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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, 27 Dec 2010 15:37:43 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/27/t1293464159iimaz7lbjvqgr6y.htm/, Retrieved Mon, 06 May 2024 13:46:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116032, Retrieved Mon, 06 May 2024 13:46:09 +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)
-       [Standard Deviation-Mean Plot] [paper SD-MP] [2010-12-27 15:37:43] [4c854bb223ec27caaa7bcfc5e77b0dbd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5,2
7,9
8,7
8,9
15,3
15,4
18,1
19,7
13
12,6
6,2
3,5
3,4
0
9,5
8,9
10,4
13,2
18,9
19
16,3
10,6
5,8
3,6
2,6
5
7,3
9,2
15,7
16,8
18,4
18,1
14,6
7,8
7,6
3,8
5,6
2,2
6,8
11,8
14,9
16,7
16,7
15,9
13,6
9,2
2,8
2,5
4,8
2,8
7,8
9
12,9
16,4
21,8
17,8
13,5
10
10,4
5,5
4
6,8
5,7
9,1
13,6
15
20,9
20,4
14
13,7
7,1
0,8
2,1
1,3
3,9
10,7
11,1
16,4
17,1
17,3
12,9
10,9
5,3
0,7
-0,2
6,5
8,6
8,5
13,3
16,2
17,5
21,2
14,8
10,3
7,3
5,1
4,4
6,2
7,7
9,3
15,6
16,3
16,6
17,4
15,3
9,7
3,7
4,6
5,4
3,1
7,9
10,1
15
15,6
19,7
18,1
17,7
10,7
6,2
4,2
4
5,9
7,1
10,5
15,1
16,8
15,3
18,4
16,1
11,3
7,9
5,6
3,4
4,8
6,5
8,5
15,1
15,7
18,7
19,2
12,9
14,4
6,2
3,3
4,6
7,2
7,8
9,9
13,6
17,1
17,8
18,6
14,7
10,5
8,6
4,4
2,3
2,8
8,8
10,7
13,9
19,3
19,5
20,4
15,3
7,9
8,3
4,5
3,2
5
6,6
11,1
12,8
16,3
17,4
18,9
15,8
11,7
6,4
2,9
4,7
2,4
7,2
10,7
13,4
18,5
18,3
16,8
16,6
14,1
6,1
3,5
1,7
2,3
4,5
9,3
14,2
17,3
23
16,3
18,4
14,2
9,1
5,9
7,2
6,8
8
14,3
14,6
17,5
17,2
17,2
14,1
10,5
6,8
4,1
6,5
6,1
6,3
9,3
16,4
16,1
18
17,6
14
10,5
6,9
2,8
0,7
3,6
6,7
12,5
14,4
16,5
18,7
19,4
15,8
11,3
9,7
2,9

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=116032&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=116032&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116032&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
111.20833333333335.2416961747013516.2
29.966666666666676.1368237762384919
310.5755.7904506026576415.8
49.891666666666675.7511197855616614.5
511.05833333333335.6680056350349419
610.9256.3456678135559520.1
79.141666666666676.2568447368147216.6
810.75833333333336.0230554513217821.4
910.56666666666675.3438721632323613.7
1011.14166666666675.8888891271202516.6
1111.16666666666675.0335841799824614.4
1210.7255.9139473050808215.9
1311.23333333333335.0220121525745114.2
1411.14166666666676.4889358047978818.1
1510.6755.7203186497384416
1611.0256.0177200454536416.1
1711.356.8919584233431721.3
1811.5254.8228857826748613.4
1910.8755.3093613723138315.2
2011.01666666666676.3509245330300118.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 11.2083333333333 & 5.24169617470135 & 16.2 \tabularnewline
2 & 9.96666666666667 & 6.13682377623849 & 19 \tabularnewline
3 & 10.575 & 5.79045060265764 & 15.8 \tabularnewline
4 & 9.89166666666667 & 5.75111978556166 & 14.5 \tabularnewline
5 & 11.0583333333333 & 5.66800563503494 & 19 \tabularnewline
6 & 10.925 & 6.34566781355595 & 20.1 \tabularnewline
7 & 9.14166666666667 & 6.25684473681472 & 16.6 \tabularnewline
8 & 10.7583333333333 & 6.02305545132178 & 21.4 \tabularnewline
9 & 10.5666666666667 & 5.34387216323236 & 13.7 \tabularnewline
10 & 11.1416666666667 & 5.88888912712025 & 16.6 \tabularnewline
11 & 11.1666666666667 & 5.03358417998246 & 14.4 \tabularnewline
12 & 10.725 & 5.91394730508082 & 15.9 \tabularnewline
13 & 11.2333333333333 & 5.02201215257451 & 14.2 \tabularnewline
14 & 11.1416666666667 & 6.48893580479788 & 18.1 \tabularnewline
15 & 10.675 & 5.72031864973844 & 16 \tabularnewline
16 & 11.025 & 6.01772004545364 & 16.1 \tabularnewline
17 & 11.35 & 6.89195842334317 & 21.3 \tabularnewline
18 & 11.525 & 4.82288578267486 & 13.4 \tabularnewline
19 & 10.875 & 5.30936137231383 & 15.2 \tabularnewline
20 & 11.0166666666667 & 6.35092453303001 & 18.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116032&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]11.2083333333333[/C][C]5.24169617470135[/C][C]16.2[/C][/ROW]
[ROW][C]2[/C][C]9.96666666666667[/C][C]6.13682377623849[/C][C]19[/C][/ROW]
[ROW][C]3[/C][C]10.575[/C][C]5.79045060265764[/C][C]15.8[/C][/ROW]
[ROW][C]4[/C][C]9.89166666666667[/C][C]5.75111978556166[/C][C]14.5[/C][/ROW]
[ROW][C]5[/C][C]11.0583333333333[/C][C]5.66800563503494[/C][C]19[/C][/ROW]
[ROW][C]6[/C][C]10.925[/C][C]6.34566781355595[/C][C]20.1[/C][/ROW]
[ROW][C]7[/C][C]9.14166666666667[/C][C]6.25684473681472[/C][C]16.6[/C][/ROW]
[ROW][C]8[/C][C]10.7583333333333[/C][C]6.02305545132178[/C][C]21.4[/C][/ROW]
[ROW][C]9[/C][C]10.5666666666667[/C][C]5.34387216323236[/C][C]13.7[/C][/ROW]
[ROW][C]10[/C][C]11.1416666666667[/C][C]5.88888912712025[/C][C]16.6[/C][/ROW]
[ROW][C]11[/C][C]11.1666666666667[/C][C]5.03358417998246[/C][C]14.4[/C][/ROW]
[ROW][C]12[/C][C]10.725[/C][C]5.91394730508082[/C][C]15.9[/C][/ROW]
[ROW][C]13[/C][C]11.2333333333333[/C][C]5.02201215257451[/C][C]14.2[/C][/ROW]
[ROW][C]14[/C][C]11.1416666666667[/C][C]6.48893580479788[/C][C]18.1[/C][/ROW]
[ROW][C]15[/C][C]10.675[/C][C]5.72031864973844[/C][C]16[/C][/ROW]
[ROW][C]16[/C][C]11.025[/C][C]6.01772004545364[/C][C]16.1[/C][/ROW]
[ROW][C]17[/C][C]11.35[/C][C]6.89195842334317[/C][C]21.3[/C][/ROW]
[ROW][C]18[/C][C]11.525[/C][C]4.82288578267486[/C][C]13.4[/C][/ROW]
[ROW][C]19[/C][C]10.875[/C][C]5.30936137231383[/C][C]15.2[/C][/ROW]
[ROW][C]20[/C][C]11.0166666666667[/C][C]6.35092453303001[/C][C]18.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116032&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116032&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
111.20833333333335.2416961747013516.2
29.966666666666676.1368237762384919
310.5755.7904506026576415.8
49.891666666666675.7511197855616614.5
511.05833333333335.6680056350349419
610.9256.3456678135559520.1
79.141666666666676.2568447368147216.6
810.75833333333336.0230554513217821.4
910.56666666666675.3438721632323613.7
1011.14166666666675.8888891271202516.6
1111.16666666666675.0335841799824614.4
1210.7255.9139473050808215.9
1311.23333333333335.0220121525745114.2
1411.14166666666676.4889358047978818.1
1510.6755.7203186497384416
1611.0256.0177200454536416.1
1711.356.8919584233431721.3
1811.5254.8228857826748613.4
1910.8755.3093613723138315.2
2011.01666666666676.3509245330300118.7






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha8.29321442723234
beta-0.230805132101025
S.D.0.219426594718156
T-STAT-1.0518557807338
p-value0.306782555543870

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 8.29321442723234 \tabularnewline
beta & -0.230805132101025 \tabularnewline
S.D. & 0.219426594718156 \tabularnewline
T-STAT & -1.0518557807338 \tabularnewline
p-value & 0.306782555543870 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116032&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.29321442723234[/C][/ROW]
[ROW][C]beta[/C][C]-0.230805132101025[/C][/ROW]
[ROW][C]S.D.[/C][C]0.219426594718156[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.0518557807338[/C][/ROW]
[ROW][C]p-value[/C][C]0.306782555543870[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116032&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116032&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)
alpha8.29321442723234
beta-0.230805132101025
S.D.0.219426594718156
T-STAT-1.0518557807338
p-value0.306782555543870






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.83418240357891
beta-0.454337201237752
S.D.0.393120319083221
T-STAT-1.15572047330774
p-value0.262906325464383
Lambda1.45433720123775

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.83418240357891 \tabularnewline
beta & -0.454337201237752 \tabularnewline
S.D. & 0.393120319083221 \tabularnewline
T-STAT & -1.15572047330774 \tabularnewline
p-value & 0.262906325464383 \tabularnewline
Lambda & 1.45433720123775 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116032&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.83418240357891[/C][/ROW]
[ROW][C]beta[/C][C]-0.454337201237752[/C][/ROW]
[ROW][C]S.D.[/C][C]0.393120319083221[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.15572047330774[/C][/ROW]
[ROW][C]p-value[/C][C]0.262906325464383[/C][/ROW]
[ROW][C]Lambda[/C][C]1.45433720123775[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116032&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116032&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)
alpha2.83418240357891
beta-0.454337201237752
S.D.0.393120319083221
T-STAT-1.15572047330774
p-value0.262906325464383
Lambda1.45433720123775


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')