FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationFri, 19 Dec 2008 09:30:21 -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/2008/Dec/19/t1229704454bzr8b7uhe5j5c64.htm/, Retrieved Tue, 10 Feb 2026 14:04:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35216, Retrieved Tue, 10 Feb 2026 14:04:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact464

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] [Paper - SMP] [2008-12-19 16:30:21] [63302faa1e3976bf98d1de42298c0b24] [Current]
- RM      [Variance Reduction Matrix] [Paper - VRM] [2008-12-19 19:41:00] [23bfa928dab4b48567707937094f7011]
- RMPD      [ARIMA Forecasting] [Paper - ARIMA For...] [2008-12-21 13:35:35] [23bfa928dab4b48567707937094f7011]
-             [ARIMA Forecasting] [Paper - ARIMA For...] [2008-12-21 14:38:28] [23bfa928dab4b48567707937094f7011]
-   P           [ARIMA Forecasting] [Paper - ARIMA For...] [2008-12-21 20:19:27] [23bfa928dab4b48567707937094f7011]
- RMP     [(Partial) Autocorrelation Function] [Paper - ACF ] [2008-12-19 19:43:42] [23bfa928dab4b48567707937094f7011]
-   PD      [(Partial) Autocorrelation Function] [Paper - ACF ] [2008-12-19 19:46:26] [23bfa928dab4b48567707937094f7011]
-   P         [(Partial) Autocorrelation Function] [Paper - ACF ] [2008-12-21 19:55:13] [23bfa928dab4b48567707937094f7011]
- RMP       [Spectral Analysis] [Paper - Cumulatie...] [2008-12-19 19:48:26] [23bfa928dab4b48567707937094f7011]
- RMPD      [Spectral Analysis] [Paper - Cumulatie...] [2008-12-19 19:49:55] [23bfa928dab4b48567707937094f7011]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
90,8
96,4
90
92,1
97,2
95,1
88,5
91
90,5
75
66,3
66
68,4
70,6
83,9
90,1
90,6
87,1
90,8
94,1
99,8
96,8
87
96,3
107,1
115,2
106,1
89,5
91,3
97,6
100,7
104,6
94,7
101,8
102,5
105,3
110,3
109,8
117,3
118,8
131,3
125,9
133,1
147
145,8
164,4
149,8
137,7
151,7
156,8
180
180,4
170,4
191,6
199,5
218,2
217,5
205
194
199,3

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35216&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35216&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35216&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
186.57511.075289858714631.2
287.95833333333339.7575572887082931.4
3101.3666666666677.2316643794474925.7
4132.617.064529932529154.6
5188.721.525798475317966.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 86.575 & 11.0752898587146 & 31.2 \tabularnewline
2 & 87.9583333333333 & 9.75755728870829 & 31.4 \tabularnewline
3 & 101.366666666667 & 7.23166437944749 & 25.7 \tabularnewline
4 & 132.6 & 17.0645299325291 & 54.6 \tabularnewline
5 & 188.7 & 21.5257984753179 & 66.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35216&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]86.575[/C][C]11.0752898587146[/C][C]31.2[/C][/ROW]
[ROW][C]2[/C][C]87.9583333333333[/C][C]9.75755728870829[/C][C]31.4[/C][/ROW]
[ROW][C]3[/C][C]101.366666666667[/C][C]7.23166437944749[/C][C]25.7[/C][/ROW]
[ROW][C]4[/C][C]132.6[/C][C]17.0645299325291[/C][C]54.6[/C][/ROW]
[ROW][C]5[/C][C]188.7[/C][C]21.5257984753179[/C][C]66.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35216&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35216&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
186.57511.075289858714631.2
287.95833333333339.7575572887082931.4
3101.3666666666677.2316643794474925.7
4132.617.064529932529154.6
5188.721.525798475317966.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.47865800158556
beta0.123992180078107
S.D.0.0321715526658474
T-STAT3.85409375064866
p-value0.0308551653566576

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.47865800158556 \tabularnewline
beta & 0.123992180078107 \tabularnewline
S.D. & 0.0321715526658474 \tabularnewline
T-STAT & 3.85409375064866 \tabularnewline
p-value & 0.0308551653566576 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35216&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.47865800158556[/C][/ROW]
[ROW][C]beta[/C][C]0.123992180078107[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0321715526658474[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.85409375064866[/C][/ROW]
[ROW][C]p-value[/C][C]0.0308551653566576[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35216&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35216&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-1.47865800158556
beta0.123992180078107
S.D.0.0321715526658474
T-STAT3.85409375064866
p-value0.0308551653566576






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.76098326916189
beta1.11350579380910
S.D.0.419977600830949
T-STAT2.65134567083094
p-value0.0769052633078542
Lambda-0.113505793809102

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.76098326916189 \tabularnewline
beta & 1.11350579380910 \tabularnewline
S.D. & 0.419977600830949 \tabularnewline
T-STAT & 2.65134567083094 \tabularnewline
p-value & 0.0769052633078542 \tabularnewline
Lambda & -0.113505793809102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35216&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.76098326916189[/C][/ROW]
[ROW][C]beta[/C][C]1.11350579380910[/C][/ROW]
[ROW][C]S.D.[/C][C]0.419977600830949[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.65134567083094[/C][/ROW]
[ROW][C]p-value[/C][C]0.0769052633078542[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.113505793809102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35216&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35216&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-2.76098326916189
beta1.11350579380910
S.D.0.419977600830949
T-STAT2.65134567083094
p-value0.0769052633078542
Lambda-0.113505793809102


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')