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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, 05 Dec 2011 20:51:26 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/05/t1323136302cyql0ttce8m7nb5.htm/, Retrieved Fri, 03 May 2024 11:43:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151353, Retrieved Fri, 03 May 2024 11:43:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- R PD      [Standard Deviation-Mean Plot] [] [2011-12-06 01:51:26] [fdaf10f0fcbe7b8f79ecbd42ec74e6ad] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3363,99
3494,17
3667,03
3813,06
3917,96
3895,51
3801,06
3570,12
3701,61
3862,27
3970,1
4138,52
4199,75
4290,89
4443,91
4502,64
4356,98
4591,27
4696,96
4621,4
4562,84
4202,52
4296,49
4435,23
4105,18
4116,68
3844,49
3720,98
3674,4
3857,62
3801,06
3504,37
3032,6
3047,03
2962,34
2197,82
2014,45
1862,83
1905,41
1810,99
1670,07
1864,44
2052,02
2029,6
2070,83
2293,41
2443,27
2513,17
2466,92
2502,66
2539,91
2482,6
2626,15
2656,32
2446,66
2467,38
2462,32
2504,58
2579,39
2649,24
2636,87
2613,94
2634,01
2711,94
2646,43
2717,79
2701,54
2572,98
2488,92
2204,91
2123,99
2149,1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'AstonUniversity' @ aston.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 & 4 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151353&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151353&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151353&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 time4 seconds
R Server'AstonUniversity' @ aston.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13766.28333333333217.593686252542774.53
24433.40666666667166.292423614292497.21
33488.71416666667569.678808124821918.86
42044.2075256.195138805808843.1
52532.0108333333376.8562424812281209.66
62516.86833333333225.169100448906593.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3766.28333333333 & 217.593686252542 & 774.53 \tabularnewline
2 & 4433.40666666667 & 166.292423614292 & 497.21 \tabularnewline
3 & 3488.71416666667 & 569.67880812482 & 1918.86 \tabularnewline
4 & 2044.2075 & 256.195138805808 & 843.1 \tabularnewline
5 & 2532.01083333333 & 76.8562424812281 & 209.66 \tabularnewline
6 & 2516.86833333333 & 225.169100448906 & 593.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151353&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]3766.28333333333[/C][C]217.593686252542[/C][C]774.53[/C][/ROW]
[ROW][C]2[/C][C]4433.40666666667[/C][C]166.292423614292[/C][C]497.21[/C][/ROW]
[ROW][C]3[/C][C]3488.71416666667[/C][C]569.67880812482[/C][C]1918.86[/C][/ROW]
[ROW][C]4[/C][C]2044.2075[/C][C]256.195138805808[/C][C]843.1[/C][/ROW]
[ROW][C]5[/C][C]2532.01083333333[/C][C]76.8562424812281[/C][C]209.66[/C][/ROW]
[ROW][C]6[/C][C]2516.86833333333[/C][C]225.169100448906[/C][C]593.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151353&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151353&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
13766.28333333333217.593686252542774.53
24433.40666666667166.292423614292497.21
33488.71416666667569.678808124821918.86
42044.2075256.195138805808843.1
52532.0108333333376.8562424812281209.66
62516.86833333333225.169100448906593.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha178.72250586921
beta0.0233980554798344
S.D.0.091429298139198
T-STAT0.255914197702925
p-value0.81063891132767

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 178.72250586921 \tabularnewline
beta & 0.0233980554798344 \tabularnewline
S.D. & 0.091429298139198 \tabularnewline
T-STAT & 0.255914197702925 \tabularnewline
p-value & 0.81063891132767 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151353&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]178.72250586921[/C][/ROW]
[ROW][C]beta[/C][C]0.0233980554798344[/C][/ROW]
[ROW][C]S.D.[/C][C]0.091429298139198[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.255914197702925[/C][/ROW]
[ROW][C]p-value[/C][C]0.81063891132767[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151353&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151353&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)
alpha178.72250586921
beta0.0233980554798344
S.D.0.091429298139198
T-STAT0.255914197702925
p-value0.81063891132767






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.60214990119381
beta0.343881904295423
S.D.1.08844910909498
T-STAT0.315937512761945
p-value0.767848584677307
Lambda0.656118095704577

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.60214990119381 \tabularnewline
beta & 0.343881904295423 \tabularnewline
S.D. & 1.08844910909498 \tabularnewline
T-STAT & 0.315937512761945 \tabularnewline
p-value & 0.767848584677307 \tabularnewline
Lambda & 0.656118095704577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151353&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.60214990119381[/C][/ROW]
[ROW][C]beta[/C][C]0.343881904295423[/C][/ROW]
[ROW][C]S.D.[/C][C]1.08844910909498[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.315937512761945[/C][/ROW]
[ROW][C]p-value[/C][C]0.767848584677307[/C][/ROW]
[ROW][C]Lambda[/C][C]0.656118095704577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151353&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151353&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)
alpha2.60214990119381
beta0.343881904295423
S.D.1.08844910909498
T-STAT0.315937512761945
p-value0.767848584677307
Lambda0.656118095704577


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')