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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, 21 Dec 2016 16:05:35 +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/21/t14823328440qed18ade08emat.htm/, Retrieved Fri, 01 Nov 2024 03:30:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302367, Retrieved Fri, 01 Nov 2024 03:30:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97

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...] [2016-12-21 15:05:35] [6f830dc7e8de22be3233942ffbe3aaba] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4526.1
4616.8
4558
4736.8
4771.1
4611.3
4687.1
4718.3
4731.6
4755.4
4849.8
4697.8
4720.2
4741.1
4794.2
4807.4
4836.9
4853
4902.9
4938
4910.4
4954.6
4937.3
5003.8
5005.6
4984.4
5050
5017.7
4984.8
5036.3
5093.6
5111.2
5090.7
5063.7
5007.5
5122.5
5172.3
5232.8
5183.3
5204.6
5255.4
5294.5
5308.9
5281.3
5413.9
5462.4
5568.7
5579.1
5590.3
5703.2
5717.7
5772.3
5876.6
6134.6
6155.6
6259.5
6180.7
6120.3
6097
6167.5
6207.1
6181.7
6196.2
6183.9
6184
6271.1
6204.9
6284.5
6293.9
6377.9
6400.2
6456.2
6372.8
6368.8
6497.8
6599.4
6696.9
6676.3
6731.7
6732.3
6760.2
6841.4
6917.5
6899.3
6972.9
6969.2
6941.6
6905.5
6971.3
6968.4
7012.2
7049.5
7095.6
7237.5
7230.5
7253.5
7289.4
7364.6
7428.1
7390.2
7279.9
7426.5
7480.1

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=302367&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=302367&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302367&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
14688.3416666666793.8991185778491323.7
24866.6588.8804355197578283.6
35047.3333333333348.8266755209101138.1
45329.76666666667142.956543513521406.8
55981.275232.137021155414669.2
66270.1333333333395.4864610425176274.5
76674.53333333333184.203466226065548.7
87050.64166666667124.538555244648348

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4688.34166666667 & 93.8991185778491 & 323.7 \tabularnewline
2 & 4866.65 & 88.8804355197578 & 283.6 \tabularnewline
3 & 5047.33333333333 & 48.8266755209101 & 138.1 \tabularnewline
4 & 5329.76666666667 & 142.956543513521 & 406.8 \tabularnewline
5 & 5981.275 & 232.137021155414 & 669.2 \tabularnewline
6 & 6270.13333333333 & 95.4864610425176 & 274.5 \tabularnewline
7 & 6674.53333333333 & 184.203466226065 & 548.7 \tabularnewline
8 & 7050.64166666667 & 124.538555244648 & 348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302367&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]4688.34166666667[/C][C]93.8991185778491[/C][C]323.7[/C][/ROW]
[ROW][C]2[/C][C]4866.65[/C][C]88.8804355197578[/C][C]283.6[/C][/ROW]
[ROW][C]3[/C][C]5047.33333333333[/C][C]48.8266755209101[/C][C]138.1[/C][/ROW]
[ROW][C]4[/C][C]5329.76666666667[/C][C]142.956543513521[/C][C]406.8[/C][/ROW]
[ROW][C]5[/C][C]5981.275[/C][C]232.137021155414[/C][C]669.2[/C][/ROW]
[ROW][C]6[/C][C]6270.13333333333[/C][C]95.4864610425176[/C][C]274.5[/C][/ROW]
[ROW][C]7[/C][C]6674.53333333333[/C][C]184.203466226065[/C][C]548.7[/C][/ROW]
[ROW][C]8[/C][C]7050.64166666667[/C][C]124.538555244648[/C][C]348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302367&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302367&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
14688.3416666666793.8991185778491323.7
24866.6588.8804355197578283.6
35047.3333333333348.8266755209101138.1
45329.76666666667142.956543513521406.8
55981.275232.137021155414669.2
66270.1333333333395.4864610425176274.5
76674.53333333333184.203466226065548.7
87050.64166666667124.538555244648348






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-57.5645669868323
beta0.0320515635159442
S.D.0.0238818359483245
T-STAT1.34208959417096
p-value0.228120989691841

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -57.5645669868323 \tabularnewline
beta & 0.0320515635159442 \tabularnewline
S.D. & 0.0238818359483245 \tabularnewline
T-STAT & 1.34208959417096 \tabularnewline
p-value & 0.228120989691841 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302367&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-57.5645669868323[/C][/ROW]
[ROW][C]beta[/C][C]0.0320515635159442[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0238818359483245[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.34208959417096[/C][/ROW]
[ROW][C]p-value[/C][C]0.228120989691841[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302367&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302367&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-57.5645669868323
beta0.0320515635159442
S.D.0.0238818359483245
T-STAT1.34208959417096
p-value0.228120989691841






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-9.87893022230084
beta1.69119281100929
S.D.1.09355938932848
T-STAT1.54650294031841
p-value0.172943698362442
Lambda-0.691192811009291

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -9.87893022230084 \tabularnewline
beta & 1.69119281100929 \tabularnewline
S.D. & 1.09355938932848 \tabularnewline
T-STAT & 1.54650294031841 \tabularnewline
p-value & 0.172943698362442 \tabularnewline
Lambda & -0.691192811009291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302367&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-9.87893022230084[/C][/ROW]
[ROW][C]beta[/C][C]1.69119281100929[/C][/ROW]
[ROW][C]S.D.[/C][C]1.09355938932848[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.54650294031841[/C][/ROW]
[ROW][C]p-value[/C][C]0.172943698362442[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.691192811009291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302367&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302367&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-9.87893022230084
beta1.69119281100929
S.D.1.09355938932848
T-STAT1.54650294031841
p-value0.172943698362442
Lambda-0.691192811009291


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')