FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 24 Dec 2008 08:04:58 -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/24/t1230131124qo8z13ua0dm1r8c.htm/, Retrieved Fri, 17 May 2024 03:03:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36605, Retrieved Fri, 17 May 2024 03:03:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact198

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMPD  [Spectral Analysis] [Identification an...] [2008-12-09 22:16:59] [1a689e9ccc515e1757f0522229a687e9]
- RMPD      [Standard Deviation-Mean Plot] [Paper SMP T2] [2008-12-24 15:04:58] [74a138e5b32af267311b5ad4cd13bf7e] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
103,3
107,9
101
94,6
94,2
92,3
107,1
102,6
103,1
104,1
92,7
87
109,3
113,9
103,3
100,8
97,4
98,9
110,8
103,5
99,8
104,9
95,2
85,7
110
113,7
101,1
103,6
96,2
98,3
119,7
109,4
103,5
118,2
98,7
96,8
121,8
124
119,6
122,5
109,7
111,6
131,2
124,4
116,9
131,8
107,4
111
134
126,2
131,2
130,1
123,1
126,3
148,6
130,1
142,3
154,4
121,6
124,8
143,6
146,9
144,6
137,1
134,7
130,8
153,5
137,6
146,5
156,7
137,6
131,4
147,4
158,5
151,5
142,5
131,3
133,4
136,9
143,2
136,4
145,9
138,8
122,9

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' @ 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36605&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36605&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36605&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' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
199.15833333333336.6998586597484320.9
2101.9583333333337.5897608458349828.2
3105.7666666666678.2682671959874723.5
4119.3258.1477409027399624.4
5132.72510.419834669775532.8
6141.758.2846517455747325.9
7140.7259.5818127910973335.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 99.1583333333333 & 6.69985865974843 & 20.9 \tabularnewline
2 & 101.958333333333 & 7.58976084583498 & 28.2 \tabularnewline
3 & 105.766666666667 & 8.26826719598747 & 23.5 \tabularnewline
4 & 119.325 & 8.14774090273996 & 24.4 \tabularnewline
5 & 132.725 & 10.4198346697755 & 32.8 \tabularnewline
6 & 141.75 & 8.28465174557473 & 25.9 \tabularnewline
7 & 140.725 & 9.58181279109733 & 35.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36605&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]99.1583333333333[/C][C]6.69985865974843[/C][C]20.9[/C][/ROW]
[ROW][C]2[/C][C]101.958333333333[/C][C]7.58976084583498[/C][C]28.2[/C][/ROW]
[ROW][C]3[/C][C]105.766666666667[/C][C]8.26826719598747[/C][C]23.5[/C][/ROW]
[ROW][C]4[/C][C]119.325[/C][C]8.14774090273996[/C][C]24.4[/C][/ROW]
[ROW][C]5[/C][C]132.725[/C][C]10.4198346697755[/C][C]32.8[/C][/ROW]
[ROW][C]6[/C][C]141.75[/C][C]8.28465174557473[/C][C]25.9[/C][/ROW]
[ROW][C]7[/C][C]140.725[/C][C]9.58181279109733[/C][C]35.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36605&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36605&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
199.15833333333336.6998586597484320.9
2101.9583333333337.5897608458349828.2
3105.7666666666678.2682671959874723.5
4119.3258.1477409027399624.4
5132.72510.419834669775532.8
6141.758.2846517455747325.9
7140.7259.5818127910973335.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.51296612237519
beta0.0492046041309298
S.D.0.0203670804155424
T-STAT2.41588893091329
p-value0.0604231596586525

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.51296612237519 \tabularnewline
beta & 0.0492046041309298 \tabularnewline
S.D. & 0.0203670804155424 \tabularnewline
T-STAT & 2.41588893091329 \tabularnewline
p-value & 0.0604231596586525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36605&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.51296612237519[/C][/ROW]
[ROW][C]beta[/C][C]0.0492046041309298[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0203670804155424[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.41588893091329[/C][/ROW]
[ROW][C]p-value[/C][C]0.0604231596586525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36605&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36605&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)
alpha2.51296612237519
beta0.0492046041309298
S.D.0.0203670804155424
T-STAT2.41588893091329
p-value0.0604231596586525






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.31359606097109
beta0.71897387684227
S.D.0.273697767385079
T-STAT2.62688981247958
p-value0.0467080329018594
Lambda0.281026123157730

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.31359606097109 \tabularnewline
beta & 0.71897387684227 \tabularnewline
S.D. & 0.273697767385079 \tabularnewline
T-STAT & 2.62688981247958 \tabularnewline
p-value & 0.0467080329018594 \tabularnewline
Lambda & 0.281026123157730 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36605&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.31359606097109[/C][/ROW]
[ROW][C]beta[/C][C]0.71897387684227[/C][/ROW]
[ROW][C]S.D.[/C][C]0.273697767385079[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.62688981247958[/C][/ROW]
[ROW][C]p-value[/C][C]0.0467080329018594[/C][/ROW]
[ROW][C]Lambda[/C][C]0.281026123157730[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36605&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36605&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-1.31359606097109
beta0.71897387684227
S.D.0.273697767385079
T-STAT2.62688981247958
p-value0.0467080329018594
Lambda0.281026123157730


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 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')