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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationTue, 02 Dec 2008 16:29:09 -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/2008/Dec/03/t1228260731ujov6roz4krcnf0.htm/, Retrieved Fri, 17 May 2024 05:14:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28535, Retrieved Fri, 17 May 2024 05:14:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact207

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] [Gilliam Schoorel] [2008-12-02 23:29:09] [4a7b7ae341cb1fe8993cedd56bcfa583] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101,4
100,7
111,7
96,9
101,9
107,2
86,7
92,7
101,4
107,1
100,8
91
96,3
96,7
106,7
104,8
103
105,7
92,4
91
107,7
112
102,1
94,8
99,4
98,7
106,2
103,9
99,5
105,3
93,9
88,3
109,3
112,1
100,3
101,5
96,5
98,8
115,9
106,5
100,7
114,6
97,2
96,8
117,2
112,6
107
106,6
98,9
98,8
110,3
104,4
100,7
117,7
89,1
94,9
112,4
104,9
109,3
104,3
102,3
103,2
118,8
102,6
112,2
116,6
93,6
100
116,4
118,9
114,5
106,2
109,8
107,3
121,9
108,8
111,8
119,8
102,5
103,4
114,4
124,1
115,6
105,2
114,1
115,3
115,8
119,9
112,1
119,7
106,2
101,5
119,3

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=28535&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=28535&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28535&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
199.95833333333337.1894440717350425
2101.16.6945024935661721
3101.5333333333336.502913100132823.8
4105.8666666666677.8313279186672420.7
5103.8083333333337.9510386209296728.6
6108.7758.4849733486483525.3
7112.057.2086438013363821.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 99.9583333333333 & 7.18944407173504 & 25 \tabularnewline
2 & 101.1 & 6.69450249356617 & 21 \tabularnewline
3 & 101.533333333333 & 6.5029131001328 & 23.8 \tabularnewline
4 & 105.866666666667 & 7.83132791866724 & 20.7 \tabularnewline
5 & 103.808333333333 & 7.95103862092967 & 28.6 \tabularnewline
6 & 108.775 & 8.48497334864835 & 25.3 \tabularnewline
7 & 112.05 & 7.20864380133638 & 21.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28535&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]99.9583333333333[/C][C]7.18944407173504[/C][C]25[/C][/ROW]
[ROW][C]2[/C][C]101.1[/C][C]6.69450249356617[/C][C]21[/C][/ROW]
[ROW][C]3[/C][C]101.533333333333[/C][C]6.5029131001328[/C][C]23.8[/C][/ROW]
[ROW][C]4[/C][C]105.866666666667[/C][C]7.83132791866724[/C][C]20.7[/C][/ROW]
[ROW][C]5[/C][C]103.808333333333[/C][C]7.95103862092967[/C][C]28.6[/C][/ROW]
[ROW][C]6[/C][C]108.775[/C][C]8.48497334864835[/C][C]25.3[/C][/ROW]
[ROW][C]7[/C][C]112.05[/C][C]7.20864380133638[/C][C]21.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28535&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28535&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
199.95833333333337.1894440717350425
2101.16.6945024935661721
3101.5333333333336.502913100132823.8
4105.8666666666677.8313279186672420.7
5103.8083333333337.9510386209296728.6
6108.7758.4849733486483525.3
7112.057.2086438013363821.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.919514116643335
beta0.0795254465742379
S.D.0.0623958410545334
T-STAT1.27453120641059
p-value0.258493705489703

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.919514116643335 \tabularnewline
beta & 0.0795254465742379 \tabularnewline
S.D. & 0.0623958410545334 \tabularnewline
T-STAT & 1.27453120641059 \tabularnewline
p-value & 0.258493705489703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28535&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.919514116643335[/C][/ROW]
[ROW][C]beta[/C][C]0.0795254465742379[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0623958410545334[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.27453120641059[/C][/ROW]
[ROW][C]p-value[/C][C]0.258493705489703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28535&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28535&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-0.919514116643335
beta0.0795254465742379
S.D.0.0623958410545334
T-STAT1.27453120641059
p-value0.258493705489703






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.39636630503619
beta1.16008755707158
S.D.0.881478423609216
T-STAT1.31607028147280
p-value0.245254619223176
Lambda-0.160087557071577

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.39636630503619 \tabularnewline
beta & 1.16008755707158 \tabularnewline
S.D. & 0.881478423609216 \tabularnewline
T-STAT & 1.31607028147280 \tabularnewline
p-value & 0.245254619223176 \tabularnewline
Lambda & -0.160087557071577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28535&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.39636630503619[/C][/ROW]
[ROW][C]beta[/C][C]1.16008755707158[/C][/ROW]
[ROW][C]S.D.[/C][C]0.881478423609216[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.31607028147280[/C][/ROW]
[ROW][C]p-value[/C][C]0.245254619223176[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.160087557071577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28535&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28535&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-3.39636630503619
beta1.16008755707158
S.D.0.881478423609216
T-STAT1.31607028147280
p-value0.245254619223176
Lambda-0.160087557071577


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')