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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, 19 Dec 2009 08:08:37 -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/19/t1261235384csraxy7pyinf7gy.htm/, Retrieved Fri, 03 May 2024 17:10:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69625, Retrieved Fri, 03 May 2024 17:10:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

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] [] [2009-12-19 15:08:37] [df67ec12d4744494b58d8461e1971283] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
110,3
103,9
101,6
94,6
95,9
104,7
102,8
98,1
119,9
80,9
95,7
113,2
105,9
108,8
102,3
99
100,7
115,5
100,7
109,9
114,6
85,4
100,5
114,8
116,5
112,9
102
106
105,3
118,8
106,1
109,3
117,2
92,5
104,2
112,2
122,4
113,1
100
110,7
112,8
109,8
117,3
109,1
115,9
96
99,8
116,8
115,7
99,4
94,3
91
93,2
103,1
94,1
91,8
102,7
82,6
89,1
104,5

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=69625&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=69625&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69625&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
1101.810.081666528902839
2104.8416666666678.6449626250134130.1
3108.5833333333337.4977370323358626.3
4110.3083333333338.0101592690252726.4
596.79166666666678.7585239866225433.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 101.8 & 10.0816665289028 & 39 \tabularnewline
2 & 104.841666666667 & 8.64496262501341 & 30.1 \tabularnewline
3 & 108.583333333333 & 7.49773703233586 & 26.3 \tabularnewline
4 & 110.308333333333 & 8.01015926902527 & 26.4 \tabularnewline
5 & 96.7916666666667 & 8.75852398662254 & 33.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69625&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]101.8[/C][C]10.0816665289028[/C][C]39[/C][/ROW]
[ROW][C]2[/C][C]104.841666666667[/C][C]8.64496262501341[/C][C]30.1[/C][/ROW]
[ROW][C]3[/C][C]108.583333333333[/C][C]7.49773703233586[/C][C]26.3[/C][/ROW]
[ROW][C]4[/C][C]110.308333333333[/C][C]8.01015926902527[/C][C]26.4[/C][/ROW]
[ROW][C]5[/C][C]96.7916666666667[/C][C]8.75852398662254[/C][C]33.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69625&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69625&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
1101.810.081666528902839
2104.8416666666678.6449626250134130.1
3108.5833333333337.4977370323358626.3
4110.3083333333338.0101592690252726.4
596.79166666666678.7585239866225433.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha20.3027414826687
beta-0.112038784227145
S.D.0.0811123257347942
T-STAT-1.38127939511275
p-value0.261095267556751

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 20.3027414826687 \tabularnewline
beta & -0.112038784227145 \tabularnewline
S.D. & 0.0811123257347942 \tabularnewline
T-STAT & -1.38127939511275 \tabularnewline
p-value & 0.261095267556751 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69625&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]20.3027414826687[/C][/ROW]
[ROW][C]beta[/C][C]-0.112038784227145[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0811123257347942[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.38127939511275[/C][/ROW]
[ROW][C]p-value[/C][C]0.261095267556751[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69625&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69625&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)
alpha20.3027414826687
beta-0.112038784227145
S.D.0.0811123257347942
T-STAT-1.38127939511275
p-value0.261095267556751






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha8.37658214571886
beta-1.34042419063867
S.D.0.95037659543428
T-STAT-1.41041372133765
p-value0.253223242416548
Lambda2.34042419063867

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 8.37658214571886 \tabularnewline
beta & -1.34042419063867 \tabularnewline
S.D. & 0.95037659543428 \tabularnewline
T-STAT & -1.41041372133765 \tabularnewline
p-value & 0.253223242416548 \tabularnewline
Lambda & 2.34042419063867 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69625&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.37658214571886[/C][/ROW]
[ROW][C]beta[/C][C]-1.34042419063867[/C][/ROW]
[ROW][C]S.D.[/C][C]0.95037659543428[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.41041372133765[/C][/ROW]
[ROW][C]p-value[/C][C]0.253223242416548[/C][/ROW]
[ROW][C]Lambda[/C][C]2.34042419063867[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69625&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69625&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)
alpha8.37658214571886
beta-1.34042419063867
S.D.0.95037659543428
T-STAT-1.41041372133765
p-value0.253223242416548
Lambda2.34042419063867


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')