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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 computationThu, 11 Dec 2008 11:07:11 -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/11/t12290188921lanz2k69y4a38l.htm/, Retrieved Fri, 17 May 2024 06:38:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32414, Retrieved Fri, 17 May 2024 06:38:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157

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...] [2008-12-11 18:07:11] [a9e6d7cd6e144e8b311d9f96a24c5a25] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
99,5
93,5
104,6
95,3
102,8
103,3
100,2
107,9
107,5
119,8
112
102,1
105,3
101,3
108,4
107,4
109,1
109,5
111,4
110,1
117
129,6
113,5
113,3
110,1
107,4
110,1
112,5
106
117,6
117,8
113,5
121,2
130,4
115,2
117,9
110,7
107,6
124,3
115,1
112,5
127,9
117,4
119,3
130,4
126
125,4
130,5
115,9
108,7
124
119,4
118,6
131,3
111,1
124,8
132,3
126,7
131,7
130,9
122,1
113,2
133,6
119,2
129,4
131,4
117,1
130,5
132,3
140,8
137,5
128,6
126,7
120,8
139,3
128,6
131,3
136,3
128,8
133,2
136,3
151,1
145
134,4

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'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32414&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32414&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1104.0416666666677.183372002989526.3
2111.3257.041193726273228.3
3114.9756.7008988542243724.4
4120.5916666666677.9087360596119322.9
5122.958.2031590367259223.6
6127.9758.3891840539416727.6
7134.3166666666678.2169263589178430.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 104.041666666667 & 7.1833720029895 & 26.3 \tabularnewline
2 & 111.325 & 7.0411937262732 & 28.3 \tabularnewline
3 & 114.975 & 6.70089885422437 & 24.4 \tabularnewline
4 & 120.591666666667 & 7.90873605961193 & 22.9 \tabularnewline
5 & 122.95 & 8.20315903672592 & 23.6 \tabularnewline
6 & 127.975 & 8.38918405394167 & 27.6 \tabularnewline
7 & 134.316666666667 & 8.21692635891784 & 30.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32414&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]104.041666666667[/C][C]7.1833720029895[/C][C]26.3[/C][/ROW]
[ROW][C]2[/C][C]111.325[/C][C]7.0411937262732[/C][C]28.3[/C][/ROW]
[ROW][C]3[/C][C]114.975[/C][C]6.70089885422437[/C][C]24.4[/C][/ROW]
[ROW][C]4[/C][C]120.591666666667[/C][C]7.90873605961193[/C][C]22.9[/C][/ROW]
[ROW][C]5[/C][C]122.95[/C][C]8.20315903672592[/C][C]23.6[/C][/ROW]
[ROW][C]6[/C][C]127.975[/C][C]8.38918405394167[/C][C]27.6[/C][/ROW]
[ROW][C]7[/C][C]134.316666666667[/C][C]8.21692635891784[/C][C]30.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32414&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
1104.0416666666677.183372002989526.3
2111.3257.041193726273228.3
3114.9756.7008988542243724.4
4120.5916666666677.9087360596119322.9
5122.958.2031590367259223.6
6127.9758.3891840539416727.6
7134.3166666666678.2169263589178430.3






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.34796696174689
beta0.0528689584841166
S.D.0.0174999394239476
T-STAT3.02109379943159
p-value0.0293795128555390

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.34796696174689 \tabularnewline
beta & 0.0528689584841166 \tabularnewline
S.D. & 0.0174999394239476 \tabularnewline
T-STAT & 3.02109379943159 \tabularnewline
p-value & 0.0293795128555390 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32414&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.34796696174689[/C][/ROW]
[ROW][C]beta[/C][C]0.0528689584841166[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0174999394239476[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.02109379943159[/C][/ROW]
[ROW][C]p-value[/C][C]0.0293795128555390[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32414&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32414&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)
alpha1.34796696174689
beta0.0528689584841166
S.D.0.0174999394239476
T-STAT3.02109379943159
p-value0.0293795128555390






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.87000219921343
beta0.816584403336966
S.D.0.283685382574773
T-STAT2.87848600419774
p-value0.0346492990701266
Lambda0.183415596663034

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.87000219921343 \tabularnewline
beta & 0.816584403336966 \tabularnewline
S.D. & 0.283685382574773 \tabularnewline
T-STAT & 2.87848600419774 \tabularnewline
p-value & 0.0346492990701266 \tabularnewline
Lambda & 0.183415596663034 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32414&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.87000219921343[/C][/ROW]
[ROW][C]beta[/C][C]0.816584403336966[/C][/ROW]
[ROW][C]S.D.[/C][C]0.283685382574773[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.87848600419774[/C][/ROW]
[ROW][C]p-value[/C][C]0.0346492990701266[/C][/ROW]
[ROW][C]Lambda[/C][C]0.183415596663034[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32414&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32414&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-1.87000219921343
beta0.816584403336966
S.D.0.283685382574773
T-STAT2.87848600419774
p-value0.0346492990701266
Lambda0.183415596663034


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')