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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 computationSat, 22 Apr 2017 22:08:33 +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/22/t14928955380b11g0s87kycbrd.htm/, Retrieved Mon, 13 May 2024 13:10:41 +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 13:10:41 +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 
91.16
91.17
91.17
91.38
92.68
92.72
92.79
92.81
92.81
92.81
92.81
92.81
92.81
92.82
92.82
92.88
93.38
93.89
94.1
94.18
94.3
94.31
94.36
94.38
94.38
94.5
94.57
94.89
96.71
97.57
97.88
97.97
98.4
98.51
98.46
98.46
98.48
98.6
98.6
98.71
99.13
99.2
99.3
100.18
101.37
101.77
102.28
102.38
102.35
103.23
105.37
106.62
107
107.24
107.31
107.35
107.42
107.58
107.64
107.64
107.68
108.51
110.37
111.31
111.57
111.66
111.69
111.9
111.95
112.04
112.13
112.14

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'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 & 1 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]1 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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
192.260.7711856279309641.65000000000001
293.68583333333330.6855582772566851.56999999999999
396.85833333333331.754427300151014.13000000000001
41001.528112323334673.89999999999999
5106.3958333333331.805665117111015.29000000000001
6111.0791666666671.484694387489364.45999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 92.26 & 0.771185627930964 & 1.65000000000001 \tabularnewline
2 & 93.6858333333333 & 0.685558277256685 & 1.56999999999999 \tabularnewline
3 & 96.8583333333333 & 1.75442730015101 & 4.13000000000001 \tabularnewline
4 & 100 & 1.52811232333467 & 3.89999999999999 \tabularnewline
5 & 106.395833333333 & 1.80566511711101 & 5.29000000000001 \tabularnewline
6 & 111.079166666667 & 1.48469438748936 & 4.45999999999999 \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]92.26[/C][C]0.771185627930964[/C][C]1.65000000000001[/C][/ROW]
[ROW][C]2[/C][C]93.6858333333333[/C][C]0.685558277256685[/C][C]1.56999999999999[/C][/ROW]
[ROW][C]3[/C][C]96.8583333333333[/C][C]1.75442730015101[/C][C]4.13000000000001[/C][/ROW]
[ROW][C]4[/C][C]100[/C][C]1.52811232333467[/C][C]3.89999999999999[/C][/ROW]
[ROW][C]5[/C][C]106.395833333333[/C][C]1.80566511711101[/C][C]5.29000000000001[/C][/ROW]
[ROW][C]6[/C][C]111.079166666667[/C][C]1.48469438748936[/C][C]4.45999999999999[/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
192.260.7711856279309641.65000000000001
293.68583333333330.6855582772566851.56999999999999
396.85833333333331.754427300151014.13000000000001
41001.528112323334673.89999999999999
5106.3958333333331.805665117111015.29000000000001
6111.0791666666671.484694387489364.45999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.98693389207183
beta0.0432319624380956
S.D.0.0250502007686177
T-STAT1.72581301193624
p-value0.159461664702694

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.98693389207183 \tabularnewline
beta & 0.0432319624380956 \tabularnewline
S.D. & 0.0250502007686177 \tabularnewline
T-STAT & 1.72581301193624 \tabularnewline
p-value & 0.159461664702694 \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]-2.98693389207183[/C][/ROW]
[ROW][C]beta[/C][C]0.0432319624380956[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0250502007686177[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.72581301193624[/C][/ROW]
[ROW][C]p-value[/C][C]0.159461664702694[/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-2.98693389207183
beta0.0432319624380956
S.D.0.0250502007686177
T-STAT1.72581301193624
p-value0.159461664702694






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-18.4722759156597
beta4.06108074356279
S.D.2.11188957803344
T-STAT1.92296073895322
p-value0.126838492216509
Lambda-3.06108074356279

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -18.4722759156597 \tabularnewline
beta & 4.06108074356279 \tabularnewline
S.D. & 2.11188957803344 \tabularnewline
T-STAT & 1.92296073895322 \tabularnewline
p-value & 0.126838492216509 \tabularnewline
Lambda & -3.06108074356279 \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]-18.4722759156597[/C][/ROW]
[ROW][C]beta[/C][C]4.06108074356279[/C][/ROW]
[ROW][C]S.D.[/C][C]2.11188957803344[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.92296073895322[/C][/ROW]
[ROW][C]p-value[/C][C]0.126838492216509[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.06108074356279[/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-18.4722759156597
beta4.06108074356279
S.D.2.11188957803344
T-STAT1.92296073895322
p-value0.126838492216509
Lambda-3.06108074356279


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')