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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 computationSun, 27 Dec 2009 04:26:52 -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/27/t12619137226o0ntbnn62uorb5.htm/, Retrieved Thu, 02 May 2024 17:04:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70842, Retrieved Thu, 02 May 2024 17:04:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160

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] [Stefan Temmerman] [2008-12-10 18:26:26] [4c0c0466a42d9212e91e81695c3ab4a9]
-  M D    [Standard Deviation-Mean Plot] [Toon Nauwelaerts 1] [2009-12-27 11:26:52] [b7e924d6f720297f82cd59f42434ec05] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13139.7
14532.2
15167
16071.1
14827.5
15082
14772.7
16083
14272.5
15223.3
14897.3
13062.6
12603.8
13629.8
14421.1
13978.3
12927.9
13429.9
13470.1
14785.8
14292
14308.8
14013
13240.9
12153.4
14289.7
15669.2
14169.5
14569.8
14469.1
14264.9
15320.9
14433.5
13691.5
14194.1
13519.2
11857.9
14616
15643.4
14077.2
14887.5
14159.9
14643
17192.5
15386.1
14287.1
17526.6
14497
14398.3
16629.6
16670.7
16614.8
16869.2
15663.9
16359.9
18447.7
16889
16505
18320.9
15052.1
15699.8
18135.3
16768.7
18883
19021
18101.9
17776.1
21489.9
17065.3
18690
18953.1
16398.9
16895.7
18553
19270
19422.1
17579.4
18637.3
18076.7
20438.6
18075.2
19563
19899.2
19227.5
17789.6
19220.8
21968.9
21131.5
19484.6
22404.1
21099
22486.5
23707.5
21897.5
23326.4
23765.4
20444

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=70842&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=70842&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70842&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
114760.9083333333942.5757249139033020.4
213758.45653.2278643224532182
314228.7333333333883.8244841527523515.8
414897.851480.402341809945668.7
516535.09166666671154.967604786414049.4
618081.91666666671526.390081105415790.1
718803.14166666671023.282014321243542.9
821523.48333333331878.658043698095975.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14760.9083333333 & 942.575724913903 & 3020.4 \tabularnewline
2 & 13758.45 & 653.227864322453 & 2182 \tabularnewline
3 & 14228.7333333333 & 883.824484152752 & 3515.8 \tabularnewline
4 & 14897.85 & 1480.40234180994 & 5668.7 \tabularnewline
5 & 16535.0916666667 & 1154.96760478641 & 4049.4 \tabularnewline
6 & 18081.9166666667 & 1526.39008110541 & 5790.1 \tabularnewline
7 & 18803.1416666667 & 1023.28201432124 & 3542.9 \tabularnewline
8 & 21523.4833333333 & 1878.65804369809 & 5975.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70842&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]14760.9083333333[/C][C]942.575724913903[/C][C]3020.4[/C][/ROW]
[ROW][C]2[/C][C]13758.45[/C][C]653.227864322453[/C][C]2182[/C][/ROW]
[ROW][C]3[/C][C]14228.7333333333[/C][C]883.824484152752[/C][C]3515.8[/C][/ROW]
[ROW][C]4[/C][C]14897.85[/C][C]1480.40234180994[/C][C]5668.7[/C][/ROW]
[ROW][C]5[/C][C]16535.0916666667[/C][C]1154.96760478641[/C][C]4049.4[/C][/ROW]
[ROW][C]6[/C][C]18081.9166666667[/C][C]1526.39008110541[/C][C]5790.1[/C][/ROW]
[ROW][C]7[/C][C]18803.1416666667[/C][C]1023.28201432124[/C][C]3542.9[/C][/ROW]
[ROW][C]8[/C][C]21523.4833333333[/C][C]1878.65804369809[/C][C]5975.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70842&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70842&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
114760.9083333333942.5757249139033020.4
213758.45653.2278643224532182
314228.7333333333883.8244841527523515.8
414897.851480.402341809945668.7
516535.09166666671154.967604786414049.4
618081.91666666671526.390081105415790.1
718803.14166666671023.282014321243542.9
821523.48333333331878.658043698095975.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-661.685638794724
beta0.111900300377824
S.D.0.040391814872307
T-STAT2.77037069840958
p-value0.0324065952780863

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -661.685638794724 \tabularnewline
beta & 0.111900300377824 \tabularnewline
S.D. & 0.040391814872307 \tabularnewline
T-STAT & 2.77037069840958 \tabularnewline
p-value & 0.0324065952780863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70842&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-661.685638794724[/C][/ROW]
[ROW][C]beta[/C][C]0.111900300377824[/C][/ROW]
[ROW][C]S.D.[/C][C]0.040391814872307[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.77037069840958[/C][/ROW]
[ROW][C]p-value[/C][C]0.0324065952780863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70842&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70842&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-661.685638794724
beta0.111900300377824
S.D.0.040391814872307
T-STAT2.77037069840958
p-value0.0324065952780863






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-8.54006827977361
beta1.60476365455309
S.D.0.603105508010987
T-STAT2.66083402196992
p-value0.0374822694103365
Lambda-0.604763654553088

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -8.54006827977361 \tabularnewline
beta & 1.60476365455309 \tabularnewline
S.D. & 0.603105508010987 \tabularnewline
T-STAT & 2.66083402196992 \tabularnewline
p-value & 0.0374822694103365 \tabularnewline
Lambda & -0.604763654553088 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70842&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8.54006827977361[/C][/ROW]
[ROW][C]beta[/C][C]1.60476365455309[/C][/ROW]
[ROW][C]S.D.[/C][C]0.603105508010987[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.66083402196992[/C][/ROW]
[ROW][C]p-value[/C][C]0.0374822694103365[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.604763654553088[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70842&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70842&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-8.54006827977361
beta1.60476365455309
S.D.0.603105508010987
T-STAT2.66083402196992
p-value0.0374822694103365
Lambda-0.604763654553088


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')