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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, 14 Dec 2009 11:06:03 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/14/t1260814062571d7lyxkvm3lkl.htm/, Retrieved Sun, 05 May 2024 13:47:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67604, Retrieved Sun, 05 May 2024 13:47:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103

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...] [2009-12-14 18:06:03] [6df9bd2792d60592b4a24994398a86db] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7787.0  
8474.2  
9154.7  
8557.2  
7951.1  
9156.7  
7865.7  
7337.4  
9131.7  
8814.6  
8598.8  
8439.6  
7451.8  
8016.2  
9544.1  
8270.7  
8102.2  
9369.0  
7657.7  
7816.6  
9391.3  
9445.4  
9533.1  
10068.7  
8955.5  
10423.9  
11617.2  
9391.1  
10872.0  
10230.4  
9221.0  
9428.6  
10934.5  
10986.0  
11724.6  
11180.9  
11163.2  
11240.9  
12107.1  
10762.3  
11340.4  
11266.8  
9542.7  
9227.7  
10571.9  
10774.4  
10392.8  
9920.2  
9884.9  
10174.5  
11395.4  
10760.2  
10570.1  
10536.0  
9902.6  
8889.0  
10837.3  
11624.1  
10509.0  
10984.9  
10649.1  
10855.7  
11677.4  
10760.2  
10046.2  
10772.8  
9987.7  
8638.7  
11063.7  
11855.7  
10684.5  
11337.4  
10478.0  
11123.9  
12909.3  
11339.9  
10462.2  
12733.5  
10519.2  
10414.9  
12476.8  
12384.6  
12266.7  
12919.9  
11497.3  
12142.0  
13919.4  
12656.8  
12034.1  
13199.7  
10881.3  
11301.2  
13643.9  
12517.0  
13981.1  
14275.7  
13435.0  
13565.7  
16216.3  
12970.0  
14079.9  
14235.0  
12213.4  
12581.0  
14130.4  
14210.8  
14378.5  
13142.8  
13714.7  
13621.9  
15379.8  
13306.3  
14391.2  
14909.9  
14025.4  
12951.2  
14344.3  
16093.4  
15413.6  
14705.7  
15972.8
16241.4
16626.4
17136.2
15622.9
18003.9
16136.1
14423.7
16789.4
16782.2
14133.8
12607

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=67604&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=67604&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67604&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
18439.05833333333595.0035087113251819.3
28722.23333333333913.9862723589492616.9
310413.8083333333961.2010389075582769.1
410692.5333333333823.1347822179362879.4
510505.6666666667733.8786750526072735.1
610694.0916666667855.4037669251273217
711669.0751041.555632106482505
812670.79166666671137.874186573233394.4
913763.23333333331045.102438940224002.9
1014404.7833333333940.1138430417823142.2
1115872.98333333331490.574860328205396.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8439.05833333333 & 595.003508711325 & 1819.3 \tabularnewline
2 & 8722.23333333333 & 913.986272358949 & 2616.9 \tabularnewline
3 & 10413.8083333333 & 961.201038907558 & 2769.1 \tabularnewline
4 & 10692.5333333333 & 823.134782217936 & 2879.4 \tabularnewline
5 & 10505.6666666667 & 733.878675052607 & 2735.1 \tabularnewline
6 & 10694.0916666667 & 855.403766925127 & 3217 \tabularnewline
7 & 11669.075 & 1041.55563210648 & 2505 \tabularnewline
8 & 12670.7916666667 & 1137.87418657323 & 3394.4 \tabularnewline
9 & 13763.2333333333 & 1045.10243894022 & 4002.9 \tabularnewline
10 & 14404.7833333333 & 940.113843041782 & 3142.2 \tabularnewline
11 & 15872.9833333333 & 1490.57486032820 & 5396.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67604&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]8439.05833333333[/C][C]595.003508711325[/C][C]1819.3[/C][/ROW]
[ROW][C]2[/C][C]8722.23333333333[/C][C]913.986272358949[/C][C]2616.9[/C][/ROW]
[ROW][C]3[/C][C]10413.8083333333[/C][C]961.201038907558[/C][C]2769.1[/C][/ROW]
[ROW][C]4[/C][C]10692.5333333333[/C][C]823.134782217936[/C][C]2879.4[/C][/ROW]
[ROW][C]5[/C][C]10505.6666666667[/C][C]733.878675052607[/C][C]2735.1[/C][/ROW]
[ROW][C]6[/C][C]10694.0916666667[/C][C]855.403766925127[/C][C]3217[/C][/ROW]
[ROW][C]7[/C][C]11669.075[/C][C]1041.55563210648[/C][C]2505[/C][/ROW]
[ROW][C]8[/C][C]12670.7916666667[/C][C]1137.87418657323[/C][C]3394.4[/C][/ROW]
[ROW][C]9[/C][C]13763.2333333333[/C][C]1045.10243894022[/C][C]4002.9[/C][/ROW]
[ROW][C]10[/C][C]14404.7833333333[/C][C]940.113843041782[/C][C]3142.2[/C][/ROW]
[ROW][C]11[/C][C]15872.9833333333[/C][C]1490.57486032820[/C][C]5396.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67604&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67604&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
18439.05833333333595.0035087113251819.3
28722.23333333333913.9862723589492616.9
310413.8083333333961.2010389075582769.1
410692.5333333333823.1347822179362879.4
510505.6666666667733.8786750526072735.1
610694.0916666667855.4037669251273217
711669.0751041.555632106482505
812670.79166666671137.874186573233394.4
913763.23333333331045.102438940224002.9
1014404.7833333333940.1138430417823142.2
1115872.98333333331490.574860328205396.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha31.2947973043778
beta0.0797319131891336
S.D.0.0200583733638431
T-STAT3.97499397098955
p-value0.00323015199734159

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 31.2947973043778 \tabularnewline
beta & 0.0797319131891336 \tabularnewline
S.D. & 0.0200583733638431 \tabularnewline
T-STAT & 3.97499397098955 \tabularnewline
p-value & 0.00323015199734159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67604&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]31.2947973043778[/C][/ROW]
[ROW][C]beta[/C][C]0.0797319131891336[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0200583733638431[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.97499397098955[/C][/ROW]
[ROW][C]p-value[/C][C]0.00323015199734159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67604&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67604&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)
alpha31.2947973043778
beta0.0797319131891336
S.D.0.0200583733638431
T-STAT3.97499397098955
p-value0.00323015199734159






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.94794147879422
beta0.940510872029627
S.D.0.246892586748967
T-STAT3.80939292027391
p-value0.00415699482356635
Lambda0.0594891279703729

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.94794147879422 \tabularnewline
beta & 0.940510872029627 \tabularnewline
S.D. & 0.246892586748967 \tabularnewline
T-STAT & 3.80939292027391 \tabularnewline
p-value & 0.00415699482356635 \tabularnewline
Lambda & 0.0594891279703729 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67604&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.94794147879422[/C][/ROW]
[ROW][C]beta[/C][C]0.940510872029627[/C][/ROW]
[ROW][C]S.D.[/C][C]0.246892586748967[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.80939292027391[/C][/ROW]
[ROW][C]p-value[/C][C]0.00415699482356635[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0594891279703729[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67604&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67604&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-1.94794147879422
beta0.940510872029627
S.D.0.246892586748967
T-STAT3.80939292027391
p-value0.00415699482356635
Lambda0.0594891279703729


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')