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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 computationSat, 18 Dec 2010 09:33:15 +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/18/t1292664704m6wzfnf3nqx9xs1.htm/, Retrieved Mon, 12 May 2025 11:44:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111807, Retrieved Mon, 12 May 2025 11:44:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact231

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-    D        [(Partial) Autocorrelation Function] [Model 1 (d = 0, D...] [2009-11-24 17:27:24] [ee7c2e7343f5b1451e62c5c16ec521f1]
-    D          [(Partial) Autocorrelation Function] [Methode 1 (D=0, d=0)] [2009-11-27 12:01:23] [76ab39dc7a55316678260825bd5ad46c]
-    D            [(Partial) Autocorrelation Function] [methode 1 (d=0 D= 0)] [2009-11-27 20:21:42] [4b453aa14d54730625f8d3de5f1f6d82]
-    D              [(Partial) Autocorrelation Function] [koffie en thee] [2009-12-16 19:04:55] [7773f496f69461f4a67891f0ef752622]
-    D                [(Partial) Autocorrelation Function] [Appelen Jonagold ...] [2009-12-17 16:51:16] [7773f496f69461f4a67891f0ef752622]
- RMPD                  [Spectral Analysis] [spectral analysis] [2010-12-15 16:58:49] [717f3d787904f94c39256c5c1fc72d4c]
- RMP                       [Standard Deviation-Mean Plot] [standard deviatio...] [2010-12-18 09:33:15] [c1f1b5e209adb4577289f490325e36f2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.6923
0.6886
0.6855
0.6745
0.6769
0.6758
0.6896
0.6843
0.6818
0.6774
0.6821
0.6885
0.6829
0.6796
0.6976
0.6924
0.6849
0.6921
0.6839
0.6727
0.6776
0.6692
0.6738
0.6740
0.6635
0.6737
0.6788
0.6828
0.6795
0.6740
0.6744
0.6764
0.6987
0.6967
0.7116
0.7357
0.7455
0.7639
0.7958
0.7864
0.7853
0.7903
0.7866
0.8039
0.7916
0.7903
0.8242
0.9567
0.8850
0.8865
0.9258
0.8948
0.8762
0.8527
0.8536
0.8805
0.9155
0.8961
0.9127
0.8857

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111807&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111807&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111807&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
10.6831083333333330.005987632455674160.0178000000000000
20.6817250.008904250772422230.0284
30.687150.02026629535146290.0722
40.8017083333333330.05244145581387670.2112
50.8887583333333330.02244510306314390.0731

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 0.683108333333333 & 0.00598763245567416 & 0.0178000000000000 \tabularnewline
2 & 0.681725 & 0.00890425077242223 & 0.0284 \tabularnewline
3 & 0.68715 & 0.0202662953514629 & 0.0722 \tabularnewline
4 & 0.801708333333333 & 0.0524414558138767 & 0.2112 \tabularnewline
5 & 0.888758333333333 & 0.0224451030631439 & 0.0731 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111807&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]0.683108333333333[/C][C]0.00598763245567416[/C][C]0.0178000000000000[/C][/ROW]
[ROW][C]2[/C][C]0.681725[/C][C]0.00890425077242223[/C][C]0.0284[/C][/ROW]
[ROW][C]3[/C][C]0.68715[/C][C]0.0202662953514629[/C][C]0.0722[/C][/ROW]
[ROW][C]4[/C][C]0.801708333333333[/C][C]0.0524414558138767[/C][C]0.2112[/C][/ROW]
[ROW][C]5[/C][C]0.888758333333333[/C][C]0.0224451030631439[/C][C]0.0731[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111807&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111807&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
10.6831083333333330.005987632455674160.0178000000000000
20.6817250.008904250772422230.0284
30.687150.02026629535146290.0722
40.8017083333333330.05244145581387670.2112
50.8887583333333330.02244510306314390.0731






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.0573273563314224
beta0.105995141982843
S.D.0.0958404583083557
T-STAT1.10595403917849
p-value0.349467612498824

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.0573273563314224 \tabularnewline
beta & 0.105995141982843 \tabularnewline
S.D. & 0.0958404583083557 \tabularnewline
T-STAT & 1.10595403917849 \tabularnewline
p-value & 0.349467612498824 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111807&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.0573273563314224[/C][/ROW]
[ROW][C]beta[/C][C]0.105995141982843[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0958404583083557[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.10595403917849[/C][/ROW]
[ROW][C]p-value[/C][C]0.349467612498824[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111807&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111807&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-0.0573273563314224
beta0.105995141982843
S.D.0.0958404583083557
T-STAT1.10595403917849
p-value0.349467612498824






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.7546680161396
beta4.53842094621272
S.D.3.0938280880544
T-STAT1.46692732014945
p-value0.238674212248471
Lambda-3.53842094621272

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.7546680161396 \tabularnewline
beta & 4.53842094621272 \tabularnewline
S.D. & 3.0938280880544 \tabularnewline
T-STAT & 1.46692732014945 \tabularnewline
p-value & 0.238674212248471 \tabularnewline
Lambda & -3.53842094621272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111807&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.7546680161396[/C][/ROW]
[ROW][C]beta[/C][C]4.53842094621272[/C][/ROW]
[ROW][C]S.D.[/C][C]3.0938280880544[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.46692732014945[/C][/ROW]
[ROW][C]p-value[/C][C]0.238674212248471[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.53842094621272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111807&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111807&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-2.7546680161396
beta4.53842094621272
S.D.3.0938280880544
T-STAT1.46692732014945
p-value0.238674212248471
Lambda-3.53842094621272


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')