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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 computationThu, 26 Nov 2015 15:40:14 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/26/t1448552433iq675s6k1laeobs.htm/, Retrieved Sun, 15 Feb 2026 08:39:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284246, Retrieved Sun, 15 Feb 2026 08:39:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact336

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] [] [2015-11-26 15:40:14] [047b71d569822bc9ea0d1a14ab5e311b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
72,04
72,26
72,53
72,41
72,91
72,84
72,92
73,03
72,98
72,99
73,15
73,34
73,8
74,46
74,54
74,92
74,19
74,34
74,54
74,4
73,78
74,42
73,54
74,45
76,31
76,44
76,64
76,44
76,49
76,52
78,15
78,54
78,79
78,75
78,28
78,44
78,75
80,54
80,84
81,11
80,47
80,53
80,35
80,29
80,27
80,1
79,8
79,84
79,92
80,26
80,69
84,5
85,45
86,19
86,4
85,98
85,87
86,06
86,43
86,43
86,37
86,84
86,73
90,99
92,61
93,83
94,2
94,01
93,47
93,27
94,3
94,53
94,59
94,69
94,67
96,55
97,14
97,32
97,97
98,49
99,11
99,09
98,76
99,2
99,61
99,54
99,68
100,75
100,38
100,79
100,39
100,39
100,12
100
99,17
99,17
99,59
99,96
99,68
101,03
100,99
101,38
101,84
101,52
101,37
101,22
101,45
101,99

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284246&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284246&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284246&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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
172.78333333333330.387822202311911.3
274.28166666666670.3907762283021591.38
377.48251.070362088267332.48
480.24083333333330.5994460826968572.36
584.5152.607449119175856.51000000000001
691.76253.226374618952088.16
797.29833333333331.802734454974314.61
899.99916666666670.5635513743352521.62
9101.0016666666670.8147150459274732.39999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 72.7833333333333 & 0.38782220231191 & 1.3 \tabularnewline
2 & 74.2816666666667 & 0.390776228302159 & 1.38 \tabularnewline
3 & 77.4825 & 1.07036208826733 & 2.48 \tabularnewline
4 & 80.2408333333333 & 0.599446082696857 & 2.36 \tabularnewline
5 & 84.515 & 2.60744911917585 & 6.51000000000001 \tabularnewline
6 & 91.7625 & 3.22637461895208 & 8.16 \tabularnewline
7 & 97.2983333333333 & 1.80273445497431 & 4.61 \tabularnewline
8 & 99.9991666666667 & 0.563551374335252 & 1.62 \tabularnewline
9 & 101.001666666667 & 0.814715045927473 & 2.39999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284246&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]72.7833333333333[/C][C]0.38782220231191[/C][C]1.3[/C][/ROW]
[ROW][C]2[/C][C]74.2816666666667[/C][C]0.390776228302159[/C][C]1.38[/C][/ROW]
[ROW][C]3[/C][C]77.4825[/C][C]1.07036208826733[/C][C]2.48[/C][/ROW]
[ROW][C]4[/C][C]80.2408333333333[/C][C]0.599446082696857[/C][C]2.36[/C][/ROW]
[ROW][C]5[/C][C]84.515[/C][C]2.60744911917585[/C][C]6.51000000000001[/C][/ROW]
[ROW][C]6[/C][C]91.7625[/C][C]3.22637461895208[/C][C]8.16[/C][/ROW]
[ROW][C]7[/C][C]97.2983333333333[/C][C]1.80273445497431[/C][C]4.61[/C][/ROW]
[ROW][C]8[/C][C]99.9991666666667[/C][C]0.563551374335252[/C][C]1.62[/C][/ROW]
[ROW][C]9[/C][C]101.001666666667[/C][C]0.814715045927473[/C][C]2.39999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284246&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284246&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
172.78333333333330.387822202311911.3
274.28166666666670.3907762283021591.38
377.48251.070362088267332.48
480.24083333333330.5994460826968572.36
584.5152.607449119175856.51000000000001
691.76253.226374618952088.16
797.29833333333331.802734454974314.61
899.99916666666670.5635513743352521.62
9101.0016666666670.8147150459274732.39999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.988897822966212
beta0.0261280807088324
S.D.0.0337561773172945
T-STAT0.774023683524318
p-value0.464251166217945

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.988897822966212 \tabularnewline
beta & 0.0261280807088324 \tabularnewline
S.D. & 0.0337561773172945 \tabularnewline
T-STAT & 0.774023683524318 \tabularnewline
p-value & 0.464251166217945 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284246&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.988897822966212[/C][/ROW]
[ROW][C]beta[/C][C]0.0261280807088324[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0337561773172945[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.774023683524318[/C][/ROW]
[ROW][C]p-value[/C][C]0.464251166217945[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284246&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284246&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-0.988897822966212
beta0.0261280807088324
S.D.0.0337561773172945
T-STAT0.774023683524318
p-value0.464251166217945






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-11.2829895261239
beta2.52358320017744
S.D.2.11870973109243
T-STAT1.19109435480633
p-value0.272433056397667
Lambda-1.52358320017744

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.2829895261239 \tabularnewline
beta & 2.52358320017744 \tabularnewline
S.D. & 2.11870973109243 \tabularnewline
T-STAT & 1.19109435480633 \tabularnewline
p-value & 0.272433056397667 \tabularnewline
Lambda & -1.52358320017744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284246&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.2829895261239[/C][/ROW]
[ROW][C]beta[/C][C]2.52358320017744[/C][/ROW]
[ROW][C]S.D.[/C][C]2.11870973109243[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.19109435480633[/C][/ROW]
[ROW][C]p-value[/C][C]0.272433056397667[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.52358320017744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284246&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284246&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-11.2829895261239
beta2.52358320017744
S.D.2.11870973109243
T-STAT1.19109435480633
p-value0.272433056397667
Lambda-1.52358320017744


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')