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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 computationWed, 24 Dec 2008 05:00:00 -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/t1230120162iqy0m3h6u5hwse5.htm/, Retrieved Sun, 19 May 2024 11:16:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36496, Retrieved Sun, 19 May 2024 11:16:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185

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] [SD Mean Plot] [2008-12-24 12:00:00] [52492148dbcac26917ed19e489351f79] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
97.5
97.1
97.5
98.5
100.5
102.8
105.2
107.4
108.0
107.6
107.0
105.8
104.3
103.8
104.4
106.2
108.5
109.8
110.3
109.7
108.7
108.9
109.7
110.4
111.4
112.6
113.6
113.8
113.2
113.6
113.9
113.4
113.8
116.0
118.3
120.5
121.9
121.2
120.2
120.6
110.2
109.2
108.7
109.9
112.2
114.5
114.7
113.2
112.1
112.6
113.6
114.0
114.5
115.0
114.9
114.8
114.3
113.7
114.5
116.0
116.6
116.2
115.7
115.6
115.2
115.0
115.7
115.9
115.6
115.9
117.0
117.9
118.8
119.9

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=36496&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=36496&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36496&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
1102.9083333333334.4307722153415210.9
2107.8916666666672.504707688745466.60000000000001
3114.5083333333332.554304151225879.1
4114.7083333333335.0202242494884113.2
5114.1666666666671.067140046473703.90000000000001
6116.0250.806930209892012.90000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 102.908333333333 & 4.43077221534152 & 10.9 \tabularnewline
2 & 107.891666666667 & 2.50470768874546 & 6.60000000000001 \tabularnewline
3 & 114.508333333333 & 2.55430415122587 & 9.1 \tabularnewline
4 & 114.708333333333 & 5.02022424948841 & 13.2 \tabularnewline
5 & 114.166666666667 & 1.06714004647370 & 3.90000000000001 \tabularnewline
6 & 116.025 & 0.80693020989201 & 2.90000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36496&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]102.908333333333[/C][C]4.43077221534152[/C][C]10.9[/C][/ROW]
[ROW][C]2[/C][C]107.891666666667[/C][C]2.50470768874546[/C][C]6.60000000000001[/C][/ROW]
[ROW][C]3[/C][C]114.508333333333[/C][C]2.55430415122587[/C][C]9.1[/C][/ROW]
[ROW][C]4[/C][C]114.708333333333[/C][C]5.02022424948841[/C][C]13.2[/C][/ROW]
[ROW][C]5[/C][C]114.166666666667[/C][C]1.06714004647370[/C][C]3.90000000000001[/C][/ROW]
[ROW][C]6[/C][C]116.025[/C][C]0.80693020989201[/C][C]2.90000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36496&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36496&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
1102.9083333333334.4307722153415210.9
2107.8916666666672.504707688745466.60000000000001
3114.5083333333332.554304151225879.1
4114.7083333333335.0202242494884113.2
5114.1666666666671.067140046473703.90000000000001
6116.0250.806930209892012.90000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha19.5601267444304
beta-0.150664617079887
S.D.0.147701789670022
T-STAT-1.02005952274839
p-value0.365375051695027

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 19.5601267444304 \tabularnewline
beta & -0.150664617079887 \tabularnewline
S.D. & 0.147701789670022 \tabularnewline
T-STAT & -1.02005952274839 \tabularnewline
p-value & 0.365375051695027 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36496&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]19.5601267444304[/C][/ROW]
[ROW][C]beta[/C][C]-0.150664617079887[/C][/ROW]
[ROW][C]S.D.[/C][C]0.147701789670022[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.02005952274839[/C][/ROW]
[ROW][C]p-value[/C][C]0.365375051695027[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36496&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36496&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)
alpha19.5601267444304
beta-0.150664617079887
S.D.0.147701789670022
T-STAT-1.02005952274839
p-value0.365375051695027






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha38.8582963727406
beta-8.0716005251996
S.D.6.71145824028652
T-STAT-1.20265972553455
p-value0.295427942550506
Lambda9.0716005251996

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 38.8582963727406 \tabularnewline
beta & -8.0716005251996 \tabularnewline
S.D. & 6.71145824028652 \tabularnewline
T-STAT & -1.20265972553455 \tabularnewline
p-value & 0.295427942550506 \tabularnewline
Lambda & 9.0716005251996 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36496&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]38.8582963727406[/C][/ROW]
[ROW][C]beta[/C][C]-8.0716005251996[/C][/ROW]
[ROW][C]S.D.[/C][C]6.71145824028652[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.20265972553455[/C][/ROW]
[ROW][C]p-value[/C][C]0.295427942550506[/C][/ROW]
[ROW][C]Lambda[/C][C]9.0716005251996[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36496&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36496&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)
alpha38.8582963727406
beta-8.0716005251996
S.D.6.71145824028652
T-STAT-1.20265972553455
p-value0.295427942550506
Lambda9.0716005251996


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')