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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, 30 Nov 2013 04:29:23 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/30/t138580377416q7y9p2in0aasc.htm/, Retrieved Fri, 03 May 2024 09:33:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=229608, Retrieved Fri, 03 May 2024 09:33:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106

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] [] [2013-11-30 09:29:23] [f7a1a28113c41406cd39c3805ab775eb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9
13
12
5
13
11
8
8
8
8
0
3
0
-1
-1
-4
1
-1
0
-1
6
0
-3
-3
4
1
0
-4
-2
3
2
5
6
6
3
4
7
5
6
1
3
6
0
3
4
7
6
6
6
6
2
2
2
3
-1
-4
4
5
3
-1
-4
0
-1
-1
3
2
-4
-3
-1
3
-2
-10

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' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229608&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229608&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229608&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' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
18.166666666666673.9733963794062613
2-0.5833333333333332.5390883594254210
32.333333333333333.1139957766460910
44.52.315952582337647
52.253.0188799849673310
6-1.53.6055512754639913

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 8.16666666666667 & 3.97339637940626 & 13 \tabularnewline
2 & -0.583333333333333 & 2.53908835942542 & 10 \tabularnewline
3 & 2.33333333333333 & 3.11399577664609 & 10 \tabularnewline
4 & 4.5 & 2.31595258233764 & 7 \tabularnewline
5 & 2.25 & 3.01887998496733 & 10 \tabularnewline
6 & -1.5 & 3.60555127546399 & 13 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229608&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]8.16666666666667[/C][C]3.97339637940626[/C][C]13[/C][/ROW]
[ROW][C]2[/C][C]-0.583333333333333[/C][C]2.53908835942542[/C][C]10[/C][/ROW]
[ROW][C]3[/C][C]2.33333333333333[/C][C]3.11399577664609[/C][C]10[/C][/ROW]
[ROW][C]4[/C][C]4.5[/C][C]2.31595258233764[/C][C]7[/C][/ROW]
[ROW][C]5[/C][C]2.25[/C][C]3.01887998496733[/C][C]10[/C][/ROW]
[ROW][C]6[/C][C]-1.5[/C][C]3.60555127546399[/C][C]13[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229608&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229608&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
18.166666666666673.9733963794062613
2-0.5833333333333332.5390883594254210
32.333333333333333.1139957766460910
44.52.315952582337647
52.253.0188799849673310
6-1.53.6055512754639913






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.96718288503542
beta0.0503582669033558
S.D.0.085348061294544
T-STAT0.590034104343211
p-value0.586887522357878

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.96718288503542 \tabularnewline
beta & 0.0503582669033558 \tabularnewline
S.D. & 0.085348061294544 \tabularnewline
T-STAT & 0.590034104343211 \tabularnewline
p-value & 0.586887522357878 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229608&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.96718288503542[/C][/ROW]
[ROW][C]beta[/C][C]0.0503582669033558[/C][/ROW]
[ROW][C]S.D.[/C][C]0.085348061294544[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.590034104343211[/C][/ROW]
[ROW][C]p-value[/C][C]0.586887522357878[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229608&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229608&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)
alpha2.96718288503542
beta0.0503582669033558
S.D.0.085348061294544
T-STAT0.590034104343211
p-value0.586887522357878






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.938422256040421
beta0.134263917562994
S.D.0.236661907922637
T-STAT0.567323735118725
p-value0.627682635177314
Lambda0.865736082437006

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.938422256040421 \tabularnewline
beta & 0.134263917562994 \tabularnewline
S.D. & 0.236661907922637 \tabularnewline
T-STAT & 0.567323735118725 \tabularnewline
p-value & 0.627682635177314 \tabularnewline
Lambda & 0.865736082437006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=229608&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.938422256040421[/C][/ROW]
[ROW][C]beta[/C][C]0.134263917562994[/C][/ROW]
[ROW][C]S.D.[/C][C]0.236661907922637[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.567323735118725[/C][/ROW]
[ROW][C]p-value[/C][C]0.627682635177314[/C][/ROW]
[ROW][C]Lambda[/C][C]0.865736082437006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=229608&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=229608&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)
alpha0.938422256040421
beta0.134263917562994
S.D.0.236661907922637
T-STAT0.567323735118725
p-value0.627682635177314
Lambda0.865736082437006


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')