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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 computationThu, 17 Mar 2016 13:42:42 +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/2016/Mar/17/t1458222319q393j25p9v1kpih.htm/, Retrieved Sat, 04 May 2024 23:47:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294197, Retrieved Sat, 04 May 2024 23:47:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153

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] [] [2016-03-17 13:42:42] [c0f67b4e93ea0adf92c2b9d3976edd70] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
87,5
87,3
87,8
88,1
88,0
87,8
87,0
87,2
87,0
89,4
89,1
87,8
87,8
88,0
86,5
84,1
84,3
84,7
85,7
86,4
86,0
86,9
89,1
90,7
89,8
89,4
88,6
86,8
86,8
89,5
88,5
91,2
92,3
92,0
92,8
92,9
92,7
94,2
94,0
94,3
94,8
94,7
95,1
97,0
97,9
97,3
96,5
98,1
99,3
99,9
99,9
99,9
99,8
99,5
99,9
100,1
100,1
100,2
100,6
100,8
100,8
100,5
101,0
100,5
99,0
97,9
97,6
97,2
96,5
96,3
96,3
96,2
95,6
93,5
93,2
93,6
94,6
96,1
98,4
99,6
99,4
99,7
100,1
99,9

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=294197&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=294197&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294197&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
187.83333333333330.7595852137645242.40000000000001
286.68333333333331.973383496495916.60000000000001
390.052.180283551200716.10000000000001
495.551.744862589015385.39999999999999
51000.4134115273055291.5
698.31666666666671.935709094096974.8
796.9752.80523050422216.89999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 87.8333333333333 & 0.759585213764524 & 2.40000000000001 \tabularnewline
2 & 86.6833333333333 & 1.97338349649591 & 6.60000000000001 \tabularnewline
3 & 90.05 & 2.18028355120071 & 6.10000000000001 \tabularnewline
4 & 95.55 & 1.74486258901538 & 5.39999999999999 \tabularnewline
5 & 100 & 0.413411527305529 & 1.5 \tabularnewline
6 & 98.3166666666667 & 1.93570909409697 & 4.8 \tabularnewline
7 & 96.975 & 2.8052305042221 & 6.89999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294197&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]87.8333333333333[/C][C]0.759585213764524[/C][C]2.40000000000001[/C][/ROW]
[ROW][C]2[/C][C]86.6833333333333[/C][C]1.97338349649591[/C][C]6.60000000000001[/C][/ROW]
[ROW][C]3[/C][C]90.05[/C][C]2.18028355120071[/C][C]6.10000000000001[/C][/ROW]
[ROW][C]4[/C][C]95.55[/C][C]1.74486258901538[/C][C]5.39999999999999[/C][/ROW]
[ROW][C]5[/C][C]100[/C][C]0.413411527305529[/C][C]1.5[/C][/ROW]
[ROW][C]6[/C][C]98.3166666666667[/C][C]1.93570909409697[/C][C]4.8[/C][/ROW]
[ROW][C]7[/C][C]96.975[/C][C]2.8052305042221[/C][C]6.89999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294197&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294197&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
187.83333333333330.7595852137645242.40000000000001
286.68333333333331.973383496495916.60000000000001
390.052.180283551200716.10000000000001
495.551.744862589015385.39999999999999
51000.4134115273055291.5
698.31666666666671.935709094096974.8
796.9752.80523050422216.89999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.4900081240623
beta-0.00857113131864613
S.D.0.0691164646135936
T-STAT-0.124009978903932
p-value0.906138476716181

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.4900081240623 \tabularnewline
beta & -0.00857113131864613 \tabularnewline
S.D. & 0.0691164646135936 \tabularnewline
T-STAT & -0.124009978903932 \tabularnewline
p-value & 0.906138476716181 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294197&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.4900081240623[/C][/ROW]
[ROW][C]beta[/C][C]-0.00857113131864613[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0691164646135936[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.124009978903932[/C][/ROW]
[ROW][C]p-value[/C][C]0.906138476716181[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294197&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294197&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)
alpha2.4900081240623
beta-0.00857113131864613
S.D.0.0691164646135936
T-STAT-0.124009978903932
p-value0.906138476716181






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha9.481926157761
beta-2.00921971067224
S.D.5.23546724334117
T-STAT-0.383770849340659
p-value0.716925376827307
Lambda3.00921971067224

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 9.481926157761 \tabularnewline
beta & -2.00921971067224 \tabularnewline
S.D. & 5.23546724334117 \tabularnewline
T-STAT & -0.383770849340659 \tabularnewline
p-value & 0.716925376827307 \tabularnewline
Lambda & 3.00921971067224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294197&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.481926157761[/C][/ROW]
[ROW][C]beta[/C][C]-2.00921971067224[/C][/ROW]
[ROW][C]S.D.[/C][C]5.23546724334117[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.383770849340659[/C][/ROW]
[ROW][C]p-value[/C][C]0.716925376827307[/C][/ROW]
[ROW][C]Lambda[/C][C]3.00921971067224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294197&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294197&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)
alpha9.481926157761
beta-2.00921971067224
S.D.5.23546724334117
T-STAT-0.383770849340659
p-value0.716925376827307
Lambda3.00921971067224


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')