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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 10:48:16 +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/t1482313841qxdr060bt5o6rsu.htm/, Retrieved Mon, 06 May 2024 20:42:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301952, Retrieved Mon, 06 May 2024 20:42:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact48

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 09:48:16] [d4ebbcc95b180bc93fc42d05f31a3dde] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3705.4
3726
3692
3721.6
3681
3684.6
3730.6
3759.4
3782.8
3806
3805
3738.2
3770.2
3816.6
3843
3908.2
3956.6
3947.2
3902.6
3998.6
3914.4
3910.2
3844.6
3865.6
3792
3798.2
3769
3768.8
3769.4
3757
3763.4
3764.2
3776.6
3839.6
3882.8
3889
3708.8
3742.6
3636
3615.8
3596.4
3623.6
3582
3541.8
3544.8
3565.8
3573.6
3624.8
3640.6
3749.6
3747.4
3716
3753.2
3794.2
3734
3810.6
3802.8
3796.4
3840.6
3855.8
3861.6
3862.4
3909.2
3935.8
3986.6
4003
4011.2
4020.8
4004.2
4023
4040.8
4089.2
4116.2
4109.6
4192
4233.2
4201.4
4248.8
4270
4269.4
4242
4289.6
4249.6
4252.2
4285
4291.8
4308.8
4274
4348.4
4292.4
4325.4
4409.2
4485.2
4491.8
4491.2
4489.4
4402.4
4392.6
4332
4383.6
4373.8
4403.8
4368
4372
4447.6
4454.6
4397.8
4377.2
4420.6
4446.6
4451.8
4496
4494.8
4505.8
4501.2
4554.6

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=301952&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=301952&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301952&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
13736.0543.9828995695538125
23889.8166666666764.3848349356972228.4
33797.546.9291535673238132
4361361.4222938501826200.8
53770.159.1747796401013215.2
63978.9833333333371.3943954170752227.6
74222.8333333333358.1388828321434180
84374.3833333333392.0164593313543217.8
94392.1166666666733.6940737528221122.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3736.05 & 43.9828995695538 & 125 \tabularnewline
2 & 3889.81666666667 & 64.3848349356972 & 228.4 \tabularnewline
3 & 3797.5 & 46.9291535673238 & 132 \tabularnewline
4 & 3613 & 61.4222938501826 & 200.8 \tabularnewline
5 & 3770.1 & 59.1747796401013 & 215.2 \tabularnewline
6 & 3978.98333333333 & 71.3943954170752 & 227.6 \tabularnewline
7 & 4222.83333333333 & 58.1388828321434 & 180 \tabularnewline
8 & 4374.38333333333 & 92.0164593313543 & 217.8 \tabularnewline
9 & 4392.11666666667 & 33.6940737528221 & 122.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301952&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]3736.05[/C][C]43.9828995695538[/C][C]125[/C][/ROW]
[ROW][C]2[/C][C]3889.81666666667[/C][C]64.3848349356972[/C][C]228.4[/C][/ROW]
[ROW][C]3[/C][C]3797.5[/C][C]46.9291535673238[/C][C]132[/C][/ROW]
[ROW][C]4[/C][C]3613[/C][C]61.4222938501826[/C][C]200.8[/C][/ROW]
[ROW][C]5[/C][C]3770.1[/C][C]59.1747796401013[/C][C]215.2[/C][/ROW]
[ROW][C]6[/C][C]3978.98333333333[/C][C]71.3943954170752[/C][C]227.6[/C][/ROW]
[ROW][C]7[/C][C]4222.83333333333[/C][C]58.1388828321434[/C][C]180[/C][/ROW]
[ROW][C]8[/C][C]4374.38333333333[/C][C]92.0164593313543[/C][C]217.8[/C][/ROW]
[ROW][C]9[/C][C]4392.11666666667[/C][C]33.6940737528221[/C][C]122.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301952&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301952&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
13736.0543.9828995695538125
23889.8166666666764.3848349356972228.4
33797.546.9291535673238132
4361361.4222938501826200.8
53770.159.1747796401013215.2
63978.9833333333371.3943954170752227.6
74222.8333333333358.1388828321434180
84374.3833333333392.0164593313543217.8
94392.1166666666733.6940737528221122.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha18.1397369499777
beta0.010283224832383
S.D.0.0218613373976268
T-STAT0.470384068702919
p-value0.652384302611477

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 18.1397369499777 \tabularnewline
beta & 0.010283224832383 \tabularnewline
S.D. & 0.0218613373976268 \tabularnewline
T-STAT & 0.470384068702919 \tabularnewline
p-value & 0.652384302611477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301952&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]18.1397369499777[/C][/ROW]
[ROW][C]beta[/C][C]0.010283224832383[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0218613373976268[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.470384068702919[/C][/ROW]
[ROW][C]p-value[/C][C]0.652384302611477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301952&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301952&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)
alpha18.1397369499777
beta0.010283224832383
S.D.0.0218613373976268
T-STAT0.470384068702919
p-value0.652384302611477






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.43384566990632
beta0.193931317473725
S.D.1.54062587163069
T-STAT0.125878268724942
p-value0.903367427778134
Lambda0.806068682526275

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.43384566990632 \tabularnewline
beta & 0.193931317473725 \tabularnewline
S.D. & 1.54062587163069 \tabularnewline
T-STAT & 0.125878268724942 \tabularnewline
p-value & 0.903367427778134 \tabularnewline
Lambda & 0.806068682526275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301952&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.43384566990632[/C][/ROW]
[ROW][C]beta[/C][C]0.193931317473725[/C][/ROW]
[ROW][C]S.D.[/C][C]1.54062587163069[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.125878268724942[/C][/ROW]
[ROW][C]p-value[/C][C]0.903367427778134[/C][/ROW]
[ROW][C]Lambda[/C][C]0.806068682526275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301952&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301952&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)
alpha2.43384566990632
beta0.193931317473725
S.D.1.54062587163069
T-STAT0.125878268724942
p-value0.903367427778134
Lambda0.806068682526275


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')