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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 computationFri, 10 Apr 2015 08:09:09 +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/2015/Apr/10/t1428649787yam8didgpczmzva.htm/, Retrieved Tue, 28 Jul 2026 20:46:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278696, Retrieved Tue, 28 Jul 2026 20:46:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact474

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] [Spreiding -en gem...] [2015-04-10 07:09:09] [c5b33e4153b13210102bee47a487e864] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100,64
100,93
101,41
102,07
102,42
102,53
102,43
102,6
102,65
102,74
102,82
103,2
102,75
103,09
103,71
104,3
104,58
104,71
104,44
104,57
104,95
105,49
106,03
106,48
106,25
106,7
107,6
108,05
108,72
109,17
109,08
109,04
109,34
109,37
108,96
108,77
108,11
108,67
109,05
109,43
109,62
109,85
109,34
109,65
109,69
109,91
110,09
110,44
109,9
110,25
111,26
111,74
111,91
111,95
111,63
111,85
112,16
112,49
112,66
113,39
112,92
113,44
114,68
115,38
115,48
115,41
114,92
115,16
115,89
116,25
116,43
116,83
116,17
116,78
117,98
118,53
118,43
118,29
117,85
118,27
119
119,33
119,17
119,57
118,62
119,09
120,19
120,17
120,29
120,35
119,88
120,04
120,52
120,43
120,34
120,75

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278696&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278696&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278696&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1102.2033333333330.7940727392068772.56
2104.5916666666671.091985958395683.73
3108.4208333333331.049332760578953.12
4109.48750.6358548290579882.33
5111.7658333333330.964510788226893.48999999999999
6115.23251.149585893821223.91
7118.2808333333331.00631152174063.39999999999999
8120.0558333333330.6117108397888252.13

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 102.203333333333 & 0.794072739206877 & 2.56 \tabularnewline
2 & 104.591666666667 & 1.09198595839568 & 3.73 \tabularnewline
3 & 108.420833333333 & 1.04933276057895 & 3.12 \tabularnewline
4 & 109.4875 & 0.635854829057988 & 2.33 \tabularnewline
5 & 111.765833333333 & 0.96451078822689 & 3.48999999999999 \tabularnewline
6 & 115.2325 & 1.14958589382122 & 3.91 \tabularnewline
7 & 118.280833333333 & 1.0063115217406 & 3.39999999999999 \tabularnewline
8 & 120.055833333333 & 0.611710839788825 & 2.13 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278696&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]102.203333333333[/C][C]0.794072739206877[/C][C]2.56[/C][/ROW]
[ROW][C]2[/C][C]104.591666666667[/C][C]1.09198595839568[/C][C]3.73[/C][/ROW]
[ROW][C]3[/C][C]108.420833333333[/C][C]1.04933276057895[/C][C]3.12[/C][/ROW]
[ROW][C]4[/C][C]109.4875[/C][C]0.635854829057988[/C][C]2.33[/C][/ROW]
[ROW][C]5[/C][C]111.765833333333[/C][C]0.96451078822689[/C][C]3.48999999999999[/C][/ROW]
[ROW][C]6[/C][C]115.2325[/C][C]1.14958589382122[/C][C]3.91[/C][/ROW]
[ROW][C]7[/C][C]118.280833333333[/C][C]1.0063115217406[/C][C]3.39999999999999[/C][/ROW]
[ROW][C]8[/C][C]120.055833333333[/C][C]0.611710839788825[/C][C]2.13[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278696&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278696&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
1102.2033333333330.7940727392068772.56
2104.5916666666671.091985958395683.73
3108.4208333333331.049332760578953.12
4109.48750.6358548290579882.33
5111.7658333333330.964510788226893.48999999999999
6115.23251.149585893821223.91
7118.2808333333331.00631152174063.39999999999999
8120.0558333333330.6117108397888252.13






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.32612086406161
beta-0.00371399911428067
S.D.0.0132603843038426
T-STAT-0.280082313542334
p-value0.788820120301771

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.32612086406161 \tabularnewline
beta & -0.00371399911428067 \tabularnewline
S.D. & 0.0132603843038426 \tabularnewline
T-STAT & -0.280082313542334 \tabularnewline
p-value & 0.788820120301771 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278696&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.32612086406161[/C][/ROW]
[ROW][C]beta[/C][C]-0.00371399911428067[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0132603843038426[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.280082313542334[/C][/ROW]
[ROW][C]p-value[/C][C]0.788820120301771[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278696&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278696&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)
alpha1.32612086406161
beta-0.00371399911428067
S.D.0.0132603843038426
T-STAT-0.280082313542334
p-value0.788820120301771






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.67844958672101
beta-0.59328095491293
S.D.1.74400570020827
T-STAT-0.340182921903341
p-value0.745312362178025
Lambda1.59328095491293

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.67844958672101 \tabularnewline
beta & -0.59328095491293 \tabularnewline
S.D. & 1.74400570020827 \tabularnewline
T-STAT & -0.340182921903341 \tabularnewline
p-value & 0.745312362178025 \tabularnewline
Lambda & 1.59328095491293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278696&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.67844958672101[/C][/ROW]
[ROW][C]beta[/C][C]-0.59328095491293[/C][/ROW]
[ROW][C]S.D.[/C][C]1.74400570020827[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.340182921903341[/C][/ROW]
[ROW][C]p-value[/C][C]0.745312362178025[/C][/ROW]
[ROW][C]Lambda[/C][C]1.59328095491293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278696&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278696&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)
alpha2.67844958672101
beta-0.59328095491293
S.D.1.74400570020827
T-STAT-0.340182921903341
p-value0.745312362178025
Lambda1.59328095491293


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')