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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 computationSat, 24 Nov 2007 06:24:43 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/24/t11959101816hnuzgowf310ubc.htm/, Retrieved Wed, 20 May 2026 04:44:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6287, Retrieved Wed, 20 May 2026 04:44:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsstandard deviation mean plot, paper, groep 4
Estimated Impact478

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] [Standard deviatio...] [2007-11-24 13:24:43] [bd7b8d7754bcf95ad80b21f541dc6b78] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
88,95
88,81
88,90
90,15
90,92
90,78
90,81
89,46
89,22
88,89
89,41
89,59
90,25
90,20
90,27
90,71
91,18
90,66
89,72
88,72
88,91
89,15
89,15
89,08
89,28
89,47
89,53
90,72
90,91
91,38
91,49
90,90
90,93
90,57
91,28
90,83
91,50
91,58
92,49
94,16
95,46
95,80
95,32
95,41
95,35
95,68
95,59
94,96
96,92
96,06
96,59
96,67
97,27
96,38
96,47
96,05
96,76
96,51
96,55
95,97
97,00
97,46
97,90
98,42
98,54
99,00
98,94
99,02
100,07
98,72
98,73
98,04
99,08
99,22
99,57
100,44
100,84
100,75
100,49
99,98
99,96
99,76
100,11
99,79
100,29
101,12
102,65
102,71
103,39
102,80
102,07
102,15
101,21
101,27
101,86
101,65
101,94
102,62
102,71
103,39
104,51
104,09
104,29
104,57
105,39
105,15
106,13
105,46
106,47
106,62
106,52
108,04
107,15
107,32
107,76
107,26
107,89

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6287&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6287&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6287&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
189.65750.8035503604741781.97
289.83333333333330.818561191507652.37000000000000
390.60750.762151559730742.58999999999999
494.44166666666671.631172658679715.64999999999999
596.51666666666670.3772468045128446.36
698.48666666666670.8084365757248349.41
799.99916666666670.56062397596271511.12
8101.9308333333330.87730432507076914.67
9104.18751.2920253656389817.22

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 89.6575 & 0.803550360474178 & 1.97 \tabularnewline
2 & 89.8333333333333 & 0.81856119150765 & 2.37000000000000 \tabularnewline
3 & 90.6075 & 0.76215155973074 & 2.58999999999999 \tabularnewline
4 & 94.4416666666667 & 1.63117265867971 & 5.64999999999999 \tabularnewline
5 & 96.5166666666667 & 0.377246804512844 & 6.36 \tabularnewline
6 & 98.4866666666667 & 0.808436575724834 & 9.41 \tabularnewline
7 & 99.9991666666667 & 0.560623975962715 & 11.12 \tabularnewline
8 & 101.930833333333 & 0.877304325070769 & 14.67 \tabularnewline
9 & 104.1875 & 1.29202536563898 & 17.22 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6287&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]89.6575[/C][C]0.803550360474178[/C][C]1.97[/C][/ROW]
[ROW][C]2[/C][C]89.8333333333333[/C][C]0.81856119150765[/C][C]2.37000000000000[/C][/ROW]
[ROW][C]3[/C][C]90.6075[/C][C]0.76215155973074[/C][C]2.58999999999999[/C][/ROW]
[ROW][C]4[/C][C]94.4416666666667[/C][C]1.63117265867971[/C][C]5.64999999999999[/C][/ROW]
[ROW][C]5[/C][C]96.5166666666667[/C][C]0.377246804512844[/C][C]6.36[/C][/ROW]
[ROW][C]6[/C][C]98.4866666666667[/C][C]0.808436575724834[/C][C]9.41[/C][/ROW]
[ROW][C]7[/C][C]99.9991666666667[/C][C]0.560623975962715[/C][C]11.12[/C][/ROW]
[ROW][C]8[/C][C]101.930833333333[/C][C]0.877304325070769[/C][C]14.67[/C][/ROW]
[ROW][C]9[/C][C]104.1875[/C][C]1.29202536563898[/C][C]17.22[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6287&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6287&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
189.65750.8035503604741781.97
289.83333333333330.818561191507652.37000000000000
390.60750.762151559730742.58999999999999
494.44166666666671.631172658679715.64999999999999
596.51666666666670.3772468045128446.36
698.48666666666670.8084365757248349.41
799.99916666666670.56062397596271511.12
8101.9308333333330.87730432507076914.67
9104.18751.2920253656389817.22






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0721991737942935
beta0.00841123910517739
S.D.0.0259181852525877
T-STAT0.324530403004878
p-value0.755019275123002

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0721991737942935 \tabularnewline
beta & 0.00841123910517739 \tabularnewline
S.D. & 0.0259181852525877 \tabularnewline
T-STAT & 0.324530403004878 \tabularnewline
p-value & 0.755019275123002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6287&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0721991737942935[/C][/ROW]
[ROW][C]beta[/C][C]0.00841123910517739[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0259181852525877[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.324530403004878[/C][/ROW]
[ROW][C]p-value[/C][C]0.755019275123002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6287&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6287&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)
alpha0.0721991737942935
beta0.00841123910517739
S.D.0.0259181852525877
T-STAT0.324530403004878
p-value0.755019275123002






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.03698081801173
beta0.620456640635401
S.D.2.83756614875124
T-STAT0.218658035834143
p-value0.833154762309197
Lambda0.379543359364599

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.03698081801173 \tabularnewline
beta & 0.620456640635401 \tabularnewline
S.D. & 2.83756614875124 \tabularnewline
T-STAT & 0.218658035834143 \tabularnewline
p-value & 0.833154762309197 \tabularnewline
Lambda & 0.379543359364599 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6287&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.03698081801173[/C][/ROW]
[ROW][C]beta[/C][C]0.620456640635401[/C][/ROW]
[ROW][C]S.D.[/C][C]2.83756614875124[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.218658035834143[/C][/ROW]
[ROW][C]p-value[/C][C]0.833154762309197[/C][/ROW]
[ROW][C]Lambda[/C][C]0.379543359364599[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6287&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6287&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-3.03698081801173
beta0.620456640635401
S.D.2.83756614875124
T-STAT0.218658035834143
p-value0.833154762309197
Lambda0.379543359364599


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')