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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, 12 Mar 2015 11:33:14 +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/12/t1426160117hgoy4y6rddog3b2.htm/, Retrieved Sun, 19 May 2024 16:09:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278262, Retrieved Sun, 19 May 2024 16:09:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115

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] [] [2015-03-12 11:33:14] [8a8c4bd73c288c653fbb494901d06130] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2
2.2
1.9
2.3
2.2
2.3
2.1
2.4
2.3
1.9
1.6
1.8
1.8
2
2.3
2.2
2.2
2
2
1.9
1.5
1.6
1.5
2
1.5
1.5
1.9
1.1
1.5
2.1
2.3
2.6
2.9
3.2
3.2
3.1
3
3.3
2.7
3.6
3.1
2.7
2.6
2.2
2.7
2.1
1.8
1.7
1.7
1.2
1.2
1.2
1.5
1.3
1.1
1.2
1.3
1.6
1.9
1.6
2.1
2.2
2.3
2.1
1.7
1.7
2.2
2
1.5
1.5
1.7
2.2
2.6
2.6
2.3
2.3
2.7
2.7
2.5
2.5
2.7
2.6
2.6
2.4
1.4
1.8
2.1
1.7
1.6
1.7
1.8
2
1.9
2
2.1
2.3

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=278262&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=278262&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278262&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
12.083333333333330.2443296332763790.8
21.916666666666670.2691175253012010.8
32.241666666666670.7525210155124432.1
42.6250.5863988713867351.9
51.40.2522624895547560.8
61.933333333333330.2933608802492350.8
72.541666666666670.1443375672974070.4
81.866666666666670.2498484389069550.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2.08333333333333 & 0.244329633276379 & 0.8 \tabularnewline
2 & 1.91666666666667 & 0.269117525301201 & 0.8 \tabularnewline
3 & 2.24166666666667 & 0.752521015512443 & 2.1 \tabularnewline
4 & 2.625 & 0.586398871386735 & 1.9 \tabularnewline
5 & 1.4 & 0.252262489554756 & 0.8 \tabularnewline
6 & 1.93333333333333 & 0.293360880249235 & 0.8 \tabularnewline
7 & 2.54166666666667 & 0.144337567297407 & 0.4 \tabularnewline
8 & 1.86666666666667 & 0.249848438906955 & 0.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278262&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]2.08333333333333[/C][C]0.244329633276379[/C][C]0.8[/C][/ROW]
[ROW][C]2[/C][C]1.91666666666667[/C][C]0.269117525301201[/C][C]0.8[/C][/ROW]
[ROW][C]3[/C][C]2.24166666666667[/C][C]0.752521015512443[/C][C]2.1[/C][/ROW]
[ROW][C]4[/C][C]2.625[/C][C]0.586398871386735[/C][C]1.9[/C][/ROW]
[ROW][C]5[/C][C]1.4[/C][C]0.252262489554756[/C][C]0.8[/C][/ROW]
[ROW][C]6[/C][C]1.93333333333333[/C][C]0.293360880249235[/C][C]0.8[/C][/ROW]
[ROW][C]7[/C][C]2.54166666666667[/C][C]0.144337567297407[/C][C]0.4[/C][/ROW]
[ROW][C]8[/C][C]1.86666666666667[/C][C]0.249848438906955[/C][C]0.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278262&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278262&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
12.083333333333330.2443296332763790.8
21.916666666666670.2691175253012010.8
32.241666666666670.7525210155124432.1
42.6250.5863988713867351.9
51.40.2522624895547560.8
61.933333333333330.2933608802492350.8
72.541666666666670.1443375672974070.4
81.866666666666670.2498484389069550.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.0461713049345319
beta0.190359068397072
S.D.0.199605794036188
T-STAT0.953675063974144
p-value0.377072603571375

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0461713049345319 \tabularnewline
beta & 0.190359068397072 \tabularnewline
S.D. & 0.199605794036188 \tabularnewline
T-STAT & 0.953675063974144 \tabularnewline
p-value & 0.377072603571375 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278262&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0461713049345319[/C][/ROW]
[ROW][C]beta[/C][C]0.190359068397072[/C][/ROW]
[ROW][C]S.D.[/C][C]0.199605794036188[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.953675063974144[/C][/ROW]
[ROW][C]p-value[/C][C]0.377072603571375[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278262&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278262&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-0.0461713049345319
beta0.190359068397072
S.D.0.199605794036188
T-STAT0.953675063974144
p-value0.377072603571375






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.64557751125192
beta0.647784282844155
S.D.1.04762394887246
T-STAT0.618336649845923
p-value0.559079351337219
Lambda0.352215717155845

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.64557751125192 \tabularnewline
beta & 0.647784282844155 \tabularnewline
S.D. & 1.04762394887246 \tabularnewline
T-STAT & 0.618336649845923 \tabularnewline
p-value & 0.559079351337219 \tabularnewline
Lambda & 0.352215717155845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278262&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.64557751125192[/C][/ROW]
[ROW][C]beta[/C][C]0.647784282844155[/C][/ROW]
[ROW][C]S.D.[/C][C]1.04762394887246[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.618336649845923[/C][/ROW]
[ROW][C]p-value[/C][C]0.559079351337219[/C][/ROW]
[ROW][C]Lambda[/C][C]0.352215717155845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278262&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278262&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-1.64557751125192
beta0.647784282844155
S.D.1.04762394887246
T-STAT0.618336649845923
p-value0.559079351337219
Lambda0.352215717155845


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')