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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 computationTue, 21 Dec 2010 15:26:28 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/21/t1292945077l2oljca3okmpc6p.htm/, Retrieved Tue, 07 May 2024 19:57:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113673, Retrieved Tue, 07 May 2024 19:57:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140

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] [web server] [2010-10-19 15:51:23] [b98453cac15ba1066b407e146608df68]
- RMP   [Variance Reduction Matrix] [Pageviews] [2010-11-29 10:12:20] [b98453cac15ba1066b407e146608df68]
- RM      [Standard Deviation-Mean Plot] [Pageviews] [2010-11-29 11:10:57] [b98453cac15ba1066b407e146608df68]
-   PD        [Standard Deviation-Mean Plot] [SMP olieproductie MT] [2010-12-21 15:26:28] [8f110cf3e3846d42560df9b5835185a6] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
78.33
78.21
78.94
77.94
77.31
75.75
77.73
77.90
77.45
77.46
77.97
77.23
76.56
76.70
76.51
76.03
76.69
76.38
76.80
76.63
77.17
78.63
78.89
76.94
77.50
79.27
79.77
78.62
78.60
77.88
78.71
79.27
80.12
81.12
81.48
82.81
82.39
82.41
82.20
81.99
81.61
83.51
84.05
82.99
83.54
84.44
84.24
83.88
84.17
84.59
84.76
85.14
85.22
84.77
84.50
84.56
83.79
83.96
84.80
84.89
84.78
84.80
84.44
84.65
84.22
84.08
85.29
85.00
84.63
84.92
84.61
84.50
84.29
84.50
84.41
84.71
84.21
83.86
84.40
83.71
84.42
85.26
85.08
85.65
85.74
85.89
86.08
85.49
85.97
85.84
86.72
85.42
83.87
85.45
85.35
84.27
83.13
83.79
83.70
83.76
83.47
83.78
84.83
84.43
84.90
85.36
85.49
85.29

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113673&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113673&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113673&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
177.74428571428571.016035713658023.19
277.32428571428570.5424284021219491.41000000000000
376.60142857142860.3547970580218391.14
478.51714285714290.9849486329366662.83
579.59714285714291.352438714393553.60000000000001
682.41714285714290.6097189047890391.90000000000001
783.90142857142860.4934041133266111.45000000000000
884.79142857142860.2845129505797910.719999999999999
984.49428571428570.4489935835791391.09999999999999
1084.68428571428570.429529088764941.21000000000001
1184.46142857142860.1742056802966500.5
1284.62571428571430.727549703751281.94000000000001
1385.96142857142860.3831200234664761.23000000000000
1484.46857142857140.9394400561225922.32000000000001
1584.12428571428570.5848890818738531.43000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 77.7442857142857 & 1.01603571365802 & 3.19 \tabularnewline
2 & 77.3242857142857 & 0.542428402121949 & 1.41000000000000 \tabularnewline
3 & 76.6014285714286 & 0.354797058021839 & 1.14 \tabularnewline
4 & 78.5171428571429 & 0.984948632936666 & 2.83 \tabularnewline
5 & 79.5971428571429 & 1.35243871439355 & 3.60000000000001 \tabularnewline
6 & 82.4171428571429 & 0.609718904789039 & 1.90000000000001 \tabularnewline
7 & 83.9014285714286 & 0.493404113326611 & 1.45000000000000 \tabularnewline
8 & 84.7914285714286 & 0.284512950579791 & 0.719999999999999 \tabularnewline
9 & 84.4942857142857 & 0.448993583579139 & 1.09999999999999 \tabularnewline
10 & 84.6842857142857 & 0.42952908876494 & 1.21000000000001 \tabularnewline
11 & 84.4614285714286 & 0.174205680296650 & 0.5 \tabularnewline
12 & 84.6257142857143 & 0.72754970375128 & 1.94000000000001 \tabularnewline
13 & 85.9614285714286 & 0.383120023466476 & 1.23000000000000 \tabularnewline
14 & 84.4685714285714 & 0.939440056122592 & 2.32000000000001 \tabularnewline
15 & 84.1242857142857 & 0.584889081873853 & 1.43000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113673&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]77.7442857142857[/C][C]1.01603571365802[/C][C]3.19[/C][/ROW]
[ROW][C]2[/C][C]77.3242857142857[/C][C]0.542428402121949[/C][C]1.41000000000000[/C][/ROW]
[ROW][C]3[/C][C]76.6014285714286[/C][C]0.354797058021839[/C][C]1.14[/C][/ROW]
[ROW][C]4[/C][C]78.5171428571429[/C][C]0.984948632936666[/C][C]2.83[/C][/ROW]
[ROW][C]5[/C][C]79.5971428571429[/C][C]1.35243871439355[/C][C]3.60000000000001[/C][/ROW]
[ROW][C]6[/C][C]82.4171428571429[/C][C]0.609718904789039[/C][C]1.90000000000001[/C][/ROW]
[ROW][C]7[/C][C]83.9014285714286[/C][C]0.493404113326611[/C][C]1.45000000000000[/C][/ROW]
[ROW][C]8[/C][C]84.7914285714286[/C][C]0.284512950579791[/C][C]0.719999999999999[/C][/ROW]
[ROW][C]9[/C][C]84.4942857142857[/C][C]0.448993583579139[/C][C]1.09999999999999[/C][/ROW]
[ROW][C]10[/C][C]84.6842857142857[/C][C]0.42952908876494[/C][C]1.21000000000001[/C][/ROW]
[ROW][C]11[/C][C]84.4614285714286[/C][C]0.174205680296650[/C][C]0.5[/C][/ROW]
[ROW][C]12[/C][C]84.6257142857143[/C][C]0.72754970375128[/C][C]1.94000000000001[/C][/ROW]
[ROW][C]13[/C][C]85.9614285714286[/C][C]0.383120023466476[/C][C]1.23000000000000[/C][/ROW]
[ROW][C]14[/C][C]84.4685714285714[/C][C]0.939440056122592[/C][C]2.32000000000001[/C][/ROW]
[ROW][C]15[/C][C]84.1242857142857[/C][C]0.584889081873853[/C][C]1.43000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113673&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113673&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
177.74428571428571.016035713658023.19
277.32428571428570.5424284021219491.41000000000000
376.60142857142860.3547970580218391.14
478.51714285714290.9849486329366662.83
579.59714285714291.352438714393553.60000000000001
682.41714285714290.6097189047890391.90000000000001
783.90142857142860.4934041133266111.45000000000000
884.79142857142860.2845129505797910.719999999999999
984.49428571428570.4489935835791391.09999999999999
1084.68428571428570.429529088764941.21000000000001
1184.46142857142860.1742056802966500.5
1284.62571428571430.727549703751281.94000000000001
1385.96142857142860.3831200234664761.23000000000000
1484.46857142857140.9394400561225922.32000000000001
1584.12428571428570.5848890818738531.43000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.95131637863424
beta-0.0404824152157039
S.D.0.0249854417115045
T-STAT-1.62024012555535
p-value0.129173026840641

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.95131637863424 \tabularnewline
beta & -0.0404824152157039 \tabularnewline
S.D. & 0.0249854417115045 \tabularnewline
T-STAT & -1.62024012555535 \tabularnewline
p-value & 0.129173026840641 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113673&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.95131637863424[/C][/ROW]
[ROW][C]beta[/C][C]-0.0404824152157039[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0249854417115045[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.62024012555535[/C][/ROW]
[ROW][C]p-value[/C][C]0.129173026840641[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113673&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113673&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)
alpha3.95131637863424
beta-0.0404824152157039
S.D.0.0249854417115045
T-STAT-1.62024012555535
p-value0.129173026840641






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha21.9138386484838
beta-5.10746455892525
S.D.3.43317605572951
T-STAT-1.48767918569209
p-value0.160685796012814
Lambda6.10746455892525

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 21.9138386484838 \tabularnewline
beta & -5.10746455892525 \tabularnewline
S.D. & 3.43317605572951 \tabularnewline
T-STAT & -1.48767918569209 \tabularnewline
p-value & 0.160685796012814 \tabularnewline
Lambda & 6.10746455892525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113673&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]21.9138386484838[/C][/ROW]
[ROW][C]beta[/C][C]-5.10746455892525[/C][/ROW]
[ROW][C]S.D.[/C][C]3.43317605572951[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.48767918569209[/C][/ROW]
[ROW][C]p-value[/C][C]0.160685796012814[/C][/ROW]
[ROW][C]Lambda[/C][C]6.10746455892525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113673&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113673&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)
alpha21.9138386484838
beta-5.10746455892525
S.D.3.43317605572951
T-STAT-1.48767918569209
p-value0.160685796012814
Lambda6.10746455892525


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 <- 7
(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')