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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 computationMon, 09 Jan 2017 10:07:52 +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/2017/Jan/09/t1483956489c7b10pz6q194gh1.htm/, Retrieved Tue, 14 May 2024 10:58:34 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 10:58:34 +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 
94.46
96.91
101.92
104.53
105.85
106.39
106.08
106.42
106.51
106.59
105.71
104.41
103.04
100.99
100.93
99.31
99.79
99.57
99.11
98.96
97.72
99.35
98.15
97.64
97.49
97.94
98.03
98.05
97.54
98.71
99.33
99.16
98.41
98.43
97.02
97.89
97.92
97.37
97.42
96.12
96.72
96.64
95.28
95.3
95.02
95.57
94.78
95.27
96.14
96.16
95.08
94.39
94.15
94.58
94.16
95.02
94.86
94.49
94.81
94.16
94.83
96.02
95.97
95.88
95.97
97.55
97.49
98.4
98.2
97.16
96.96
96.37
96.34
96.86
96.32
95.44
92.85
92.56
91.74
92.44
93.19
92.62
94.04
93.8
96.73
98.99
100.38
101.07
99.92
101.78
100.91
100.49
101.17
100.25
98.94
99.4
100.02
99.91
99.22
98.84
98.42
97.59
97.07
96.59
95.96
94.22
94.48
93.14
93.73
94.24
98.52
99.09
99.84
99.13
100.88
100.83
101.6
101.8
102.77
103.14

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'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=&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=&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1103.8154.055233431236512.13
299.54666666666671.531851721600275.40000000000001
398.16666666666670.6802049601986062.31
496.11751.067342707168353.14
594.83333333333330.6952217871538072.00999999999999
696.73333333333331.068510716612223.57000000000001
794.01666666666671.774753930873665.12
8100.00251.353790134131855.05
997.12166666666672.302614456076696.88
1099.63083333333333.006839048004749.41

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 103.815 & 4.0552334312365 & 12.13 \tabularnewline
2 & 99.5466666666667 & 1.53185172160027 & 5.40000000000001 \tabularnewline
3 & 98.1666666666667 & 0.680204960198606 & 2.31 \tabularnewline
4 & 96.1175 & 1.06734270716835 & 3.14 \tabularnewline
5 & 94.8333333333333 & 0.695221787153807 & 2.00999999999999 \tabularnewline
6 & 96.7333333333333 & 1.06851071661222 & 3.57000000000001 \tabularnewline
7 & 94.0166666666667 & 1.77475393087366 & 5.12 \tabularnewline
8 & 100.0025 & 1.35379013413185 & 5.05 \tabularnewline
9 & 97.1216666666667 & 2.30261445607669 & 6.88 \tabularnewline
10 & 99.6308333333333 & 3.00683904800474 & 9.41 \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]103.815[/C][C]4.0552334312365[/C][C]12.13[/C][/ROW]
[ROW][C]2[/C][C]99.5466666666667[/C][C]1.53185172160027[/C][C]5.40000000000001[/C][/ROW]
[ROW][C]3[/C][C]98.1666666666667[/C][C]0.680204960198606[/C][C]2.31[/C][/ROW]
[ROW][C]4[/C][C]96.1175[/C][C]1.06734270716835[/C][C]3.14[/C][/ROW]
[ROW][C]5[/C][C]94.8333333333333[/C][C]0.695221787153807[/C][C]2.00999999999999[/C][/ROW]
[ROW][C]6[/C][C]96.7333333333333[/C][C]1.06851071661222[/C][C]3.57000000000001[/C][/ROW]
[ROW][C]7[/C][C]94.0166666666667[/C][C]1.77475393087366[/C][C]5.12[/C][/ROW]
[ROW][C]8[/C][C]100.0025[/C][C]1.35379013413185[/C][C]5.05[/C][/ROW]
[ROW][C]9[/C][C]97.1216666666667[/C][C]2.30261445607669[/C][C]6.88[/C][/ROW]
[ROW][C]10[/C][C]99.6308333333333[/C][C]3.00683904800474[/C][C]9.41[/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
1103.8154.055233431236512.13
299.54666666666671.531851721600275.40000000000001
398.16666666666670.6802049601986062.31
496.11751.067342707168353.14
594.83333333333330.6952217871538072.00999999999999
696.73333333333331.068510716612223.57000000000001
794.01666666666671.774753930873665.12
8100.00251.353790134131855.05
997.12166666666672.302614456076696.88
1099.63083333333333.006839048004749.41






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-23.2318897346036
beta0.254958466409671
S.D.0.0979481479142456
T-STAT2.60299425603115
p-value0.031471027836894

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -23.2318897346036 \tabularnewline
beta & 0.254958466409671 \tabularnewline
S.D. & 0.0979481479142456 \tabularnewline
T-STAT & 2.60299425603115 \tabularnewline
p-value & 0.031471027836894 \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]-23.2318897346036[/C][/ROW]
[ROW][C]beta[/C][C]0.254958466409671[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0979481479142456[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.60299425603115[/C][/ROW]
[ROW][C]p-value[/C][C]0.031471027836894[/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-23.2318897346036
beta0.254958466409671
S.D.0.0979481479142456
T-STAT2.60299425603115
p-value0.031471027836894






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-54.0160044690005
beta11.8698392805585
S.D.5.79307100038604
T-STAT2.04897182854613
p-value0.0746272119000249
Lambda-10.8698392805585

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -54.0160044690005 \tabularnewline
beta & 11.8698392805585 \tabularnewline
S.D. & 5.79307100038604 \tabularnewline
T-STAT & 2.04897182854613 \tabularnewline
p-value & 0.0746272119000249 \tabularnewline
Lambda & -10.8698392805585 \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]-54.0160044690005[/C][/ROW]
[ROW][C]beta[/C][C]11.8698392805585[/C][/ROW]
[ROW][C]S.D.[/C][C]5.79307100038604[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.04897182854613[/C][/ROW]
[ROW][C]p-value[/C][C]0.0746272119000249[/C][/ROW]
[ROW][C]Lambda[/C][C]-10.8698392805585[/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-54.0160044690005
beta11.8698392805585
S.D.5.79307100038604
T-STAT2.04897182854613
p-value0.0746272119000249
Lambda-10.8698392805585


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')