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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 computationSat, 13 Dec 2014 14:42:05 +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/2014/Dec/13/t141848271488v5tqpykg74r4v.htm/, Retrieved Thu, 16 May 2024 22:10:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267137, Retrieved Thu, 16 May 2024 22:10:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89

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] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Spectral Analysis] [] [2014-11-26 13:41:56] [ea990983fba95a758c0bb6d29c9aee24]
- RMPD      [Standard Deviation-Mean Plot] [] [2014-12-13 14:42:05] [baa7d013c3374cabca6c222951a47a9f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.5
2.5
6.0
6.5
1.0
1.0
5.5
8.5
6.5
4.5
2.0
5.0
0.5
5.0
5.0
2.5
5.0
5.5
3.5
3.0
4.0
0.5
6.5
4.5
7.5
5.5
4.0
7.5
7.0
4.0
5.5
2.5
5.5
0.5
3.5
2.5
4.5
4.5
4.5
6.0
2.5
5.0
0.0
5.0
6.5
5.0
6.0
4.5
5.5
1.0
7.5
6.0
5.0
1.0
5.0
6.5
7.0
4.5
0.0
8.5
3.5
7.5
3.5
6.0
1.5
9.0
3.5
3.5
4.0
6.5
7.5
6.0
5.0
5.5
3.5
7.5
1.0
6.5
6.5
6.5
7.0
3.5
1.5
4.0
7.5
4.5
0.0
3.5
5.5
5.0
4.5
2.5
7.5
7.0
0.0
4.5
3.0
1.5
3.5
2.5
5.5
8.0
1.0
5.0
4.5
3.0
3.0
8.0
2.5
7.0
0.0
1.0
3.5
5.5
5.5
0.5
7.5
9
9.5
8.5
7
8
10
7
8.5
9
9.5
4
6
8
5.5
9.5
7.5
7
7.5
8
7
7
6
10
2.5
9
8
6
8.5
6
9
8
8
9
5.5
5
7
5.5
9
2
8.5
9
8.5
9
7.5
10
9
7.5
6
10.5
8.5
8
10
10.5
6.5
9.5
8.5
7.5
5
8
10
7
7.5
7.5
9.5
6
10
7
3
6
7
10
7
3.5
8
10
5.5
6
6.5
6.5
8.5
4
9.5
8
8.5
5.5
7
9
8
10
8
6
8
5
9
4.5
8.5
7
9.5
8.5
7.5
7.5
5
7
8
5.5
8.5
7.5
9.5
7
8
8.5
3.5
6.5
6.5
10.5
8.5
8
10
10
9.5
9
10
7.5
4.5
4.5
0.5
6.5
4.5
5.5
5
6
4
8
10.5
8.5
6.5
8
8.5
5.5
7
5
3.5
5
9
8.5
5
9.5
3
1.5
6
0.5
6.5
7.5
4.5
8
9
7.5
8.5
7
9.5
6.5
9.5
6
8
9.5
8
8
9

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'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267137&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267137&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267137&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14.708333333333332.535729528641467.5
23.791666666666671.888461775834476
34.6252.185957248188797
44.51.745123074586596.5
54.791666666666672.742413778650728.5
65.166666666666672.229281716090857.5
74.833333333333332.146173479954646.5
84.333333333333332.53460892925177.5
94.041666666666672.260916279795087
1053.424510582152259.5
117.666666666666671.825741858350556
127.1251.847910367759417.5
136.8752.143966163233677
148.51.18705135065464.5
158.1251.63935963107555.5
167.252.407375032157347
177.041666666666671.67139480855385.5
187.666666666666671.723280873710665.5
197.458333333333331.251514234352884.5
208.291666666666672.038920540309747
215.666666666666672.552479483786610
226.751.948192635612446
235.791666666666672.799824128675798.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4.70833333333333 & 2.53572952864146 & 7.5 \tabularnewline
2 & 3.79166666666667 & 1.88846177583447 & 6 \tabularnewline
3 & 4.625 & 2.18595724818879 & 7 \tabularnewline
4 & 4.5 & 1.74512307458659 & 6.5 \tabularnewline
5 & 4.79166666666667 & 2.74241377865072 & 8.5 \tabularnewline
6 & 5.16666666666667 & 2.22928171609085 & 7.5 \tabularnewline
7 & 4.83333333333333 & 2.14617347995464 & 6.5 \tabularnewline
8 & 4.33333333333333 & 2.5346089292517 & 7.5 \tabularnewline
9 & 4.04166666666667 & 2.26091627979508 & 7 \tabularnewline
10 & 5 & 3.42451058215225 & 9.5 \tabularnewline
11 & 7.66666666666667 & 1.82574185835055 & 6 \tabularnewline
12 & 7.125 & 1.84791036775941 & 7.5 \tabularnewline
13 & 6.875 & 2.14396616323367 & 7 \tabularnewline
14 & 8.5 & 1.1870513506546 & 4.5 \tabularnewline
15 & 8.125 & 1.6393596310755 & 5.5 \tabularnewline
16 & 7.25 & 2.40737503215734 & 7 \tabularnewline
17 & 7.04166666666667 & 1.6713948085538 & 5.5 \tabularnewline
18 & 7.66666666666667 & 1.72328087371066 & 5.5 \tabularnewline
19 & 7.45833333333333 & 1.25151423435288 & 4.5 \tabularnewline
20 & 8.29166666666667 & 2.03892054030974 & 7 \tabularnewline
21 & 5.66666666666667 & 2.5524794837866 & 10 \tabularnewline
22 & 6.75 & 1.94819263561244 & 6 \tabularnewline
23 & 5.79166666666667 & 2.79982412867579 & 8.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267137&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]4.70833333333333[/C][C]2.53572952864146[/C][C]7.5[/C][/ROW]
[ROW][C]2[/C][C]3.79166666666667[/C][C]1.88846177583447[/C][C]6[/C][/ROW]
[ROW][C]3[/C][C]4.625[/C][C]2.18595724818879[/C][C]7[/C][/ROW]
[ROW][C]4[/C][C]4.5[/C][C]1.74512307458659[/C][C]6.5[/C][/ROW]
[ROW][C]5[/C][C]4.79166666666667[/C][C]2.74241377865072[/C][C]8.5[/C][/ROW]
[ROW][C]6[/C][C]5.16666666666667[/C][C]2.22928171609085[/C][C]7.5[/C][/ROW]
[ROW][C]7[/C][C]4.83333333333333[/C][C]2.14617347995464[/C][C]6.5[/C][/ROW]
[ROW][C]8[/C][C]4.33333333333333[/C][C]2.5346089292517[/C][C]7.5[/C][/ROW]
[ROW][C]9[/C][C]4.04166666666667[/C][C]2.26091627979508[/C][C]7[/C][/ROW]
[ROW][C]10[/C][C]5[/C][C]3.42451058215225[/C][C]9.5[/C][/ROW]
[ROW][C]11[/C][C]7.66666666666667[/C][C]1.82574185835055[/C][C]6[/C][/ROW]
[ROW][C]12[/C][C]7.125[/C][C]1.84791036775941[/C][C]7.5[/C][/ROW]
[ROW][C]13[/C][C]6.875[/C][C]2.14396616323367[/C][C]7[/C][/ROW]
[ROW][C]14[/C][C]8.5[/C][C]1.1870513506546[/C][C]4.5[/C][/ROW]
[ROW][C]15[/C][C]8.125[/C][C]1.6393596310755[/C][C]5.5[/C][/ROW]
[ROW][C]16[/C][C]7.25[/C][C]2.40737503215734[/C][C]7[/C][/ROW]
[ROW][C]17[/C][C]7.04166666666667[/C][C]1.6713948085538[/C][C]5.5[/C][/ROW]
[ROW][C]18[/C][C]7.66666666666667[/C][C]1.72328087371066[/C][C]5.5[/C][/ROW]
[ROW][C]19[/C][C]7.45833333333333[/C][C]1.25151423435288[/C][C]4.5[/C][/ROW]
[ROW][C]20[/C][C]8.29166666666667[/C][C]2.03892054030974[/C][C]7[/C][/ROW]
[ROW][C]21[/C][C]5.66666666666667[/C][C]2.5524794837866[/C][C]10[/C][/ROW]
[ROW][C]22[/C][C]6.75[/C][C]1.94819263561244[/C][C]6[/C][/ROW]
[ROW][C]23[/C][C]5.79166666666667[/C][C]2.79982412867579[/C][C]8.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267137&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267137&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
14.708333333333332.535729528641467.5
23.791666666666671.888461775834476
34.6252.185957248188797
44.51.745123074586596.5
54.791666666666672.742413778650728.5
65.166666666666672.229281716090857.5
74.833333333333332.146173479954646.5
84.333333333333332.53460892925177.5
94.041666666666672.260916279795087
1053.424510582152259.5
117.666666666666671.825741858350556
127.1251.847910367759417.5
136.8752.143966163233677
148.51.18705135065464.5
158.1251.63935963107555.5
167.252.407375032157347
177.041666666666671.67139480855385.5
187.666666666666671.723280873710665.5
197.458333333333331.251514234352884.5
208.291666666666672.038920540309747
215.666666666666672.552479483786610
226.751.948192635612446
235.791666666666672.799824128675798.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.25391678095542
beta-0.186499274718537
S.D.0.0616044433189172
T-STAT-3.02736725909619
p-value0.00640777121325412

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.25391678095542 \tabularnewline
beta & -0.186499274718537 \tabularnewline
S.D. & 0.0616044433189172 \tabularnewline
T-STAT & -3.02736725909619 \tabularnewline
p-value & 0.00640777121325412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267137&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.25391678095542[/C][/ROW]
[ROW][C]beta[/C][C]-0.186499274718537[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0616044433189172[/C][/ROW]
[ROW][C]T-STAT[/C][C]-3.02736725909619[/C][/ROW]
[ROW][C]p-value[/C][C]0.00640777121325412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267137&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267137&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)
alpha3.25391678095542
beta-0.186499274718537
S.D.0.0616044433189172
T-STAT-3.02736725909619
p-value0.00640777121325412






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.64987926544875
beta-0.522614217932025
S.D.0.17835101312157
T-STAT-2.93025651374233
p-value0.00799669372974801
Lambda1.52261421793202

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.64987926544875 \tabularnewline
beta & -0.522614217932025 \tabularnewline
S.D. & 0.17835101312157 \tabularnewline
T-STAT & -2.93025651374233 \tabularnewline
p-value & 0.00799669372974801 \tabularnewline
Lambda & 1.52261421793202 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267137&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.64987926544875[/C][/ROW]
[ROW][C]beta[/C][C]-0.522614217932025[/C][/ROW]
[ROW][C]S.D.[/C][C]0.17835101312157[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.93025651374233[/C][/ROW]
[ROW][C]p-value[/C][C]0.00799669372974801[/C][/ROW]
[ROW][C]Lambda[/C][C]1.52261421793202[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267137&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267137&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)
alpha1.64987926544875
beta-0.522614217932025
S.D.0.17835101312157
T-STAT-2.93025651374233
p-value0.00799669372974801
Lambda1.52261421793202


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')