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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, 26 May 2012 07:15:14 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/26/t1338030944kv9e3rfhbhxg9wh.htm/, Retrieved Thu, 02 May 2024 14:31:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167577, Retrieved Thu, 02 May 2024 14:31:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact112

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] [jens vanpachtenbe...] [2012-05-26 11:15:14] [4080e77d9380e2af46712fd05e0afa1e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.31
2.31
2.32
2.33
2.34
2.36
2.37
2.37
2.38
2.39
2.4
2.4
2.39
2.4
2.42
2.42
2.44
2.44
2.44
2.45
2.46
2.47
2.48
2.48
2.49
2.5
2.51
2.52
2.52
2.52
2.54
2.54
2.54
2.56
2.57
2.58
2.58
2.58
2.58
2.59
2.6
2.61
2.61
2.62
2.63
2.65
2.67
2.68
2.67
2.68
2.68
2.68
2.68
2.69
2.69
2.69
2.7
2.71
2.72
2.71
2.72
2.73
2.74
2.74
2.75
2.75
2.76
2.75
2.78
2.79
2.8
2.81
2.81
2.82
2.82
2.83
2.83
2.84
2.84
2.84
2.86
2.87
2.88
2.88

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167577&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167577&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167577&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'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12.356666666666670.03366501646120690.0899999999999999
22.440833333333330.02937479851639480.0899999999999999
32.53250.02767506261797960.0899999999999999
42.616666666666670.03472838329177740.1
52.691666666666670.01527525231651950.0500000000000003
62.760.02860387767736770.0899999999999999
72.843333333333330.02386832565759420.0699999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2.35666666666667 & 0.0336650164612069 & 0.0899999999999999 \tabularnewline
2 & 2.44083333333333 & 0.0293747985163948 & 0.0899999999999999 \tabularnewline
3 & 2.5325 & 0.0276750626179796 & 0.0899999999999999 \tabularnewline
4 & 2.61666666666667 & 0.0347283832917774 & 0.1 \tabularnewline
5 & 2.69166666666667 & 0.0152752523165195 & 0.0500000000000003 \tabularnewline
6 & 2.76 & 0.0286038776773677 & 0.0899999999999999 \tabularnewline
7 & 2.84333333333333 & 0.0238683256575942 & 0.0699999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167577&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]2.35666666666667[/C][C]0.0336650164612069[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]2[/C][C]2.44083333333333[/C][C]0.0293747985163948[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]3[/C][C]2.5325[/C][C]0.0276750626179796[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]4[/C][C]2.61666666666667[/C][C]0.0347283832917774[/C][C]0.1[/C][/ROW]
[ROW][C]5[/C][C]2.69166666666667[/C][C]0.0152752523165195[/C][C]0.0500000000000003[/C][/ROW]
[ROW][C]6[/C][C]2.76[/C][C]0.0286038776773677[/C][C]0.0899999999999999[/C][/ROW]
[ROW][C]7[/C][C]2.84333333333333[/C][C]0.0238683256575942[/C][C]0.0699999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167577&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167577&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
12.356666666666670.03366501646120690.0899999999999999
22.440833333333330.02937479851639480.0899999999999999
32.53250.02767506261797960.0899999999999999
42.616666666666670.03472838329177740.1
52.691666666666670.01527525231651950.0500000000000003
62.760.02860387767736770.0899999999999999
72.843333333333330.02386832565759420.0699999999999998






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.0779284844012534
beta-0.0193134037973467
S.D.0.0144195983508858
T-STAT-1.33938569767169
p-value0.238100848648319

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.0779284844012534 \tabularnewline
beta & -0.0193134037973467 \tabularnewline
S.D. & 0.0144195983508858 \tabularnewline
T-STAT & -1.33938569767169 \tabularnewline
p-value & 0.238100848648319 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167577&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0779284844012534[/C][/ROW]
[ROW][C]beta[/C][C]-0.0193134037973467[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0144195983508858[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.33938569767169[/C][/ROW]
[ROW][C]p-value[/C][C]0.238100848648319[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167577&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167577&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)
alpha0.0779284844012534
beta-0.0193134037973467
S.D.0.0144195983508858
T-STAT-1.33938569767169
p-value0.238100848648319






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.74140252775839
beta-1.96492737277209
S.D.1.62282002746778
T-STAT-1.21081040381177
p-value0.28007309102854
Lambda2.96492737277209

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.74140252775839 \tabularnewline
beta & -1.96492737277209 \tabularnewline
S.D. & 1.62282002746778 \tabularnewline
T-STAT & -1.21081040381177 \tabularnewline
p-value & 0.28007309102854 \tabularnewline
Lambda & 2.96492737277209 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167577&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.74140252775839[/C][/ROW]
[ROW][C]beta[/C][C]-1.96492737277209[/C][/ROW]
[ROW][C]S.D.[/C][C]1.62282002746778[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.21081040381177[/C][/ROW]
[ROW][C]p-value[/C][C]0.28007309102854[/C][/ROW]
[ROW][C]Lambda[/C][C]2.96492737277209[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167577&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167577&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-1.74140252775839
beta-1.96492737277209
S.D.1.62282002746778
T-STAT-1.21081040381177
p-value0.28007309102854
Lambda2.96492737277209


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')