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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 computationWed, 03 Dec 2008 12:36:45 -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/2008/Dec/03/t1228333068gdwtmkqbtkcjzun.htm/, Retrieved Fri, 17 May 2024 02:03:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28861, Retrieved Fri, 17 May 2024 02:03:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact199

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] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD    [Standard Deviation-Mean Plot] [T8 15] [2008-12-03 19:36:45] [fb0ffb935e9c1a725d69519be28b148f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3389
3497
4404
3849
3734
3060
3507
3287
3215
3764
2734
2837
2766
3851
3289
3848
3348
3682
4058
3655
3811
3341
3032
3475
3353
3186
3902
4164
3499
4145
3796
3711
3949
3740
3243
4407
4814
3908
5250
3937
4004
5560
3922
3759
4138
4634
3996
4308
4142
4429
5219
4929
5754
5592
4163
4962
5208
4755
4491
5732
5730
5024
6056
4901
5353
5578
4618
4724
5011
5298
4143
4617
4727
4207
5112
4190
4098
5071
4177
4598
3757
5591
4218
3780

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=28861&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=28861&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28861&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
13439.75465.0323791268341670
23513376.4453358843631292
33757.91666666667383.8222738179581221
44352.5584.6611295131881801
54948572.2321525077361612
65087.75540.7795929783391913
74460.5566.5791287109941834

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3439.75 & 465.032379126834 & 1670 \tabularnewline
2 & 3513 & 376.445335884363 & 1292 \tabularnewline
3 & 3757.91666666667 & 383.822273817958 & 1221 \tabularnewline
4 & 4352.5 & 584.661129513188 & 1801 \tabularnewline
5 & 4948 & 572.232152507736 & 1612 \tabularnewline
6 & 5087.75 & 540.779592978339 & 1913 \tabularnewline
7 & 4460.5 & 566.579128710994 & 1834 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28861&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]3439.75[/C][C]465.032379126834[/C][C]1670[/C][/ROW]
[ROW][C]2[/C][C]3513[/C][C]376.445335884363[/C][C]1292[/C][/ROW]
[ROW][C]3[/C][C]3757.91666666667[/C][C]383.822273817958[/C][C]1221[/C][/ROW]
[ROW][C]4[/C][C]4352.5[/C][C]584.661129513188[/C][C]1801[/C][/ROW]
[ROW][C]5[/C][C]4948[/C][C]572.232152507736[/C][C]1612[/C][/ROW]
[ROW][C]6[/C][C]5087.75[/C][C]540.779592978339[/C][C]1913[/C][/ROW]
[ROW][C]7[/C][C]4460.5[/C][C]566.579128710994[/C][C]1834[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28861&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28861&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
13439.75465.0323791268341670
23513376.4453358843631292
33757.91666666667383.8222738179581221
44352.5584.6611295131881801
54948572.2321525077361612
65087.75540.7795929783391913
74460.5566.5791287109941834






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha51.8067368605828
beta0.105783712506122
S.D.0.0371087229677473
T-STAT2.85064276121985
p-value0.0357967439741381

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 51.8067368605828 \tabularnewline
beta & 0.105783712506122 \tabularnewline
S.D. & 0.0371087229677473 \tabularnewline
T-STAT & 2.85064276121985 \tabularnewline
p-value & 0.0357967439741381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28861&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]51.8067368605828[/C][/ROW]
[ROW][C]beta[/C][C]0.105783712506122[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0371087229677473[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.85064276121985[/C][/ROW]
[ROW][C]p-value[/C][C]0.0357967439741381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28861&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28861&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)
alpha51.8067368605828
beta0.105783712506122
S.D.0.0371087229677473
T-STAT2.85064276121985
p-value0.0357967439741381






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.68615122170266
beta0.945469045140955
S.D.0.327238710650032
T-STAT2.88923349949296
p-value0.0342173821437146
Lambda0.0545309548590455

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.68615122170266 \tabularnewline
beta & 0.945469045140955 \tabularnewline
S.D. & 0.327238710650032 \tabularnewline
T-STAT & 2.88923349949296 \tabularnewline
p-value & 0.0342173821437146 \tabularnewline
Lambda & 0.0545309548590455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28861&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.68615122170266[/C][/ROW]
[ROW][C]beta[/C][C]0.945469045140955[/C][/ROW]
[ROW][C]S.D.[/C][C]0.327238710650032[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.88923349949296[/C][/ROW]
[ROW][C]p-value[/C][C]0.0342173821437146[/C][/ROW]
[ROW][C]Lambda[/C][C]0.0545309548590455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28861&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28861&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-1.68615122170266
beta0.945469045140955
S.D.0.327238710650032
T-STAT2.88923349949296
p-value0.0342173821437146
Lambda0.0545309548590455


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')