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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, 03 Dec 2009 10:45:49 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/03/t125986239708qnflifzpjgnm6.htm/, Retrieved Fri, 09 May 2025 23:07:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62980, Retrieved Fri, 09 May 2025 23:07:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact204

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       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-    D        [Standard Deviation-Mean Plot] [standard deviatio...] [2009-11-24 21:20:13] [8b1aef4e7013bd33fbc2a5833375c5f5]
-    D          [Standard Deviation-Mean Plot] [SHw WS8] [2009-11-26 18:11:50] [af2352cd9a951bedd08ebe247d0de1a2]
-    D            [Standard Deviation-Mean Plot] [WS8 - review ] [2009-12-03 16:26:13] [af2352cd9a951bedd08ebe247d0de1a2]
-    D                [Standard Deviation-Mean Plot] [WS8 - review ] [2009-12-03 17:45:49] [d9efc2d105d810fc0b0ac636e31105d1] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
593530
610943
612613
611324
594167
595454
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379
533590
517945
506174
501866
516141
528222
532638
536322
536535
523597
536214
586570
596594
580523

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' @ 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62980&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62980&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62980&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' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1591023.91666666715717.702252025745157
2597142.83333333320950.694363990356109
3562721.2543097.969939799127147
4513922.41666666729563.607097727295234
5524801.91666666711909.799162174534669

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 591023.916666667 & 15717.7022520257 & 45157 \tabularnewline
2 & 597142.833333333 & 20950.6943639903 & 56109 \tabularnewline
3 & 562721.25 & 43097.969939799 & 127147 \tabularnewline
4 & 513922.416666667 & 29563.6070977272 & 95234 \tabularnewline
5 & 524801.916666667 & 11909.7991621745 & 34669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62980&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]591023.916666667[/C][C]15717.7022520257[/C][C]45157[/C][/ROW]
[ROW][C]2[/C][C]597142.833333333[/C][C]20950.6943639903[/C][C]56109[/C][/ROW]
[ROW][C]3[/C][C]562721.25[/C][C]43097.969939799[/C][C]127147[/C][/ROW]
[ROW][C]4[/C][C]513922.416666667[/C][C]29563.6070977272[/C][C]95234[/C][/ROW]
[ROW][C]5[/C][C]524801.916666667[/C][C]11909.7991621745[/C][C]34669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62980&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62980&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
1591023.91666666715717.702252025745157
2597142.83333333320950.694363990356109
3562721.2543097.969939799127147
4513922.41666666729563.607097727295234
5524801.91666666711909.799162174534669






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha38609.819285794
beta-0.0257416855937999
S.D.0.189915940732922
T-STAT-0.135542522099292
p-value0.900766542822452

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 38609.819285794 \tabularnewline
beta & -0.0257416855937999 \tabularnewline
S.D. & 0.189915940732922 \tabularnewline
T-STAT & -0.135542522099292 \tabularnewline
p-value & 0.900766542822452 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62980&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]38609.819285794[/C][/ROW]
[ROW][C]beta[/C][C]-0.0257416855937999[/C][/ROW]
[ROW][C]S.D.[/C][C]0.189915940732922[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.135542522099292[/C][/ROW]
[ROW][C]p-value[/C][C]0.900766542822452[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62980&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62980&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)
alpha38609.819285794
beta-0.0257416855937999
S.D.0.189915940732922
T-STAT-0.135542522099292
p-value0.900766542822452






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha12.6523317240617
beta-0.201034123129114
S.D.4.31072380993585
T-STAT-0.0466358161628791
p-value0.965734327491847
Lambda1.20103412312911

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 12.6523317240617 \tabularnewline
beta & -0.201034123129114 \tabularnewline
S.D. & 4.31072380993585 \tabularnewline
T-STAT & -0.0466358161628791 \tabularnewline
p-value & 0.965734327491847 \tabularnewline
Lambda & 1.20103412312911 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62980&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]12.6523317240617[/C][/ROW]
[ROW][C]beta[/C][C]-0.201034123129114[/C][/ROW]
[ROW][C]S.D.[/C][C]4.31072380993585[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.0466358161628791[/C][/ROW]
[ROW][C]p-value[/C][C]0.965734327491847[/C][/ROW]
[ROW][C]Lambda[/C][C]1.20103412312911[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62980&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62980&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)
alpha12.6523317240617
beta-0.201034123129114
S.D.4.31072380993585
T-STAT-0.0466358161628791
p-value0.965734327491847
Lambda1.20103412312911


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')