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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 computationWed, 12 Dec 2007 12:57:56 -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/Dec/12/t119748862359aych47c2xgv7s.htm/, Retrieved Thu, 02 May 2024 14:43:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3266, Retrieved Thu, 02 May 2024 14:43:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact217

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...] [2007-11-28 15:52:16] [aa0d06577c57214974bc715dada29347]
-    D  [Standard Deviation-Mean Plot] [Tijdreeks 1: indu...] [2007-12-12 19:34:29] [74be16979710d4c4e7c6647856088456]
-    D      [Standard Deviation-Mean Plot] [Tijdreeks 2: omze...] [2007-12-12 19:57:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
106,0
100,9
114,3
101,2
109,2
111,6
91,7
93,7
105,7
109,5
105,3
102,8
100,6
97,6
110,3
107,2
107,2
108,1
97,1
92,2
112,2
111,6
115,7
111,3
104,2
103,2
112,7
106,4
102,6
110,6
95,2
89,0
112,5
116,8
107,2
113,6
101,8
102,6
122,7
110,3
110,5
121,6
100,3
100,7
123,4
127,1
124,1
131,2
111,6
114,2
130,1
125,9
119,0
133,8
107,5
113,5
134,4
126,8
135,6
139,9
129,8
131,0
153,1
134,1
144,1
155,9
123,3
128,1
144,3
153,0
149,9
150,9
141,0
138,9
157,4
142,9
151,7
161,0
138,6
136,0
151,9

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 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=3266&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]3 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=3266&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3266&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1104.3256.7737628860452213.7
2105.9257.3054307321210218.1
3106.1666666666678.046719640306666.5
4114.69166666666711.500391956429830
5124.35833333333310.854363038414437.3
6141.45833333333311.522188738834947.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 104.325 & 6.77376288604522 & 13.7 \tabularnewline
2 & 105.925 & 7.30543073212102 & 18.1 \tabularnewline
3 & 106.166666666667 & 8.04671964030666 & 6.5 \tabularnewline
4 & 114.691666666667 & 11.5003919564298 & 30 \tabularnewline
5 & 124.358333333333 & 10.8543630384144 & 37.3 \tabularnewline
6 & 141.458333333333 & 11.5221887388349 & 47.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3266&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]104.325[/C][C]6.77376288604522[/C][C]13.7[/C][/ROW]
[ROW][C]2[/C][C]105.925[/C][C]7.30543073212102[/C][C]18.1[/C][/ROW]
[ROW][C]3[/C][C]106.166666666667[/C][C]8.04671964030666[/C][C]6.5[/C][/ROW]
[ROW][C]4[/C][C]114.691666666667[/C][C]11.5003919564298[/C][C]30[/C][/ROW]
[ROW][C]5[/C][C]124.358333333333[/C][C]10.8543630384144[/C][C]37.3[/C][/ROW]
[ROW][C]6[/C][C]141.458333333333[/C][C]11.5221887388349[/C][C]47.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3266&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3266&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
1104.3256.7737628860452213.7
2105.9257.3054307321210218.1
3106.1666666666678.046719640306666.5
4114.69166666666711.500391956429830
5124.35833333333310.854363038414437.3
6141.45833333333311.522188738834947.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.83394538617932
beta0.121973712105647
S.D.0.0447359455326736
T-STAT2.72652585417159
p-value0.0526311921994315

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.83394538617932 \tabularnewline
beta & 0.121973712105647 \tabularnewline
S.D. & 0.0447359455326736 \tabularnewline
T-STAT & 2.72652585417159 \tabularnewline
p-value & 0.0526311921994315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3266&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.83394538617932[/C][/ROW]
[ROW][C]beta[/C][C]0.121973712105647[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0447359455326736[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.72652585417159[/C][/ROW]
[ROW][C]p-value[/C][C]0.0526311921994315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3266&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3266&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-4.83394538617932
beta0.121973712105647
S.D.0.0447359455326736
T-STAT2.72652585417159
p-value0.0526311921994315






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.66455642852636
beta1.65816320292111
S.D.0.577230422371016
T-STAT2.87261921523486
p-value0.0453487879205228
Lambda-0.658163202921111

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.66455642852636 \tabularnewline
beta & 1.65816320292111 \tabularnewline
S.D. & 0.577230422371016 \tabularnewline
T-STAT & 2.87261921523486 \tabularnewline
p-value & 0.0453487879205228 \tabularnewline
Lambda & -0.658163202921111 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3266&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.66455642852636[/C][/ROW]
[ROW][C]beta[/C][C]1.65816320292111[/C][/ROW]
[ROW][C]S.D.[/C][C]0.577230422371016[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.87261921523486[/C][/ROW]
[ROW][C]p-value[/C][C]0.0453487879205228[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.658163202921111[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3266&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3266&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-5.66455642852636
beta1.65816320292111
S.D.0.577230422371016
T-STAT2.87261921523486
p-value0.0453487879205228
Lambda-0.658163202921111


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')