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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, 24 Apr 2016 16:21:35 +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/Apr/24/t1461511325uwe6cb95xd68dnk.htm/, Retrieved Sat, 14 Feb 2026 05:52:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294639, Retrieved Sat, 14 Feb 2026 05:52:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact362

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] [] [2016-04-24 15:21:35] [383002b29a4d7fe40259202a4bc884b2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
87,16
87,16
87,16
87,16
87,16
87,16
87,16
87,16
87,16
89,24
89,24
89,24
89,24
89,24
89,24
89,24
89,24
89,24
89,24
89,24
89,24
91
91
91
91
91
91
91
91
91
91
91
91
92,51
92,51
92,51
92,51
92,51
92,51
92,51
92,51
92,51
92,51
92,51
92,51
96,67
96,67
96,67
96,67
96,67
96,67
96,67
96,67
96,67
96,67
96,67
96,67
96,19
96,19
96,19
96,19
96,19
96,19
96,19
96,19
96,19
96,19
96,19
96,19
99,13
99,13
99,13
99,13
99,13
99,13
99,13
99,13
99,13
99,13
99,13
99,13
99,58
99,58
99,58
99,58
99,58
99,58
99,58
99,58
99,58
99,58
99,58
99,58
101,27
101,27
101,27
101,25
101,25
101,25
101,25
101,25
101,25
101,25
101,25
101,25
102,55
102,55
102,55
102,55
102,55
102,55
102,55
102,55
102,55
102,55
102,55
102,55
132,09
132,09
132,09

Tables (Output of Computation)





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=294639&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=294639&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294639&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
187.680.9407153950826222.08
289.680.7959899496852981.76000000000001
391.37750.6829231954686371.51000000000001
493.551.881430790165244.16
596.550.2170881680959920.480000000000004
696.9251.329665029587942.94
799.24250.2035201575899920.450000000000003
8100.00250.764331258504631.69
9101.5750.5879471219266381.3
10109.93513.359967678240729.54

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 87.68 & 0.940715395082622 & 2.08 \tabularnewline
2 & 89.68 & 0.795989949685298 & 1.76000000000001 \tabularnewline
3 & 91.3775 & 0.682923195468637 & 1.51000000000001 \tabularnewline
4 & 93.55 & 1.88143079016524 & 4.16 \tabularnewline
5 & 96.55 & 0.217088168095992 & 0.480000000000004 \tabularnewline
6 & 96.925 & 1.32966502958794 & 2.94 \tabularnewline
7 & 99.2425 & 0.203520157589992 & 0.450000000000003 \tabularnewline
8 & 100.0025 & 0.76433125850463 & 1.69 \tabularnewline
9 & 101.575 & 0.587947121926638 & 1.3 \tabularnewline
10 & 109.935 & 13.3599676782407 & 29.54 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294639&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]87.68[/C][C]0.940715395082622[/C][C]2.08[/C][/ROW]
[ROW][C]2[/C][C]89.68[/C][C]0.795989949685298[/C][C]1.76000000000001[/C][/ROW]
[ROW][C]3[/C][C]91.3775[/C][C]0.682923195468637[/C][C]1.51000000000001[/C][/ROW]
[ROW][C]4[/C][C]93.55[/C][C]1.88143079016524[/C][C]4.16[/C][/ROW]
[ROW][C]5[/C][C]96.55[/C][C]0.217088168095992[/C][C]0.480000000000004[/C][/ROW]
[ROW][C]6[/C][C]96.925[/C][C]1.32966502958794[/C][C]2.94[/C][/ROW]
[ROW][C]7[/C][C]99.2425[/C][C]0.203520157589992[/C][C]0.450000000000003[/C][/ROW]
[ROW][C]8[/C][C]100.0025[/C][C]0.76433125850463[/C][C]1.69[/C][/ROW]
[ROW][C]9[/C][C]101.575[/C][C]0.587947121926638[/C][C]1.3[/C][/ROW]
[ROW][C]10[/C][C]109.935[/C][C]13.3599676782407[/C][C]29.54[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294639&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294639&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
187.680.9407153950826222.08
289.680.7959899496852981.76000000000001
391.37750.6829231954686371.51000000000001
493.551.881430790165244.16
596.550.2170881680959920.480000000000004
696.9251.329665029587942.94
799.24250.2035201575899920.450000000000003
8100.00250.764331258504631.69
9101.5750.5879471219266381.3
10109.93513.359967678240729.54






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-38.1557653183778
beta0.416258610866462
S.D.0.157997726867599
T-STAT2.63458607360397
p-value0.0299640825428278

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -38.1557653183778 \tabularnewline
beta & 0.416258610866462 \tabularnewline
S.D. & 0.157997726867599 \tabularnewline
T-STAT & 2.63458607360397 \tabularnewline
p-value & 0.0299640825428278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294639&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-38.1557653183778[/C][/ROW]
[ROW][C]beta[/C][C]0.416258610866462[/C][/ROW]
[ROW][C]S.D.[/C][C]0.157997726867599[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.63458607360397[/C][/ROW]
[ROW][C]p-value[/C][C]0.0299640825428278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294639&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294639&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-38.1557653183778
beta0.416258610866462
S.D.0.157997726867599
T-STAT2.63458607360397
p-value0.0299640825428278






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-31.9643726215259
beta6.97213431771048
S.D.5.72916041793117
T-STAT1.21695568095616
p-value0.258300727931529
Lambda-5.97213431771048

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -31.9643726215259 \tabularnewline
beta & 6.97213431771048 \tabularnewline
S.D. & 5.72916041793117 \tabularnewline
T-STAT & 1.21695568095616 \tabularnewline
p-value & 0.258300727931529 \tabularnewline
Lambda & -5.97213431771048 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294639&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-31.9643726215259[/C][/ROW]
[ROW][C]beta[/C][C]6.97213431771048[/C][/ROW]
[ROW][C]S.D.[/C][C]5.72916041793117[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.21695568095616[/C][/ROW]
[ROW][C]p-value[/C][C]0.258300727931529[/C][/ROW]
[ROW][C]Lambda[/C][C]-5.97213431771048[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294639&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294639&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-31.9643726215259
beta6.97213431771048
S.D.5.72916041793117
T-STAT1.21695568095616
p-value0.258300727931529
Lambda-5.97213431771048


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')