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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, 28 Apr 2017 12:28:10 +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/28/t1493379094eq5d66m0kmp52zq.htm/, Retrieved Fri, 10 May 2024 00:39:13 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 10 May 2024 00:39:13 +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 
90,36
90,67
91,21
91,35
91,62
91,28
91,17
91,13
91,55
91,62
91,73
91,91
92,5
92,93
92,77
93,42
93,82
94,02
94,13
93,7
93,84
94,22
95,03
95,03
95,25
96,11
96,16
96,1
96,52
96,35
96,35
96,66
96,86
97,84
98,04
98,06
98,79
99,38
99,75
100,4
100,97
101,16
100,42
99,88
99,8
99,78
99,78
99,89
100,38
100,1
100,02
101,15
100,02
99,99
100,14
98,93
98,52
98,42
98,78
99,04
99,53
99,97
99,95
101,68
101,29
101,45
100,98
100,64
100,6
101,59
101,15
101,03

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' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
191.30.4432934591318611.55
293.78416666666670.798902182353822.53
396.69166666666670.8712982302636742.81
41000.6534662820820832.36999999999999
599.62416666666670.8551497299339212.73
6100.8216666666670.6976041249530552.15000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 91.3 & 0.443293459131861 & 1.55 \tabularnewline
2 & 93.7841666666667 & 0.79890218235382 & 2.53 \tabularnewline
3 & 96.6916666666667 & 0.871298230263674 & 2.81 \tabularnewline
4 & 100 & 0.653466282082083 & 2.36999999999999 \tabularnewline
5 & 99.6241666666667 & 0.855149729933921 & 2.73 \tabularnewline
6 & 100.821666666667 & 0.697604124953055 & 2.15000000000001 \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]91.3[/C][C]0.443293459131861[/C][C]1.55[/C][/ROW]
[ROW][C]2[/C][C]93.7841666666667[/C][C]0.79890218235382[/C][C]2.53[/C][/ROW]
[ROW][C]3[/C][C]96.6916666666667[/C][C]0.871298230263674[/C][C]2.81[/C][/ROW]
[ROW][C]4[/C][C]100[/C][C]0.653466282082083[/C][C]2.36999999999999[/C][/ROW]
[ROW][C]5[/C][C]99.6241666666667[/C][C]0.855149729933921[/C][C]2.73[/C][/ROW]
[ROW][C]6[/C][C]100.821666666667[/C][C]0.697604124953055[/C][C]2.15000000000001[/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
191.30.4432934591318611.55
293.78416666666670.798902182353822.53
396.69166666666670.8712982302636742.81
41000.6534662820820832.36999999999999
599.62416666666670.8551497299339212.73
6100.8216666666670.6976041249530552.15000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.05967789097812
beta0.0183397182995946
S.D.0.0188363749468767
T-STAT0.973633108881999
p-value0.385370679240832

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.05967789097812 \tabularnewline
beta & 0.0183397182995946 \tabularnewline
S.D. & 0.0188363749468767 \tabularnewline
T-STAT & 0.973633108881999 \tabularnewline
p-value & 0.385370679240832 \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]-1.05967789097812[/C][/ROW]
[ROW][C]beta[/C][C]0.0183397182995946[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0188363749468767[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.973633108881999[/C][/ROW]
[ROW][C]p-value[/C][C]0.385370679240832[/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)
alpha-1.05967789097812
beta0.0183397182995946
S.D.0.0188363749468767
T-STAT0.973633108881999
p-value0.385370679240832






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-15.1089912025758
beta3.2257577357547
S.D.2.72545357494329
T-STAT1.18356730248902
p-value0.302117144313823
Lambda-2.2257577357547

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -15.1089912025758 \tabularnewline
beta & 3.2257577357547 \tabularnewline
S.D. & 2.72545357494329 \tabularnewline
T-STAT & 1.18356730248902 \tabularnewline
p-value & 0.302117144313823 \tabularnewline
Lambda & -2.2257577357547 \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]-15.1089912025758[/C][/ROW]
[ROW][C]beta[/C][C]3.2257577357547[/C][/ROW]
[ROW][C]S.D.[/C][C]2.72545357494329[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.18356730248902[/C][/ROW]
[ROW][C]p-value[/C][C]0.302117144313823[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.2257577357547[/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)
alpha-15.1089912025758
beta3.2257577357547
S.D.2.72545357494329
T-STAT1.18356730248902
p-value0.302117144313823
Lambda-2.2257577357547


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')