104
1.3488
1.41808
1.47134
1.68322
1.70044
1.77484
1.97748
2.01864
2.02782
2.06022
2.09566
2.11208
2.18618
2.21408
2.2331
2.35866
2.38616
2.73634
2.83652
2.97824
3.01558
3.4037
3.44552
3.52076
3.57186
3.66186
3.7395
3.76536
3.81634
3.99266
4.20574
4.21998
4.99366
6.14584




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







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)
0.050.8509940.8513010.856520.856520.8672960.850380.8555990.85038
0.11.0733481.0740021.078581.078581.0937141.072041.0766181.07204
0.151.2313661.2320891.234741.234741.2491851.229921.2325711.22992
0.21.3381441.3416961.34881.34881.3626561.331041.3381441.3488
0.251.444711.4580251.471341.471341.524311.471341.4313951.47134
0.31.6935521.6987181.700441.700441.722761.700441.6849421.70044
0.351.9166881.9795381.977481.977481.9918861.977482.0165821.97748
0.42.0259842.03432.027822.027822.040782.027822.053742.02782
0.452.0921162.1014072.095662.095662.1030492.095662.1063332.09566
0.52.186182.200132.186182.200132.200132.186182.200132.20013
0.552.2456562.3147142.358662.358662.3021582.23312.2770462.35866
0.62.4561962.6663042.736342.736342.5962682.386162.4561962.73634
0.652.8790362.9711542.978242.978242.9286382.836522.8436062.97824
0.73.1708283.4078823.40373.40373.2872643.015583.4413383.4037
0.753.483143.5335353.520763.520763.501953.520763.5590853.52076
0.83.625863.6929163.661863.661863.643863.661863.7084443.66186
0.853.7576023.7933993.765363.765363.7614813.765363.7883013.81634
0.93.9573964.1418163.992663.992663.9750283.992664.0565844.20574
0.954.2185564.8776084.219984.219984.2192684.219984.3360324.99366

\begin{tabular}{lllllllll}
\hline
Percentiles - Ungrouped Data \tabularnewline
p & Weighted Average at Xnp & Weighted Average at X(n+1)p & Empirical Distribution Function & Empirical Distribution Function - Averaging & Empirical Distribution Function - Interpolation & Closest Observation & True Basic - Statistics Graphics Toolkit & MS Excel (old versions) \tabularnewline
0.05 & 0.850994 & 0.851301 & 0.85652 & 0.85652 & 0.867296 & 0.85038 & 0.855599 & 0.85038 \tabularnewline
0.1 & 1.073348 & 1.074002 & 1.07858 & 1.07858 & 1.093714 & 1.07204 & 1.076618 & 1.07204 \tabularnewline
0.15 & 1.231366 & 1.232089 & 1.23474 & 1.23474 & 1.249185 & 1.22992 & 1.232571 & 1.22992 \tabularnewline
0.2 & 1.338144 & 1.341696 & 1.3488 & 1.3488 & 1.362656 & 1.33104 & 1.338144 & 1.3488 \tabularnewline
0.25 & 1.44471 & 1.458025 & 1.47134 & 1.47134 & 1.52431 & 1.47134 & 1.431395 & 1.47134 \tabularnewline
0.3 & 1.693552 & 1.698718 & 1.70044 & 1.70044 & 1.72276 & 1.70044 & 1.684942 & 1.70044 \tabularnewline
0.35 & 1.916688 & 1.979538 & 1.97748 & 1.97748 & 1.991886 & 1.97748 & 2.016582 & 1.97748 \tabularnewline
0.4 & 2.025984 & 2.0343 & 2.02782 & 2.02782 & 2.04078 & 2.02782 & 2.05374 & 2.02782 \tabularnewline
0.45 & 2.092116 & 2.101407 & 2.09566 & 2.09566 & 2.103049 & 2.09566 & 2.106333 & 2.09566 \tabularnewline
0.5 & 2.18618 & 2.20013 & 2.18618 & 2.20013 & 2.20013 & 2.18618 & 2.20013 & 2.20013 \tabularnewline
0.55 & 2.245656 & 2.314714 & 2.35866 & 2.35866 & 2.302158 & 2.2331 & 2.277046 & 2.35866 \tabularnewline
0.6 & 2.456196 & 2.666304 & 2.73634 & 2.73634 & 2.596268 & 2.38616 & 2.456196 & 2.73634 \tabularnewline
0.65 & 2.879036 & 2.971154 & 2.97824 & 2.97824 & 2.928638 & 2.83652 & 2.843606 & 2.97824 \tabularnewline
0.7 & 3.170828 & 3.407882 & 3.4037 & 3.4037 & 3.287264 & 3.01558 & 3.441338 & 3.4037 \tabularnewline
0.75 & 3.48314 & 3.533535 & 3.52076 & 3.52076 & 3.50195 & 3.52076 & 3.559085 & 3.52076 \tabularnewline
0.8 & 3.62586 & 3.692916 & 3.66186 & 3.66186 & 3.64386 & 3.66186 & 3.708444 & 3.66186 \tabularnewline
0.85 & 3.757602 & 3.793399 & 3.76536 & 3.76536 & 3.761481 & 3.76536 & 3.788301 & 3.81634 \tabularnewline
0.9 & 3.957396 & 4.141816 & 3.99266 & 3.99266 & 3.975028 & 3.99266 & 4.056584 & 4.20574 \tabularnewline
0.95 & 4.218556 & 4.877608 & 4.21998 & 4.21998 & 4.219268 & 4.21998 & 4.336032 & 4.99366 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Percentiles - Ungrouped Data[/C][/ROW]
[ROW][C]p[/C][C]Weighted Average at Xnp[/C][C]Weighted Average at X(n+1)p[/C][C]Empirical Distribution Function[/C][C]Empirical Distribution Function - Averaging[/C][C]Empirical Distribution Function - Interpolation[/C][C]Closest Observation[/C][C]True Basic - Statistics Graphics Toolkit[/C][C]MS Excel (old versions)[/C][/ROW]
[ROW][C]0.05[/C][C]0.850994[/C][C]0.851301[/C][C]0.85652[/C][C]0.85652[/C][C]0.867296[/C][C]0.85038[/C][C]0.855599[/C][C]0.85038[/C][/ROW]
[ROW][C]0.1[/C][C]1.073348[/C][C]1.074002[/C][C]1.07858[/C][C]1.07858[/C][C]1.093714[/C][C]1.07204[/C][C]1.076618[/C][C]1.07204[/C][/ROW]
[ROW][C]0.15[/C][C]1.231366[/C][C]1.232089[/C][C]1.23474[/C][C]1.23474[/C][C]1.249185[/C][C]1.22992[/C][C]1.232571[/C][C]1.22992[/C][/ROW]
[ROW][C]0.2[/C][C]1.338144[/C][C]1.341696[/C][C]1.3488[/C][C]1.3488[/C][C]1.362656[/C][C]1.33104[/C][C]1.338144[/C][C]1.3488[/C][/ROW]
[ROW][C]0.25[/C][C]1.44471[/C][C]1.458025[/C][C]1.47134[/C][C]1.47134[/C][C]1.52431[/C][C]1.47134[/C][C]1.431395[/C][C]1.47134[/C][/ROW]
[ROW][C]0.3[/C][C]1.693552[/C][C]1.698718[/C][C]1.70044[/C][C]1.70044[/C][C]1.72276[/C][C]1.70044[/C][C]1.684942[/C][C]1.70044[/C][/ROW]
[ROW][C]0.35[/C][C]1.916688[/C][C]1.979538[/C][C]1.97748[/C][C]1.97748[/C][C]1.991886[/C][C]1.97748[/C][C]2.016582[/C][C]1.97748[/C][/ROW]
[ROW][C]0.4[/C][C]2.025984[/C][C]2.0343[/C][C]2.02782[/C][C]2.02782[/C][C]2.04078[/C][C]2.02782[/C][C]2.05374[/C][C]2.02782[/C][/ROW]
[ROW][C]0.45[/C][C]2.092116[/C][C]2.101407[/C][C]2.09566[/C][C]2.09566[/C][C]2.103049[/C][C]2.09566[/C][C]2.106333[/C][C]2.09566[/C][/ROW]
[ROW][C]0.5[/C][C]2.18618[/C][C]2.20013[/C][C]2.18618[/C][C]2.20013[/C][C]2.20013[/C][C]2.18618[/C][C]2.20013[/C][C]2.20013[/C][/ROW]
[ROW][C]0.55[/C][C]2.245656[/C][C]2.314714[/C][C]2.35866[/C][C]2.35866[/C][C]2.302158[/C][C]2.2331[/C][C]2.277046[/C][C]2.35866[/C][/ROW]
[ROW][C]0.6[/C][C]2.456196[/C][C]2.666304[/C][C]2.73634[/C][C]2.73634[/C][C]2.596268[/C][C]2.38616[/C][C]2.456196[/C][C]2.73634[/C][/ROW]
[ROW][C]0.65[/C][C]2.879036[/C][C]2.971154[/C][C]2.97824[/C][C]2.97824[/C][C]2.928638[/C][C]2.83652[/C][C]2.843606[/C][C]2.97824[/C][/ROW]
[ROW][C]0.7[/C][C]3.170828[/C][C]3.407882[/C][C]3.4037[/C][C]3.4037[/C][C]3.287264[/C][C]3.01558[/C][C]3.441338[/C][C]3.4037[/C][/ROW]
[ROW][C]0.75[/C][C]3.48314[/C][C]3.533535[/C][C]3.52076[/C][C]3.52076[/C][C]3.50195[/C][C]3.52076[/C][C]3.559085[/C][C]3.52076[/C][/ROW]
[ROW][C]0.8[/C][C]3.62586[/C][C]3.692916[/C][C]3.66186[/C][C]3.66186[/C][C]3.64386[/C][C]3.66186[/C][C]3.708444[/C][C]3.66186[/C][/ROW]
[ROW][C]0.85[/C][C]3.757602[/C][C]3.793399[/C][C]3.76536[/C][C]3.76536[/C][C]3.761481[/C][C]3.76536[/C][C]3.788301[/C][C]3.81634[/C][/ROW]
[ROW][C]0.9[/C][C]3.957396[/C][C]4.141816[/C][C]3.99266[/C][C]3.99266[/C][C]3.975028[/C][C]3.99266[/C][C]4.056584[/C][C]4.20574[/C][/ROW]
[ROW][C]0.95[/C][C]4.218556[/C][C]4.877608[/C][C]4.21998[/C][C]4.21998[/C][C]4.219268[/C][C]4.21998[/C][C]4.336032[/C][C]4.99366[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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)
0.050.8509940.8513010.856520.856520.8672960.850380.8555990.85038
0.11.0733481.0740021.078581.078581.0937141.072041.0766181.07204
0.151.2313661.2320891.234741.234741.2491851.229921.2325711.22992
0.21.3381441.3416961.34881.34881.3626561.331041.3381441.3488
0.251.444711.4580251.471341.471341.524311.471341.4313951.47134
0.31.6935521.6987181.700441.700441.722761.700441.6849421.70044
0.351.9166881.9795381.977481.977481.9918861.977482.0165821.97748
0.42.0259842.03432.027822.027822.040782.027822.053742.02782
0.452.0921162.1014072.095662.095662.1030492.095662.1063332.09566
0.52.186182.200132.186182.200132.200132.186182.200132.20013
0.552.2456562.3147142.358662.358662.3021582.23312.2770462.35866
0.62.4561962.6663042.736342.736342.5962682.386162.4561962.73634
0.652.8790362.9711542.978242.978242.9286382.836522.8436062.97824
0.73.1708283.4078823.40373.40373.2872643.015583.4413383.4037
0.753.483143.5335353.520763.520763.501953.520763.5590853.52076
0.83.625863.6929163.661863.661863.643863.661863.7084443.66186
0.853.7576023.7933993.765363.765363.7614813.765363.7883013.81634
0.93.9573964.1418163.992663.992663.9750283.992664.0565844.20574
0.954.2185564.8776084.219984.219984.2192684.219984.3360324.99366



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('method_1.htm', 'Weighted Average at Xnp',''),1,TRUE)
a<-table.element(a,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),1,TRUE)
a<-table.element(a,hyperlink('method_3.htm','Empirical Distribution Function',''),1,TRUE)
a<-table.element(a,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),1,TRUE)
a<-table.element(a,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),1,TRUE)
a<-table.element(a,hyperlink('method_6.htm','Closest Observation',''),1,TRUE)
a<-table.element(a,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),1,TRUE)
a<-table.element(a,hyperlink('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')