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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 04:41:35 -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/t1261914120r0h8dnwuoxvhbf1.htm/, Retrieved Thu, 02 May 2024 19:39:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70848, Retrieved Thu, 02 May 2024 19:39:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154

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 11:41:35] [b7e924d6f720297f82cd59f42434ec05] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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 time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70848&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]2 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=70848&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70848&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
114716.251034.575295823013479.2
213720.9166666667733.5986601967212632.4
314204.1083333333948.6434558293643811.3
415109.551151.203068335673449.4
516643.55984.6146855957973395.6
618181.5751389.636389410105091
718877.6333333333896.4836248905882859.200
821744.68333333331521.338009679964544.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14716.25 & 1034.57529582301 & 3479.2 \tabularnewline
2 & 13720.9166666667 & 733.598660196721 & 2632.4 \tabularnewline
3 & 14204.1083333333 & 948.643455829364 & 3811.3 \tabularnewline
4 & 15109.55 & 1151.20306833567 & 3449.4 \tabularnewline
5 & 16643.55 & 984.614685595797 & 3395.6 \tabularnewline
6 & 18181.575 & 1389.63638941010 & 5091 \tabularnewline
7 & 18877.6333333333 & 896.483624890588 & 2859.200 \tabularnewline
8 & 21744.6833333333 & 1521.33800967996 & 4544.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70848&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]14716.25[/C][C]1034.57529582301[/C][C]3479.2[/C][/ROW]
[ROW][C]2[/C][C]13720.9166666667[/C][C]733.598660196721[/C][C]2632.4[/C][/ROW]
[ROW][C]3[/C][C]14204.1083333333[/C][C]948.643455829364[/C][C]3811.3[/C][/ROW]
[ROW][C]4[/C][C]15109.55[/C][C]1151.20306833567[/C][C]3449.4[/C][/ROW]
[ROW][C]5[/C][C]16643.55[/C][C]984.614685595797[/C][C]3395.6[/C][/ROW]
[ROW][C]6[/C][C]18181.575[/C][C]1389.63638941010[/C][C]5091[/C][/ROW]
[ROW][C]7[/C][C]18877.6333333333[/C][C]896.483624890588[/C][C]2859.200[/C][/ROW]
[ROW][C]8[/C][C]21744.6833333333[/C][C]1521.33800967996[/C][C]4544.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70848&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70848&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
114716.251034.575295823013479.2
213720.9166666667733.5986601967212632.4
314204.1083333333948.6434558293643811.3
415109.551151.203068335673449.4
516643.55984.6146855957973395.6
618181.5751389.636389410105091
718877.6333333333896.4836248905882859.200
821744.68333333331521.338009679964544.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-37.5735452714647
beta0.0672732594513211
S.D.0.0268697036177416
T-STAT2.50368446218743
p-value0.046296913782106

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -37.5735452714647 \tabularnewline
beta & 0.0672732594513211 \tabularnewline
S.D. & 0.0268697036177416 \tabularnewline
T-STAT & 2.50368446218743 \tabularnewline
p-value & 0.046296913782106 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70848&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-37.5735452714647[/C][/ROW]
[ROW][C]beta[/C][C]0.0672732594513211[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0268697036177416[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.50368446218743[/C][/ROW]
[ROW][C]p-value[/C][C]0.046296913782106[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70848&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70848&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-37.5735452714647
beta0.0672732594513211
S.D.0.0268697036177416
T-STAT2.50368446218743
p-value0.046296913782106






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.83812129419588
beta1.00945807628435
S.D.0.437550179300136
T-STAT2.30706813535990
p-value0.060511427117168
Lambda-0.00945807628435236

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.83812129419588 \tabularnewline
beta & 1.00945807628435 \tabularnewline
S.D. & 0.437550179300136 \tabularnewline
T-STAT & 2.30706813535990 \tabularnewline
p-value & 0.060511427117168 \tabularnewline
Lambda & -0.00945807628435236 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70848&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.83812129419588[/C][/ROW]
[ROW][C]beta[/C][C]1.00945807628435[/C][/ROW]
[ROW][C]S.D.[/C][C]0.437550179300136[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.30706813535990[/C][/ROW]
[ROW][C]p-value[/C][C]0.060511427117168[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.00945807628435236[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70848&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70848&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-2.83812129419588
beta1.00945807628435
S.D.0.437550179300136
T-STAT2.30706813535990
p-value0.060511427117168
Lambda-0.00945807628435236


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')