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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSun, 25 May 2008 13:22:28 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/25/t1211743395trnd3lbicz74t2h.htm/, Retrieved Thu, 30 Apr 2026 16:44:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13203, Retrieved Thu, 30 Apr 2026 16:44:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact357

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [Nicky Van Calster...] [2008-05-25 19:22:28] [9e4ffec01482233a36a742caf4f37457] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,70291
0,6885
0,67127
0,66502
0,65825
0,65025
0,65779
0,66014
0,64683
0,64587
0,63702
0,62651
0,61834
0,61466
0,61063
0,59802
0,60151
0,62927
0,62304
0,6071
0,60773
0,58933
0,60039
0,61342
0,6348
0,634
0,62915
0,62168
0,61328
0,6089
0,60857
0,62672
0,62291
0,62393
0,61838
0,62012
0,61659
0,6116
0,61573
0,61407
0,62823
0,64405
0,6387
0,63633
0,63059
0,62994
0,63709
0,64217
0,65711
0,66977
0,68255
0,68902
0,71322
0,70224
0,70045
0,69919
0,69693
0,69763
0,69278
0,70196
0,69215
0,6769
0,67124
0,66532
0,67157
0,66428
0,66576
0,66942
0,6813
0,69144
0,69862
0,695
0,69867
0,68968
0,69233
0,68293
0,68399
0,66895
0,68756
0,68527
0,6776
0,68137
0,67933
0,67922
0,68598
0,68297
0,68935
0,69463
0,6833
0,68666
0,68782
0,67669
0,67511
0,67254
0,67397
0,67286
0,66341
0,668
0,68021
0,67934
0,68136
0,67562
0,6744
0,67766
0,68887
0,69614
0,70896
0,72064
0,74725

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13203&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13203&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13203&T=0

As an alternative you can also use a QR Code:  
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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
10.6591966666666670.02115695086010670.0764
20.6094533333333330.01124082359756240.03994
30.621870.008688265858982650.02623
40.62875750.01156909372187180.03245
50.6919041666666670.01550253378605830.05611
60.6785833333333330.01265828678148920.0343400000000000
70.6839083333333330.007694316477803980.0297200000000000
80.6818233333333330.007387978359634270.0220899999999999
90.6845508333333330.01667476070883680.0572299999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 0.659196666666667 & 0.0211569508601067 & 0.0764 \tabularnewline
2 & 0.609453333333333 & 0.0112408235975624 & 0.03994 \tabularnewline
3 & 0.62187 & 0.00868826585898265 & 0.02623 \tabularnewline
4 & 0.6287575 & 0.0115690937218718 & 0.03245 \tabularnewline
5 & 0.691904166666667 & 0.0155025337860583 & 0.05611 \tabularnewline
6 & 0.678583333333333 & 0.0126582867814892 & 0.0343400000000000 \tabularnewline
7 & 0.683908333333333 & 0.00769431647780398 & 0.0297200000000000 \tabularnewline
8 & 0.681823333333333 & 0.00738797835963427 & 0.0220899999999999 \tabularnewline
9 & 0.684550833333333 & 0.0166747607088368 & 0.0572299999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13203&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]0.659196666666667[/C][C]0.0211569508601067[/C][C]0.0764[/C][/ROW]
[ROW][C]2[/C][C]0.609453333333333[/C][C]0.0112408235975624[/C][C]0.03994[/C][/ROW]
[ROW][C]3[/C][C]0.62187[/C][C]0.00868826585898265[/C][C]0.02623[/C][/ROW]
[ROW][C]4[/C][C]0.6287575[/C][C]0.0115690937218718[/C][C]0.03245[/C][/ROW]
[ROW][C]5[/C][C]0.691904166666667[/C][C]0.0155025337860583[/C][C]0.05611[/C][/ROW]
[ROW][C]6[/C][C]0.678583333333333[/C][C]0.0126582867814892[/C][C]0.0343400000000000[/C][/ROW]
[ROW][C]7[/C][C]0.683908333333333[/C][C]0.00769431647780398[/C][C]0.0297200000000000[/C][/ROW]
[ROW][C]8[/C][C]0.681823333333333[/C][C]0.00738797835963427[/C][C]0.0220899999999999[/C][/ROW]
[ROW][C]9[/C][C]0.684550833333333[/C][C]0.0166747607088368[/C][C]0.0572299999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13203&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13203&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
10.6591966666666670.02115695086010670.0764
20.6094533333333330.01124082359756240.03994
30.621870.008688265858982650.02623
40.62875750.01156909372187180.03245
50.6919041666666670.01550253378605830.05611
60.6785833333333330.01265828678148920.0343400000000000
70.6839083333333330.007694316477803980.0297200000000000
80.6818233333333330.007387978359634270.0220899999999999
90.6845508333333330.01667476070883680.0572299999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.00447908931091324
beta0.0257379783495949
S.D.0.0538404289963802
T-STAT0.478041851251321
p-value0.64718849087433

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.00447908931091324 \tabularnewline
beta & 0.0257379783495949 \tabularnewline
S.D. & 0.0538404289963802 \tabularnewline
T-STAT & 0.478041851251321 \tabularnewline
p-value & 0.64718849087433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13203&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.00447908931091324[/C][/ROW]
[ROW][C]beta[/C][C]0.0257379783495949[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0538404289963802[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.478041851251321[/C][/ROW]
[ROW][C]p-value[/C][C]0.64718849087433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13203&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13203&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.00447908931091324
beta0.0257379783495949
S.D.0.0538404289963802
T-STAT0.478041851251321
p-value0.64718849087433






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.01274830746721
beta1.02420943085848
S.D.2.77542235423162
T-STAT0.369028313581498
p-value0.7230158111197
Lambda-0.0242094308584839

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.01274830746721 \tabularnewline
beta & 1.02420943085848 \tabularnewline
S.D. & 2.77542235423162 \tabularnewline
T-STAT & 0.369028313581498 \tabularnewline
p-value & 0.7230158111197 \tabularnewline
Lambda & -0.0242094308584839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13203&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.01274830746721[/C][/ROW]
[ROW][C]beta[/C][C]1.02420943085848[/C][/ROW]
[ROW][C]S.D.[/C][C]2.77542235423162[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.369028313581498[/C][/ROW]
[ROW][C]p-value[/C][C]0.7230158111197[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.0242094308584839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13203&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13203&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.01274830746721
beta1.02420943085848
S.D.2.77542235423162
T-STAT0.369028313581498
p-value0.7230158111197
Lambda-0.0242094308584839


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')