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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 computationMon, 12 Dec 2016 18:16:03 +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/12/t14815630115jjahxdiby7miuu.htm/, Retrieved Fri, 03 May 2024 20:19:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298940, Retrieved Fri, 03 May 2024 20:19:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77

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...] [2016-12-12 17:16:03] [2a4be59ea15844c348dc523b08af79fc] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6151.2
5847.6
5662.8
5807.7
5907
6036.3
5668.2
5578.5
5760.6
5918.1
6030
6242.4
6425.1
6610.8
6943.5
5316.3
4356.6
4073.1
4239.9
4401.3
4590.6
4671
4772.1
4875.3
4601.7
4482.3
4455.6
4487.7
4606.8
4727.7
4617.9
4507.8
4398.6
4334.7
4272.9
4209.6
3963.3
3717
3469.5
3587.1
3703.5
3819.6
3777
3732.9
3687.6
3756.3
3824.7
3893.7
4039.2
4184.7
4329.9
4867.8
5405.7
5943.6
6440.7
6938.4
7435.8
6696.3
5957.1
5217.9
4781.7
4345.2
3909
3944.7
3980.1
4015.5
3983.7
3951.6
3919.8
3992.1
4064.4
4136.7
3950.1
3763.2
3577.2
3690.3
3804
3917.7
3900.9
3884.1
3867
3915
3962.4
4009.5
3820.2
3631.2
3441.9
3557.7
3674.1
3789.9
3886.2
3981.9
4078.2
4181.4
4284.9
4388.4
4190.1
3991.8
3793.5
3734.7
3675.9
3617.4
3557.7
3498
3438.6
3478.5
3518.7
3558.9
3401.1
3230.7
3060.3
3043.5
3026.4
3009.6
3159
3308.1
3457.5
3327.6
3198
3068.1
3108
3147.6
3187.5

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298940&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]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298940&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298940&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 time0 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
15884.2203.883335624701663.9
25106.3996.3509348891812870.4
34475.275152.604754632232518.099999999999
43744.35131.29097801864493.8
55621.4251131.467022879433396.6
64085.375249.847870531431872.7
73853.45124.453813996124432.3
83893297.372282745811946.5
93671.15226.421106067273751.5
103190.825154.956657429806447.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5884.2 & 203.883335624701 & 663.9 \tabularnewline
2 & 5106.3 & 996.350934889181 & 2870.4 \tabularnewline
3 & 4475.275 & 152.604754632232 & 518.099999999999 \tabularnewline
4 & 3744.35 & 131.29097801864 & 493.8 \tabularnewline
5 & 5621.425 & 1131.46702287943 & 3396.6 \tabularnewline
6 & 4085.375 & 249.847870531431 & 872.7 \tabularnewline
7 & 3853.45 & 124.453813996124 & 432.3 \tabularnewline
8 & 3893 & 297.372282745811 & 946.5 \tabularnewline
9 & 3671.15 & 226.421106067273 & 751.5 \tabularnewline
10 & 3190.825 & 154.956657429806 & 447.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298940&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]5884.2[/C][C]203.883335624701[/C][C]663.9[/C][/ROW]
[ROW][C]2[/C][C]5106.3[/C][C]996.350934889181[/C][C]2870.4[/C][/ROW]
[ROW][C]3[/C][C]4475.275[/C][C]152.604754632232[/C][C]518.099999999999[/C][/ROW]
[ROW][C]4[/C][C]3744.35[/C][C]131.29097801864[/C][C]493.8[/C][/ROW]
[ROW][C]5[/C][C]5621.425[/C][C]1131.46702287943[/C][C]3396.6[/C][/ROW]
[ROW][C]6[/C][C]4085.375[/C][C]249.847870531431[/C][C]872.7[/C][/ROW]
[ROW][C]7[/C][C]3853.45[/C][C]124.453813996124[/C][C]432.3[/C][/ROW]
[ROW][C]8[/C][C]3893[/C][C]297.372282745811[/C][C]946.5[/C][/ROW]
[ROW][C]9[/C][C]3671.15[/C][C]226.421106067273[/C][C]751.5[/C][/ROW]
[ROW][C]10[/C][C]3190.825[/C][C]154.956657429806[/C][C]447.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298940&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298940&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
15884.2203.883335624701663.9
25106.3996.3509348891812870.4
34475.275152.604754632232518.099999999999
43744.35131.29097801864493.8
55621.4251131.467022879433396.6
64085.375249.847870531431872.7
73853.45124.453813996124432.3
83893297.372282745811946.5
93671.15226.421106067273751.5
103190.825154.956657429806447.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-735.909875328302
beta0.253363787082646
S.D.0.116303793934184
T-STAT2.17846536653847
p-value0.0610082251981756

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -735.909875328302 \tabularnewline
beta & 0.253363787082646 \tabularnewline
S.D. & 0.116303793934184 \tabularnewline
T-STAT & 2.17846536653847 \tabularnewline
p-value & 0.0610082251981756 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298940&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-735.909875328302[/C][/ROW]
[ROW][C]beta[/C][C]0.253363787082646[/C][/ROW]
[ROW][C]S.D.[/C][C]0.116303793934184[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.17846536653847[/C][/ROW]
[ROW][C]p-value[/C][C]0.0610082251981756[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298940&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298940&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-735.909875328302
beta0.253363787082646
S.D.0.116303793934184
T-STAT2.17846536653847
p-value0.0610082251981756






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-14.669249289604
beta2.42046696248159
S.D.1.10850317965229
T-STAT2.18354534918053
p-value0.0605270139239067
Lambda-1.42046696248159

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -14.669249289604 \tabularnewline
beta & 2.42046696248159 \tabularnewline
S.D. & 1.10850317965229 \tabularnewline
T-STAT & 2.18354534918053 \tabularnewline
p-value & 0.0605270139239067 \tabularnewline
Lambda & -1.42046696248159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298940&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-14.669249289604[/C][/ROW]
[ROW][C]beta[/C][C]2.42046696248159[/C][/ROW]
[ROW][C]S.D.[/C][C]1.10850317965229[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.18354534918053[/C][/ROW]
[ROW][C]p-value[/C][C]0.0605270139239067[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.42046696248159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298940&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298940&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-14.669249289604
beta2.42046696248159
S.D.1.10850317965229
T-STAT2.18354534918053
p-value0.0605270139239067
Lambda-1.42046696248159


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')