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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 computationFri, 21 Apr 2017 15:47:33 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Apr/21/t1492786072148q6f9j1zvca7p.htm/, Retrieved Mon, 13 May 2024 19:55:19 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 13 May 2024 19:55:19 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
70,3
90,2
107,3
104,6
102,7
124,5
117,8
104,2
99,9
91,5
95,7
91,4
86,2
91,5
115,5
113,9
131,9
121,2
105,2
107,5
113,8
100,5
104,8
103,8
93,1
106,2
117,5
109,9
123,6
139,3
111
122
110,9
108
103,7
107,3
92
83,4
110,7
109
121,3
121,4
129,9
109,7
113,1
109,4
101
109
92,8
91,1
114,5
118,6
120,2
135,9
122,8
106
118,1
108,9
97,3
113,9
88,3
88,3
114,6
118,8
111,9
130,1
124,3
112,2
110
105,8
105,1
106,7

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'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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1100.00833333333314.01073992811754.2
2107.98333333333312.467618664023845.7
3112.70833333333311.710636837999746.2
4109.15833333333312.685959191407746.5
5111.67513.182641823797944.8
6109.67512.463045374225441.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100.008333333333 & 14.010739928117 & 54.2 \tabularnewline
2 & 107.983333333333 & 12.4676186640238 & 45.7 \tabularnewline
3 & 112.708333333333 & 11.7106368379997 & 46.2 \tabularnewline
4 & 109.158333333333 & 12.6859591914077 & 46.5 \tabularnewline
5 & 111.675 & 13.1826418237979 & 44.8 \tabularnewline
6 & 109.675 & 12.4630453742254 & 41.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]100.008333333333[/C][C]14.010739928117[/C][C]54.2[/C][/ROW]
[ROW][C]2[/C][C]107.983333333333[/C][C]12.4676186640238[/C][C]45.7[/C][/ROW]
[ROW][C]3[/C][C]112.708333333333[/C][C]11.7106368379997[/C][C]46.2[/C][/ROW]
[ROW][C]4[/C][C]109.158333333333[/C][C]12.6859591914077[/C][C]46.5[/C][/ROW]
[ROW][C]5[/C][C]111.675[/C][C]13.1826418237979[/C][C]44.8[/C][/ROW]
[ROW][C]6[/C][C]109.675[/C][C]12.4630453742254[/C][C]41.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1100.00833333333314.01073992811754.2
2107.98333333333312.467618664023845.7
3112.70833333333311.710636837999746.2
4109.15833333333312.685959191407746.5
5111.67513.182641823797944.8
6109.67512.463045374225441.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha27.5907722794155
beta-0.136705854793405
S.D.0.0523377869509378
T-STAT-2.611991502842
p-value0.0592957935064165

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 27.5907722794155 \tabularnewline
beta & -0.136705854793405 \tabularnewline
S.D. & 0.0523377869509378 \tabularnewline
T-STAT & -2.611991502842 \tabularnewline
p-value & 0.0592957935064165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]27.5907722794155[/C][/ROW]
[ROW][C]beta[/C][C]-0.136705854793405[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0523377869509378[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.611991502842[/C][/ROW]
[ROW][C]p-value[/C][C]0.0592957935064165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)
alpha27.5907722794155
beta-0.136705854793405
S.D.0.0523377869509378
T-STAT-2.611991502842
p-value0.0592957935064165






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha7.76326605584014
beta-1.11366504109583
S.D.0.438304796023705
T-STAT-2.540846121692
p-value0.0639234350825356
Lambda2.11366504109583

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.76326605584014 \tabularnewline
beta & -1.11366504109583 \tabularnewline
S.D. & 0.438304796023705 \tabularnewline
T-STAT & -2.540846121692 \tabularnewline
p-value & 0.0639234350825356 \tabularnewline
Lambda & 2.11366504109583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.76326605584014[/C][/ROW]
[ROW][C]beta[/C][C]-1.11366504109583[/C][/ROW]
[ROW][C]S.D.[/C][C]0.438304796023705[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.540846121692[/C][/ROW]
[ROW][C]p-value[/C][C]0.0639234350825356[/C][/ROW]
[ROW][C]Lambda[/C][C]2.11366504109583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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)
alpha7.76326605584014
beta-1.11366504109583
S.D.0.438304796023705
T-STAT-2.540846121692
p-value0.0639234350825356
Lambda2.11366504109583


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')