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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationThu, 16 Dec 2010 10:22:52 +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/2010/Dec/16/t12924948481w9x4z5fl7bqfut.htm/, Retrieved Fri, 03 May 2024 05:52:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110827, Retrieved Fri, 03 May 2024 05:52:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [Spectral Analysis] [spectrum analyse ...] [2010-12-14 18:46:58] [d6e648f00513dd750579ba7880c5fbf5]
- RMP     [Standard Deviation-Mean Plot] [standard deviatio...] [2010-12-14 19:01:46] [d6e648f00513dd750579ba7880c5fbf5]
-    D        [Standard Deviation-Mean Plot] [] [2010-12-16 10:22:52] [7c1b7ddc8e9000e55b944088fdfb52dc] [Current]
-    D          [Standard Deviation-Mean Plot] [] [2010-12-18 12:05:16] [58af523ef9b33032fd2497c80088399b]
-                 [Standard Deviation-Mean Plot] [] [2010-12-29 09:48:17] [126c9e58bb659a0bfb4675d843c2c69e]
-               [Standard Deviation-Mean Plot] [] [2010-12-29 09:27:55] [126c9e58bb659a0bfb4675d843c2c69e]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
41.85
41.75
41.75
41.75
41.58
41.61
41.42
41.37
41.37
41.33
41.37
41.34
41.33
41.29
41.29
41.27
41.04
40.90
40.89
40.72
40.72
40.58
40.24
40.07
40.12
40.10
40.10
40.08
40.06
39.99
40.05
39.66
39.66
39.67
39.56
39.64
39.73
39.70
39.70
39.68
39.76
40.00
39.96
40.01
40.01
40.01
40.00
39.91
39.86
39.79
39.79
39.80
39.64
39.55
39.36
39.28

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110827&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110827&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110827&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
141.54083333333330.1954230066168050.520000000000003
240.86166666666670.4177609871975151.26000000000000
339.89083333333330.2270946271864870.559999999999995
439.87250.1439144316472930.329999999999998

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 41.5408333333333 & 0.195423006616805 & 0.520000000000003 \tabularnewline
2 & 40.8616666666667 & 0.417760987197515 & 1.26000000000000 \tabularnewline
3 & 39.8908333333333 & 0.227094627186487 & 0.559999999999995 \tabularnewline
4 & 39.8725 & 0.143914431647293 & 0.329999999999998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110827&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]41.5408333333333[/C][C]0.195423006616805[/C][C]0.520000000000003[/C][/ROW]
[ROW][C]2[/C][C]40.8616666666667[/C][C]0.417760987197515[/C][C]1.26000000000000[/C][/ROW]
[ROW][C]3[/C][C]39.8908333333333[/C][C]0.227094627186487[/C][C]0.559999999999995[/C][/ROW]
[ROW][C]4[/C][C]39.8725[/C][C]0.143914431647293[/C][C]0.329999999999998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110827&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110827&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
141.54083333333330.1954230066168050.520000000000003
240.86166666666670.4177609871975151.26000000000000
339.89083333333330.2270946271864870.559999999999995
439.87250.1439144316472930.329999999999998






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.50226762526823
beta0.0431241489651294
S.D.0.099656114171262
T-STAT0.432729585372145
p-value0.707405006956447

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.50226762526823 \tabularnewline
beta & 0.0431241489651294 \tabularnewline
S.D. & 0.099656114171262 \tabularnewline
T-STAT & 0.432729585372145 \tabularnewline
p-value & 0.707405006956447 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110827&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.50226762526823[/C][/ROW]
[ROW][C]beta[/C][C]0.0431241489651294[/C][/ROW]
[ROW][C]S.D.[/C][C]0.099656114171262[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.432729585372145[/C][/ROW]
[ROW][C]p-value[/C][C]0.707405006956447[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110827&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110827&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-1.50226762526823
beta0.0431241489651294
S.D.0.099656114171262
T-STAT0.432729585372145
p-value0.707405006956447






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-28.5571799703362
beta7.31342662196394
S.D.15.0183580722356
T-STAT0.48696579125279
p-value0.674424068903112
Lambda-6.31342662196394

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -28.5571799703362 \tabularnewline
beta & 7.31342662196394 \tabularnewline
S.D. & 15.0183580722356 \tabularnewline
T-STAT & 0.48696579125279 \tabularnewline
p-value & 0.674424068903112 \tabularnewline
Lambda & -6.31342662196394 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110827&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-28.5571799703362[/C][/ROW]
[ROW][C]beta[/C][C]7.31342662196394[/C][/ROW]
[ROW][C]S.D.[/C][C]15.0183580722356[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.48696579125279[/C][/ROW]
[ROW][C]p-value[/C][C]0.674424068903112[/C][/ROW]
[ROW][C]Lambda[/C][C]-6.31342662196394[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110827&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110827&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-28.5571799703362
beta7.31342662196394
S.D.15.0183580722356
T-STAT0.48696579125279
p-value0.674424068903112
Lambda-6.31342662196394


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')