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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, 23 Nov 2007 05:49:02 -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/2007/Nov/23/t1195821637ptkidku95gi8g0p.htm/, Retrieved Mon, 29 Apr 2024 02:19:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6153, Retrieved Mon, 29 Apr 2024 02:19:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact210

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] [] [2007-11-23 12:49:02] [22d719c250b0837edaa2d173fd414084] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105,3
103
103,8
103,4
105,8
101,4
97
94,3
96,6
97,1
95,7
96,9
97,4
95,3
93,6
91,5
93,1
91,7
94,3
93,9
90,9
88,3
91,3
91,7
92,4
92
95,6
95,8
96,4
99
107
109,7
116,2
115,9
113,8
112,6
113,7
115,9
110,3
111,3
113,4
108,2
104,8
106
110,9
115
118,4
121,4
128,8
131,7
141,7
142,9
139,4
134,7
125
113,6
111,5
108,5
112,3
116,6
115,5
120,1
132,9
128,1
129,3
132,5
131
124,9
120,8
122
122,1
127,4
135,2
137,3
135
136
138,4
134,7
138,4
133,9
133,6
141,2
151,8
155,4
156,6
161,6
160,7
156
159,5
168,7
169,9
169,9
185,9

Tables (Output of Computation)





Summary of compuational 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 compuational 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=6153&T=0

[TABLE]
[ROW][C]Summary of compuational 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=6153&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6153&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 compuational 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
1100.0254.1367806982549313.4
292.752.370078633141265.40000000000001
3103.8666666666679.538661363423122.6
4112.4416666666674.8888478533631429.9
5125.55833333333312.694484008514349.8
6125.555.5120529091008641.2
7139.2416666666677.0944867625672961.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100.025 & 4.13678069825493 & 13.4 \tabularnewline
2 & 92.75 & 2.37007863314126 & 5.40000000000001 \tabularnewline
3 & 103.866666666667 & 9.5386613634231 & 22.6 \tabularnewline
4 & 112.441666666667 & 4.88884785336314 & 29.9 \tabularnewline
5 & 125.558333333333 & 12.6944840085143 & 49.8 \tabularnewline
6 & 125.55 & 5.51205290910086 & 41.2 \tabularnewline
7 & 139.241666666667 & 7.09448676256729 & 61.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6153&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]100.025[/C][C]4.13678069825493[/C][C]13.4[/C][/ROW]
[ROW][C]2[/C][C]92.75[/C][C]2.37007863314126[/C][C]5.40000000000001[/C][/ROW]
[ROW][C]3[/C][C]103.866666666667[/C][C]9.5386613634231[/C][C]22.6[/C][/ROW]
[ROW][C]4[/C][C]112.441666666667[/C][C]4.88884785336314[/C][C]29.9[/C][/ROW]
[ROW][C]5[/C][C]125.558333333333[/C][C]12.6944840085143[/C][C]49.8[/C][/ROW]
[ROW][C]6[/C][C]125.55[/C][C]5.51205290910086[/C][C]41.2[/C][/ROW]
[ROW][C]7[/C][C]139.241666666667[/C][C]7.09448676256729[/C][C]61.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6153&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6153&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
1100.0254.1367806982549313.4
292.752.370078633141265.40000000000001
3103.8666666666679.538661363423122.6
4112.4416666666674.8888478533631429.9
5125.55833333333312.694484008514349.8
6125.555.5120529091008641.2
7139.2416666666677.0944867625672961.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.95101582383727
beta0.101187303083716
S.D.0.0830768256869849
T-STAT1.21799674273747
p-value0.277560579742320

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.95101582383727 \tabularnewline
beta & 0.101187303083716 \tabularnewline
S.D. & 0.0830768256869849 \tabularnewline
T-STAT & 1.21799674273747 \tabularnewline
p-value & 0.277560579742320 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6153&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.95101582383727[/C][/ROW]
[ROW][C]beta[/C][C]0.101187303083716[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0830768256869849[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.21799674273747[/C][/ROW]
[ROW][C]p-value[/C][C]0.277560579742320[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6153&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6153&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-4.95101582383727
beta0.101187303083716
S.D.0.0830768256869849
T-STAT1.21799674273747
p-value0.277560579742320






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-9.28120846750714
beta2.33519830650304
S.D.1.35098907435019
T-STAT1.72851013441855
p-value0.144468600907869
Lambda-1.33519830650304

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -9.28120846750714 \tabularnewline
beta & 2.33519830650304 \tabularnewline
S.D. & 1.35098907435019 \tabularnewline
T-STAT & 1.72851013441855 \tabularnewline
p-value & 0.144468600907869 \tabularnewline
Lambda & -1.33519830650304 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6153&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-9.28120846750714[/C][/ROW]
[ROW][C]beta[/C][C]2.33519830650304[/C][/ROW]
[ROW][C]S.D.[/C][C]1.35098907435019[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.72851013441855[/C][/ROW]
[ROW][C]p-value[/C][C]0.144468600907869[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.33519830650304[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6153&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6153&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-9.28120846750714
beta2.33519830650304
S.D.1.35098907435019
T-STAT1.72851013441855
p-value0.144468600907869
Lambda-1.33519830650304


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')