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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 computationWed, 11 Mar 2015 09:53:48 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Mar/11/t1426068042oo6xpgl97opydat.htm/, Retrieved Sun, 19 May 2024 15:40:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278163, Retrieved Sun, 19 May 2024 15:40:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123

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] [] [2015-03-11 09:53:48] [10a961572d82585f4ece1fe77e85ff9b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
96.86
96.89
96.9
96.94
96.88
96.89
96.89
96.95
97.03
97.29
97.37
97.41
97.41
97.32
97.33
97.38
97.47
97.5
97.5
97.58
97.7
97.9
97.98
98.03
98.03
97.94
98.12
98.19
98.34
98.42
98.43
98.45
98.77
99.24
99.46
99.54
99.55
99.24
99.43
99.47
99.57
99.62
99.64
99.75
99.85
100.28
100.52
100.57
100.57
100.27
100.27
100.18
100.16
100.18
100.18
100.59
100.69
101.06
101.15
101.16
101.16
100.81
100.94
101.13
101.29
101.34
101.35
101.7
102.05
102.48
102.66
102.72
102.73
102.18
102.22
102.37
102.53
102.61
102.62
103
103.17
103.52
103.69
103.73
99.57
99.09
99.14
99.36
99.6
99.65
99.8
100.15
100.45
100.89
101.13
101.17

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278163&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278163&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278163&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
197.0250.2064637322322570.549999999999997
297.59166666666670.252544625519510.710000000000008
398.57750.5531747216994571.60000000000001
499.79083333333330.4346881501476511.33
5100.5383333333330.396778695664641
6101.6358333333330.6775552085299471.91
7102.8641666666670.5522591343881511.55
81000.7475779071593322.08

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 97.025 & 0.206463732232257 & 0.549999999999997 \tabularnewline
2 & 97.5916666666667 & 0.25254462551951 & 0.710000000000008 \tabularnewline
3 & 98.5775 & 0.553174721699457 & 1.60000000000001 \tabularnewline
4 & 99.7908333333333 & 0.434688150147651 & 1.33 \tabularnewline
5 & 100.538333333333 & 0.39677869566464 & 1 \tabularnewline
6 & 101.635833333333 & 0.677555208529947 & 1.91 \tabularnewline
7 & 102.864166666667 & 0.552259134388151 & 1.55 \tabularnewline
8 & 100 & 0.747577907159332 & 2.08 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278163&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]97.025[/C][C]0.206463732232257[/C][C]0.549999999999997[/C][/ROW]
[ROW][C]2[/C][C]97.5916666666667[/C][C]0.25254462551951[/C][C]0.710000000000008[/C][/ROW]
[ROW][C]3[/C][C]98.5775[/C][C]0.553174721699457[/C][C]1.60000000000001[/C][/ROW]
[ROW][C]4[/C][C]99.7908333333333[/C][C]0.434688150147651[/C][C]1.33[/C][/ROW]
[ROW][C]5[/C][C]100.538333333333[/C][C]0.39677869566464[/C][C]1[/C][/ROW]
[ROW][C]6[/C][C]101.635833333333[/C][C]0.677555208529947[/C][C]1.91[/C][/ROW]
[ROW][C]7[/C][C]102.864166666667[/C][C]0.552259134388151[/C][C]1.55[/C][/ROW]
[ROW][C]8[/C][C]100[/C][C]0.747577907159332[/C][C]2.08[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278163&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278163&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
197.0250.2064637322322570.549999999999997
297.59166666666670.252544625519510.710000000000008
398.57750.5531747216994571.60000000000001
499.79083333333330.4346881501476511.33
5100.5383333333330.396778695664641
6101.6358333333330.6775552085299471.91
7102.8641666666670.5522591343881511.55
81000.7475779071593322.08






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-5.88496586678469
beta0.0637835599330243
S.D.0.0297222613659836
T-STAT2.14598610609161
p-value0.0755235892329333

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -5.88496586678469 \tabularnewline
beta & 0.0637835599330243 \tabularnewline
S.D. & 0.0297222613659836 \tabularnewline
T-STAT & 2.14598610609161 \tabularnewline
p-value & 0.0755235892329333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278163&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.88496586678469[/C][/ROW]
[ROW][C]beta[/C][C]0.0637835599330243[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0297222613659836[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.14598610609161[/C][/ROW]
[ROW][C]p-value[/C][C]0.0755235892329333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278163&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278163&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-5.88496586678469
beta0.0637835599330243
S.D.0.0297222613659836
T-STAT2.14598610609161
p-value0.0755235892329333






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-77.7773008858321
beta16.7202022459612
S.D.6.48706412748013
T-STAT2.57746831500124
p-value0.0419118723073717
Lambda-15.7202022459612

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -77.7773008858321 \tabularnewline
beta & 16.7202022459612 \tabularnewline
S.D. & 6.48706412748013 \tabularnewline
T-STAT & 2.57746831500124 \tabularnewline
p-value & 0.0419118723073717 \tabularnewline
Lambda & -15.7202022459612 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278163&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-77.7773008858321[/C][/ROW]
[ROW][C]beta[/C][C]16.7202022459612[/C][/ROW]
[ROW][C]S.D.[/C][C]6.48706412748013[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.57746831500124[/C][/ROW]
[ROW][C]p-value[/C][C]0.0419118723073717[/C][/ROW]
[ROW][C]Lambda[/C][C]-15.7202022459612[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278163&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278163&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-77.7773008858321
beta16.7202022459612
S.D.6.48706412748013
T-STAT2.57746831500124
p-value0.0419118723073717
Lambda-15.7202022459612


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')