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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 computationFri, 09 May 2008 06:19:21 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/09/t1210335617tsdjar75yipl9dc.htm/, Retrieved Tue, 14 May 2024 17:28:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12144, Retrieved Tue, 14 May 2024 17:28:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205

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...] [2008-05-09 12:19:21] [3c8131ba61d1cf691c39623fabb076c5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3722.7
3707.1
3697.4
3691.4
3679.4
3660.6
3647.5
3639
3623.5
3612.2
3604.2
3596.9
3603.9
3606.9
3607.7
3611.4
3611.9
3618.4
3629.5
3640.6
3646.8
3647.3
3649.5
3649.7
3652.5
3665.8
3674.3
3705.8
3735.8
3735.4
3747.7
3765.5
3779.7
3795.5
3813.1
3826.9
3833.3
3844.8
3851.3
3851.8
3854.1
3858.4
3861.6
3856.3
3855.8
3860.4
3855.1
3839.5
3833
3833.6
3826.8
3818.2
3811.4
3806.8
3810.3
3818.2
3858.7
3868.7
3872.6
3872.4
3876.4
3883.2
3883.4
3881.8
3887.1
3893.3
3902.8
3914.7
3929.8
3947.3
3971.8
3991.3
3993
3997.2
4016.2
4041.7
4060.5
4076.7
4102.7
4125.8
4140.1
4146.7
4157.9
4154.7
4145.3
4149
4142.4
4141
4146.1
4147.6
4142.7
4148.1
4159
4167
4178.5
4192.5
4209.2
4223.7
4231.6
4236.9
4253
4270.5
4285.7
4302.8
4321.5
4340.3
4356.5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12144&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]1 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=12144&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12144&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13656.82542.7463581649202125.800000000000
23626.9666666666718.762405996776645.7999999999997
33741.557.9348536955714174.4
43851.866666666678.5744157853818528.2999999999997
53835.8916666666725.406386395884165.7999999999997
63913.57538.4780013892236114.9
74084.4333333333362.114108093431164.900000000000
84154.9333333333316.337816329737651.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3656.825 & 42.7463581649202 & 125.800000000000 \tabularnewline
2 & 3626.96666666667 & 18.7624059967766 & 45.7999999999997 \tabularnewline
3 & 3741.5 & 57.9348536955714 & 174.4 \tabularnewline
4 & 3851.86666666667 & 8.57441578538185 & 28.2999999999997 \tabularnewline
5 & 3835.89166666667 & 25.4063863958841 & 65.7999999999997 \tabularnewline
6 & 3913.575 & 38.4780013892236 & 114.9 \tabularnewline
7 & 4084.43333333333 & 62.114108093431 & 164.900000000000 \tabularnewline
8 & 4154.93333333333 & 16.3378163297376 & 51.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12144&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]3656.825[/C][C]42.7463581649202[/C][C]125.800000000000[/C][/ROW]
[ROW][C]2[/C][C]3626.96666666667[/C][C]18.7624059967766[/C][C]45.7999999999997[/C][/ROW]
[ROW][C]3[/C][C]3741.5[/C][C]57.9348536955714[/C][C]174.4[/C][/ROW]
[ROW][C]4[/C][C]3851.86666666667[/C][C]8.57441578538185[/C][C]28.2999999999997[/C][/ROW]
[ROW][C]5[/C][C]3835.89166666667[/C][C]25.4063863958841[/C][C]65.7999999999997[/C][/ROW]
[ROW][C]6[/C][C]3913.575[/C][C]38.4780013892236[/C][C]114.9[/C][/ROW]
[ROW][C]7[/C][C]4084.43333333333[/C][C]62.114108093431[/C][C]164.900000000000[/C][/ROW]
[ROW][C]8[/C][C]4154.93333333333[/C][C]16.3378163297376[/C][C]51.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12144&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12144&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
13656.82542.7463581649202125.800000000000
23626.9666666666718.762405996776645.7999999999997
33741.557.9348536955714174.4
43851.866666666678.5744157853818528.2999999999997
53835.8916666666725.406386395884165.7999999999997
63913.57538.4780013892236114.9
74084.4333333333362.114108093431164.900000000000
84154.9333333333316.337816329737651.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha23.1792876288257
beta0.00275124952204368
S.D.0.0425587595315636
T-STAT0.0646459049165477
p-value0.95055596035154

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 23.1792876288257 \tabularnewline
beta & 0.00275124952204368 \tabularnewline
S.D. & 0.0425587595315636 \tabularnewline
T-STAT & 0.0646459049165477 \tabularnewline
p-value & 0.95055596035154 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12144&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]23.1792876288257[/C][/ROW]
[ROW][C]beta[/C][C]0.00275124952204368[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0425587595315636[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.0646459049165477[/C][/ROW]
[ROW][C]p-value[/C][C]0.95055596035154[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12144&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12144&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)
alpha23.1792876288257
beta0.00275124952204368
S.D.0.0425587595315636
T-STAT0.0646459049165477
p-value0.95055596035154






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha7.16667721888393
beta-0.463711195024559
S.D.5.75543762373677
T-STAT-0.0805692330175043
p-value0.938404759300929
Lambda1.46371119502456

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.16667721888393 \tabularnewline
beta & -0.463711195024559 \tabularnewline
S.D. & 5.75543762373677 \tabularnewline
T-STAT & -0.0805692330175043 \tabularnewline
p-value & 0.938404759300929 \tabularnewline
Lambda & 1.46371119502456 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12144&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.16667721888393[/C][/ROW]
[ROW][C]beta[/C][C]-0.463711195024559[/C][/ROW]
[ROW][C]S.D.[/C][C]5.75543762373677[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0805692330175043[/C][/ROW]
[ROW][C]p-value[/C][C]0.938404759300929[/C][/ROW]
[ROW][C]Lambda[/C][C]1.46371119502456[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12144&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12144&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)
alpha7.16667721888393
beta-0.463711195024559
S.D.5.75543762373677
T-STAT-0.0805692330175043
p-value0.938404759300929
Lambda1.46371119502456


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')