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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 computationSun, 23 Nov 2014 15:27:16 +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/2014/Nov/23/t1416756447r43juctuc3svcbk.htm/, Retrieved Sun, 19 May 2024 13:31:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=258026, Retrieved Sun, 19 May 2024 13:31:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73

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] [] [2014-11-23 15:27:16] [af43fcfc4e3257f4a3dbe682dec77e63] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
109.03
110.43
111.01
111.01
110.76
111.13
111.07
111.09
110.96
110.64
110.62
110.59
111.33
113.94
114.61
114.64
114.62
114.71
114.72
114.66
114.76
114.68
114.75
114.74
116.36
117.53
118.82
119.83
119.97
121.29
120.94
121.02
120.98
121.02
120.89
120.76
123.28
123.98
125.91
125.84
125.98
127.24
127.23
127.82
127.59
127.74
127.44
127.35
128.54
129.3
130.67
130.76
131.34
130.69
130.96
130.68
130.61
130.59
130.44
129.04
131.46
132.77
134.48
134.52
136.11
136.12
136.03
135.84
137.75
137.45
136.84
136.79
140.12
140.68
140.35
140.42
140.19
140.14
140.13
139.45
139.59
139.44
139.53
139.28

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=258026&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=258026&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258026&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
1110.6950.5737357643312172.09999999999999
2114.3466666666670.9753631802222873.43000000000001
3119.9508333333331.586943651020784.93000000000001
4126.451.504466078653214.53999999999999
5130.3016666666670.8553131625671442.80000000000001
6135.5133333333331.888984014241676.28999999999999
7139.9433333333330.4605596069078911.40000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 110.695 & 0.573735764331217 & 2.09999999999999 \tabularnewline
2 & 114.346666666667 & 0.975363180222287 & 3.43000000000001 \tabularnewline
3 & 119.950833333333 & 1.58694365102078 & 4.93000000000001 \tabularnewline
4 & 126.45 & 1.50446607865321 & 4.53999999999999 \tabularnewline
5 & 130.301666666667 & 0.855313162567144 & 2.80000000000001 \tabularnewline
6 & 135.513333333333 & 1.88898401424167 & 6.28999999999999 \tabularnewline
7 & 139.943333333333 & 0.460559606907891 & 1.40000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258026&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]110.695[/C][C]0.573735764331217[/C][C]2.09999999999999[/C][/ROW]
[ROW][C]2[/C][C]114.346666666667[/C][C]0.975363180222287[/C][C]3.43000000000001[/C][/ROW]
[ROW][C]3[/C][C]119.950833333333[/C][C]1.58694365102078[/C][C]4.93000000000001[/C][/ROW]
[ROW][C]4[/C][C]126.45[/C][C]1.50446607865321[/C][C]4.53999999999999[/C][/ROW]
[ROW][C]5[/C][C]130.301666666667[/C][C]0.855313162567144[/C][C]2.80000000000001[/C][/ROW]
[ROW][C]6[/C][C]135.513333333333[/C][C]1.88898401424167[/C][C]6.28999999999999[/C][/ROW]
[ROW][C]7[/C][C]139.943333333333[/C][C]0.460559606907891[/C][C]1.40000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258026&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258026&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
1110.6950.5737357643312172.09999999999999
2114.3466666666670.9753631802222873.43000000000001
3119.9508333333331.586943651020784.93000000000001
4126.451.504466078653214.53999999999999
5130.3016666666670.8553131625671442.80000000000001
6135.5133333333331.888984014241676.28999999999999
7139.9433333333330.4605596069078911.40000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.344326758522674
beta0.00619593363543941
S.D.0.0222773856794013
T-STAT0.278126604468156
p-value0.792049801413249

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.344326758522674 \tabularnewline
beta & 0.00619593363543941 \tabularnewline
S.D. & 0.0222773856794013 \tabularnewline
T-STAT & 0.278126604468156 \tabularnewline
p-value & 0.792049801413249 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258026&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.344326758522674[/C][/ROW]
[ROW][C]beta[/C][C]0.00619593363543941[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0222773856794013[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.278126604468156[/C][/ROW]
[ROW][C]p-value[/C][C]0.792049801413249[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258026&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258026&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)
alpha0.344326758522674
beta0.00619593363543941
S.D.0.0222773856794013
T-STAT0.278126604468156
p-value0.792049801413249






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.35062867267117
beta0.279600122537968
S.D.2.74532444802404
T-STAT0.101845930355959
p-value0.9228372162534
Lambda0.720399877462032

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.35062867267117 \tabularnewline
beta & 0.279600122537968 \tabularnewline
S.D. & 2.74532444802404 \tabularnewline
T-STAT & 0.101845930355959 \tabularnewline
p-value & 0.9228372162534 \tabularnewline
Lambda & 0.720399877462032 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258026&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.35062867267117[/C][/ROW]
[ROW][C]beta[/C][C]0.279600122537968[/C][/ROW]
[ROW][C]S.D.[/C][C]2.74532444802404[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.101845930355959[/C][/ROW]
[ROW][C]p-value[/C][C]0.9228372162534[/C][/ROW]
[ROW][C]Lambda[/C][C]0.720399877462032[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258026&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258026&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-1.35062867267117
beta0.279600122537968
S.D.2.74532444802404
T-STAT0.101845930355959
p-value0.9228372162534
Lambda0.720399877462032


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')