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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, 07 Dec 2016 19:13:09 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/07/t1481134430oda8ss1xjmgzt38.htm/, Retrieved Tue, 07 May 2024 09:13:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298274, Retrieved Tue, 07 May 2024 09:13:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact39

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] [N1316] [2016-12-07 18:13:09] [85f5800284aab30c091766186b093bb4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4440
4835
4055
3645
3425
3350
3670
5130
5930
6185
6240
5790
5475
5561.65
8031.65
8961.65
8045
7588.35
8200
7290
6661.65
6385
6268.35
6248.35
6165
6196.65
6050
5705
5530
5311.65
5145
4855
4556.65
4356.65
3823.35
3570
3735
4191.65
3990
3705
4065
3766.65
3666.65
3681.65
3931.65
4268.35
4291.65
4530
5053.35
4996.65
4913.35
4935
4848.35
4788.35
4771.65
4643.35
4778
4983.35
4953.35
5581.65
5185
5746.65
4240
4095

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298274&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298274&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298274&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14724.583333333331111.075356116632890
27059.720833333331120.848912139683486.65
35105.4125890.1133263204082626.65
43985.27083333333286.874327456794863.35
54937.2234.415161043975938.299999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4724.58333333333 & 1111.07535611663 & 2890 \tabularnewline
2 & 7059.72083333333 & 1120.84891213968 & 3486.65 \tabularnewline
3 & 5105.4125 & 890.113326320408 & 2626.65 \tabularnewline
4 & 3985.27083333333 & 286.874327456794 & 863.35 \tabularnewline
5 & 4937.2 & 234.415161043975 & 938.299999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298274&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]4724.58333333333[/C][C]1111.07535611663[/C][C]2890[/C][/ROW]
[ROW][C]2[/C][C]7059.72083333333[/C][C]1120.84891213968[/C][C]3486.65[/C][/ROW]
[ROW][C]3[/C][C]5105.4125[/C][C]890.113326320408[/C][C]2626.65[/C][/ROW]
[ROW][C]4[/C][C]3985.27083333333[/C][C]286.874327456794[/C][C]863.35[/C][/ROW]
[ROW][C]5[/C][C]4937.2[/C][C]234.415161043975[/C][C]938.299999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298274&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298274&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
14724.583333333331111.075356116632890
27059.720833333331120.848912139683486.65
35105.4125890.1133263204082626.65
43985.27083333333286.874327456794863.35
54937.2234.415161043975938.299999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-454.420110281439
beta0.229171883804295
S.D.0.176852532067204
T-STAT1.29583603426843
p-value0.285722833401155

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -454.420110281439 \tabularnewline
beta & 0.229171883804295 \tabularnewline
S.D. & 0.176852532067204 \tabularnewline
T-STAT & 1.29583603426843 \tabularnewline
p-value & 0.285722833401155 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298274&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-454.420110281439[/C][/ROW]
[ROW][C]beta[/C][C]0.229171883804295[/C][/ROW]
[ROW][C]S.D.[/C][C]0.176852532067204[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.29583603426843[/C][/ROW]
[ROW][C]p-value[/C][C]0.285722833401155[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298274&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298274&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-454.420110281439
beta0.229171883804295
S.D.0.176852532067204
T-STAT1.29583603426843
p-value0.285722833401155






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-11.7646691610602
beta2.1278710652619
S.D.1.73699014233016
T-STAT1.22503347221498
p-value0.307973734299703
Lambda-1.1278710652619

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.7646691610602 \tabularnewline
beta & 2.1278710652619 \tabularnewline
S.D. & 1.73699014233016 \tabularnewline
T-STAT & 1.22503347221498 \tabularnewline
p-value & 0.307973734299703 \tabularnewline
Lambda & -1.1278710652619 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298274&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.7646691610602[/C][/ROW]
[ROW][C]beta[/C][C]2.1278710652619[/C][/ROW]
[ROW][C]S.D.[/C][C]1.73699014233016[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.22503347221498[/C][/ROW]
[ROW][C]p-value[/C][C]0.307973734299703[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.1278710652619[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298274&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298274&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-11.7646691610602
beta2.1278710652619
S.D.1.73699014233016
T-STAT1.22503347221498
p-value0.307973734299703
Lambda-1.1278710652619


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = -1.0 ; par2 = 1 ; par3 = 0 ; par4 = 1 ;
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')