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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, 07 Aug 2015 18:00:31 +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/2015/Aug/07/t1438967007czi6rc1rys4dxgs.htm/, Retrieved Wed, 15 May 2024 04:30:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279921, Retrieved Wed, 15 May 2024 04:30:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112

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] [] [2015-08-07 17:00:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19064.00
18993.00
18921.00
18772.00
20246.00
20168.00
19064.00
18330.00
18401.00
18401.00
18480.00
18622.00
18843.00
18843.00
18701.00
18330.00
20246.00
20538.00
20097.00
19064.00
19506.00
18843.00
19142.00
19285.00
19434.00
19064.00
19142.00
18622.00
20246.00
20759.00
20318.00
19506.00
20389.00
19434.00
20318.00
20246.00
20467.00
19655.00
20538.00
20467.00
21792.00
21493.00
20318.00
19726.00
20538.00
19434.00
20246.00
20389.00
20688.00
20026.00
20389.00
20610.00
21422.00
20759.00
19876.00
18921.00
19805.00
17375.00
18551.00
19213.00
19876.00
18921.00
18921.00
18921.00
19434.00
18701.00
17739.00
16934.00
17518.00
15238.00
16635.00
17447.00
17596.00
16784.00
16855.00
16635.00
17375.00
16855.00
15830.00
15089.00
16342.00
13621.00
15388.00
16193.00
16193.00
15238.00
14355.00
14284.00
15089.00
14355.00
12959.00
11997.00
13030.00
10601.00
12809.00
13984.00
14355.00
13543.00
12517.00
13251.00
13543.00
13322.00
11113.00
10088.00
10821.00
8613.00
10893.00
11705.00
12367.00
11263.00
10230.00
10821.00
11113.00
10529.00
8321.00
7359.00
8242.00
5813.00
8463.00
10088.00

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'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279921&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279921&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279921&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
118955.1666666667642.3586980571661916
219286.5681.5857846362272208
319789.8333333333668.5488808311672137
420421.9166666667684.0144148312742358
519802.91666666671126.407843007094047
618023.751342.980614833364638
716213.58333333331104.436381009323975
813741.16666666671539.336092625855592
911980.33333333331718.875231250385742
109550.751902.320837341016554

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 18955.1666666667 & 642.358698057166 & 1916 \tabularnewline
2 & 19286.5 & 681.585784636227 & 2208 \tabularnewline
3 & 19789.8333333333 & 668.548880831167 & 2137 \tabularnewline
4 & 20421.9166666667 & 684.014414831274 & 2358 \tabularnewline
5 & 19802.9166666667 & 1126.40784300709 & 4047 \tabularnewline
6 & 18023.75 & 1342.98061483336 & 4638 \tabularnewline
7 & 16213.5833333333 & 1104.43638100932 & 3975 \tabularnewline
8 & 13741.1666666667 & 1539.33609262585 & 5592 \tabularnewline
9 & 11980.3333333333 & 1718.87523125038 & 5742 \tabularnewline
10 & 9550.75 & 1902.32083734101 & 6554 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279921&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]18955.1666666667[/C][C]642.358698057166[/C][C]1916[/C][/ROW]
[ROW][C]2[/C][C]19286.5[/C][C]681.585784636227[/C][C]2208[/C][/ROW]
[ROW][C]3[/C][C]19789.8333333333[/C][C]668.548880831167[/C][C]2137[/C][/ROW]
[ROW][C]4[/C][C]20421.9166666667[/C][C]684.014414831274[/C][C]2358[/C][/ROW]
[ROW][C]5[/C][C]19802.9166666667[/C][C]1126.40784300709[/C][C]4047[/C][/ROW]
[ROW][C]6[/C][C]18023.75[/C][C]1342.98061483336[/C][C]4638[/C][/ROW]
[ROW][C]7[/C][C]16213.5833333333[/C][C]1104.43638100932[/C][C]3975[/C][/ROW]
[ROW][C]8[/C][C]13741.1666666667[/C][C]1539.33609262585[/C][C]5592[/C][/ROW]
[ROW][C]9[/C][C]11980.3333333333[/C][C]1718.87523125038[/C][C]5742[/C][/ROW]
[ROW][C]10[/C][C]9550.75[/C][C]1902.32083734101[/C][C]6554[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279921&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279921&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
118955.1666666667642.3586980571661916
219286.5681.5857846362272208
319789.8333333333668.5488808311672137
420421.9166666667684.0144148312742358
519802.91666666671126.407843007094047
618023.751342.980614833364638
716213.58333333331104.436381009323975
813741.16666666671539.336092625855592
911980.33333333331718.875231250385742
109550.751902.320837341016554






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3039.38789225511
beta-0.113151792219188
S.D.0.0185894327362386
T-STAT-6.08688784777213
p-value0.000293686871073616

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3039.38789225511 \tabularnewline
beta & -0.113151792219188 \tabularnewline
S.D. & 0.0185894327362386 \tabularnewline
T-STAT & -6.08688784777213 \tabularnewline
p-value & 0.000293686871073616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279921&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3039.38789225511[/C][/ROW]
[ROW][C]beta[/C][C]-0.113151792219188[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0185894327362386[/C][/ROW]
[ROW][C]T-STAT[/C][C]-6.08688784777213[/C][/ROW]
[ROW][C]p-value[/C][C]0.000293686871073616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279921&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279921&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)
alpha3039.38789225511
beta-0.113151792219188
S.D.0.0185894327362386
T-STAT-6.08688784777213
p-value0.000293686871073616






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha20.4036124606247
beta-1.38589065989076
S.D.0.316605261909547
T-STAT-4.37734563074541
p-value0.00235715681397513
Lambda2.38589065989076

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 20.4036124606247 \tabularnewline
beta & -1.38589065989076 \tabularnewline
S.D. & 0.316605261909547 \tabularnewline
T-STAT & -4.37734563074541 \tabularnewline
p-value & 0.00235715681397513 \tabularnewline
Lambda & 2.38589065989076 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279921&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]20.4036124606247[/C][/ROW]
[ROW][C]beta[/C][C]-1.38589065989076[/C][/ROW]
[ROW][C]S.D.[/C][C]0.316605261909547[/C][/ROW]
[ROW][C]T-STAT[/C][C]-4.37734563074541[/C][/ROW]
[ROW][C]p-value[/C][C]0.00235715681397513[/C][/ROW]
[ROW][C]Lambda[/C][C]2.38589065989076[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279921&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279921&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)
alpha20.4036124606247
beta-1.38589065989076
S.D.0.316605261909547
T-STAT-4.37734563074541
p-value0.00235715681397513
Lambda2.38589065989076


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')