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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 computationThu, 22 Nov 2007 05:42:00 -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/2007/Nov/22/t1195734898tiamstgmw9purhb.htm/, Retrieved Fri, 03 May 2024 00:59:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5947, Retrieved Fri, 03 May 2024 00:59:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact196

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] [WS 7 Q1 G6 machin...] [2007-11-22 12:42:00] [fef19078983b9fa83d10cb717d6f9786] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105,1
113,3
99,1
100,3
93,5
98,8
106,2
98,3
102,1
117,1
101,5
80,5
105,9
109,5
97,2
114,5
93,5
100,9
121,1
116,5
109,3
118,1
108,3
105,4
116,2
111,2
105,8
122,7
99,5
107,9
124,6
115
110,3
132,7
99,7
96,5
118,7
112,9
130,5
137,9
115
116,8
140,9
120,7
134,2
147,3
112,4
107,1
128,4
137,7
135
151
137,4
132,4
161,3
139,8
146
154,6
142,1
120,5

Tables (Output of Computation)





Summary of compuational 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 compuational 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=5947&T=0

[TABLE]
[ROW][C]Summary of compuational 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=5947&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5947&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 compuational 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
1101.3166666666679.2801678406974512
2108.358.4161641014073711.6
3111.84166666666711.015068879686735.5
4124.53333333333313.072478608500347
5140.51666666666711.420542363600267.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 101.316666666667 & 9.28016784069745 & 12 \tabularnewline
2 & 108.35 & 8.41616410140737 & 11.6 \tabularnewline
3 & 111.841666666667 & 11.0150688796867 & 35.5 \tabularnewline
4 & 124.533333333333 & 13.0724786085003 & 47 \tabularnewline
5 & 140.516666666667 & 11.4205423636002 & 67.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5947&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]101.316666666667[/C][C]9.28016784069745[/C][C]12[/C][/ROW]
[ROW][C]2[/C][C]108.35[/C][C]8.41616410140737[/C][C]11.6[/C][/ROW]
[ROW][C]3[/C][C]111.841666666667[/C][C]11.0150688796867[/C][C]35.5[/C][/ROW]
[ROW][C]4[/C][C]124.533333333333[/C][C]13.0724786085003[/C][C]47[/C][/ROW]
[ROW][C]5[/C][C]140.516666666667[/C][C]11.4205423636002[/C][C]67.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5947&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5947&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
1101.3166666666679.2801678406974512
2108.358.4161641014073711.6
3111.84166666666711.015068879686735.5
4124.53333333333313.072478608500347
5140.51666666666711.420542363600267.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.40659789460632
beta0.0787158406879573
S.D.0.0512334051818215
T-STAT1.53641633634547
p-value0.222022288619541

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.40659789460632 \tabularnewline
beta & 0.0787158406879573 \tabularnewline
S.D. & 0.0512334051818215 \tabularnewline
T-STAT & 1.53641633634547 \tabularnewline
p-value & 0.222022288619541 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5947&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.40659789460632[/C][/ROW]
[ROW][C]beta[/C][C]0.0787158406879573[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0512334051818215[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.53641633634547[/C][/ROW]
[ROW][C]p-value[/C][C]0.222022288619541[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5947&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5947&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)
alpha1.40659789460632
beta0.0787158406879573
S.D.0.0512334051818215
T-STAT1.53641633634547
p-value0.222022288619541






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.09511429322234
beta0.934772181632538
S.D.0.568010874797172
T-STAT1.64569416380686
p-value0.198378466784975
Lambda0.0652278183674616

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.09511429322234 \tabularnewline
beta & 0.934772181632538 \tabularnewline
S.D. & 0.568010874797172 \tabularnewline
T-STAT & 1.64569416380686 \tabularnewline
p-value & 0.198378466784975 \tabularnewline
Lambda & 0.0652278183674616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5947&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.09511429322234[/C][/ROW]
[ROW][C]beta[/C][C]0.934772181632538[/C][/ROW]
[ROW][C]S.D.[/C][C]0.568010874797172[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.64569416380686[/C][/ROW]
[ROW][C]p-value[/C][C]0.198378466784975[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0652278183674616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5947&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5947&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-2.09511429322234
beta0.934772181632538
S.D.0.568010874797172
T-STAT1.64569416380686
p-value0.198378466784975
Lambda0.0652278183674616


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')